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Zakynthos Island, Greece May 23, 2005 Performance Analysis of a Multiple Vehicle Tandem System with Inter-vehicle Buffers and Blocking Matthew E. H. Petering 1,2, Jaeyoung Seo 2, and Chulung Lee 2 1 IOE Department, University of Michigan—Ann Arbor 2 ISE Department, National University of Singapore
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Zakynthos Island, Greece May 23, 2005 Port of Hong Kong
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Zakynthos Island, Greece May 23, 2005 Quay Cranes Single trolley quay crane
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Zakynthos Island, Greece May 23, 2005 The Double Trolley Quay Crane Intermediate platform Trolley #2 Trolley #1
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Zakynthos Island, Greece May 23, 2005 The Double Trolley Quay Crane Intermediate platform Trolley #2 Trolley #1 Trolley #2
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Zakynthos Island, Greece May 23, 2005 The Double Trolley Quay Crane Intermediate platform Trolley #2 Trolley #1
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Zakynthos Island, Greece May 23, 2005 Literature Review
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Zakynthos Island, Greece May 23, 2005 Literature Review Few exact analytical results for general types of manufacturing systems or material handling systems
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Zakynthos Island, Greece May 23, 2005 Literature Review Production lines with blocking phenomena: No buffers ; Exponential service time Buffers with positive, non-identical capacities ; Erlang service time Unreliable stations ; Exponential time to failure ; Erlang repair time Coxian-2 service time Papadopoulos and O’Kelly 1989 Papadopoulos et al. 1989, 1990 Heavey et al. 1993 Vidalis and Papadopoulos 1999 Few exact analytical results for general types of manufacturing systems or material handling systems
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Zakynthos Island, Greece May 23, 2005 System Description
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Zakynthos Island, Greece May 23, 2005 N stations (buffers), origin, destination N+1 vehicles Poisson rates of travel: R 1 +, R 1 -, R 2 +, R 2 -, …, R N+1 +, R N+1 - Buffer capacities: C 1, C 2, …, C N Blocking System Description
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Zakynthos Island, Greece May 23, 2005 Markovian State Description
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Zakynthos Island, Greece May 23, 2005 Buffer status = number of items occupying the buffer Vehicle status = M +, M -, I +, I - Markovian State Description
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Zakynthos Island, Greece May 23, 2005 Markovian State Description Buffer status = number of items occupying the buffer Vehicle status = M +, M -, I +, I -
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Zakynthos Island, Greece May 23, 2005 Markovian State Description State = ( M -, 2, I +, 3, M + ) Buffer status = number of items occupying the buffer Vehicle status = M +, M -, I +, I -
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Zakynthos Island, Greece May 23, 2005 Number of States
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Zakynthos Island, Greece May 23, 2005 Theorem. Let be the number of states in the CTMC representation of a system with n buffers (n+1 vehicles) with capacities C 1,C 2,...,C n from the origin to the destination respectively. Assuming S 0 = 0 and S 1 = 2, the following is true for all n ≥ 1: Number of States
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Zakynthos Island, Greece May 23, 2005 Number of States
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Zakynthos Island, Greece May 23, 2005 Computing System Performance
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Zakynthos Island, Greece May 23, 2005 Computing System Performance avg. throughput rate avg. number of items in system avg. sojourn time In steady state:
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Zakynthos Island, Greece May 23, 2005 Computing System Performance avg. throughput rate avg. number of items in system avg. sojourn time In steady state: A = transpose of state transition matrix x = column vector of steady state probabilities A x = 0, e T x = 1
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Zakynthos Island, Greece May 23, 2005 Generating the State Transition Matrix
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Zakynthos Island, Greece May 23, 2005 Generating the State Transition Matrix Recursive Method Finds the transition matrix for successively larger subsystems of original system
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Zakynthos Island, Greece May 23, 2005 Generating the State Transition Matrix Definition. A B-buffer subsystem of an original system is a system with B buffers and B+1 vehicles whose vehicle rates are equal to the rates of the final B+1 vehicles in the original system (from origin to destination respectively) and whose buffer capacities are equal to the capacities of the final B buffers in the original system (from origin to destination respectively). Recursive Method Finds the transition matrix for successively larger subsystems of original system
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Zakynthos Island, Greece May 23, 2005 Generating the State Transition Matrix Recursive Method Finds the transition matrix for successively larger subsystems of original system
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Zakynthos Island, Greece May 23, 2005 Generating the State Transition Matrix Recursive Method Finds the transition matrix for successively larger subsystems of original system
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Zakynthos Island, Greece May 23, 2005 Generating the State Transition Matrix Recursive Method Finds the transition matrix for successively larger subsystems of original system
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Zakynthos Island, Greece May 23, 2005 Generating the State Transition Matrix First construct A 1 Recursive method successively constructs A 2, A 3, …, A N A B = transpose of the transition matrix for the B-buffer subsystem
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Zakynthos Island, Greece May 23, 2005 Generating the State Transition Matrix DBDB EBEB EBEB EBEB EBEB EBEB EBEB EBEB HBHB GBGB FBFB HBHB DBDB DBDB DBDB DBDB DBDB DBDB... C N-B +1 copies of D B and E B C N-B +2 copies of D B and E B A B+1 is constructed recursively using A B as a building block
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Zakynthos Island, Greece May 23, 2005 Computing Steady State Probabilities
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Zakynthos Island, Greece May 23, 2005 1) set x 1 = 1 2) solve resulting nonsingular system A’ x’ = b using Gauss-Seidel method (Cooper and Gross, 1991) 3) renormalize so sum of x i = 1 Find the unique x satisfying A N x = 0, e T x = 1 Computing Steady State Probabilities
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Zakynthos Island, Greece May 23, 2005 Computing System Performance
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Zakynthos Island, Greece May 23, 2005 Computing System Performance T = avg. throughput rate = ( R i + ) x Prob( v i = M + ) for any i In steady state: Buffer status = b i Vehicle status = v i L = avg. number of items in system = ( x i ) x (number of items in system for State i ) W = avg. sojourn time for an item = L / T Likelihood vehicle i waits at forward buffer = Prob( v i = M +, b i = C i, v i+1 ≠ I - ) / Prob( v i = M + ) all i
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Zakynthos Island, Greece May 23, 2005 Results and Observations
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Zakynthos Island, Greece May 23, 2005 Results and Observations Likelihood of Vehicles Waiting System#States#IterT'put#ItemsSojrn1st2nd 2 0 2,1,2,1 854.4800.761.583.50 2 7 2,1,2,1 361625.62534.1876.696.08870 2 77 2,1,2,1 316111296.662039.1759.17.00950 2 0 2,1,8,9 818.6628.4201.6338.05450 2 7 2,1,8,9 3653.6667.4233.6350.00000 2 0 2,1,98,99 89.6667.3401.5102.00060 Throughput increases as buffer capacity or vehicle speed is increased 2-vehicle systems
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Zakynthos Island, Greece May 23, 2005 Results and Observations Throughput deteriorates as system grows Number of Vehicles in System#States#Iter T'put#ItemsSojrn 2854.3636 12.75 33090.3195 1.54.695 4112340.2976 26.721 54182076.2845 2.58.788 6156017857.2757 310.88 75822191274.2695 3.512.99 Zero buffer capacity, all vehicle rates = 1
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Zakynthos Island, Greece May 23, 2005 Results and Observations System#States#IterT'put#ItemsSojrn 2 1 2,2,2,2 12144.82141.51.826 3 1,1 3,3,3,3,3,3 702481.1412.52.191 4 1,1,1 4,4,4,4,4,4,4,4 40813351.4593.52.398 5 1,1,1,1 5,5,5,5,5,5,5,5,5,5 2378105751.7774.5002.532 Constant pure sojourn time Throughput increases almost linearly
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Zakynthos Island, Greece May 23, 2005 Results and Observations System#States#Iter T'put#ItemsSojrn 3 0,0 1,2,1,2,9998,9999 3064.48001.2402.583 3 0,0 1,2,9998,9999,1,2 30146564.54171.7713.269 3 0,0 9998,9999,1,2,1,2 30194.48002.2404.667 Fast vehicle should be placed in the center
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Zakynthos Island, Greece May 23, 2005 Results and Observations Likelihood of Vehicles Waiting SystemT'put#ItemsSojrn1st2nd3rd4th 5 1,0,0,0 (ALL = 1).29503.48311.81.6173.6341.4895.3389 5 0,1,0,0 (ALL = 1).30343.20610.57.6288.3953.5382.3589 5 0,0,1,0 (ALL = 1).30342.7949.210.6411.4618.2070.3712 5 0,0,0,1 (ALL = 1).29502.5178.534.6611.5105.3659.0746 Large buffer should be placed in the center
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Zakynthos Island, Greece May 23, 2005 Results and Observations SystemT'put#ItemsSojrn 4 0,0,0 3,3,3,3,3,3,3,3.892722.240 4 0,0,0 2,6,2,6,2,6,2,6.85662.5963.030 4 0,0,0 2,6,2,6,6,2,6,2.856222.336 Constant expected pure round-trip travel time for all vehicles Throughput depends on vehicle forward/reverse rates
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Zakynthos Island, Greece May 23, 2005 Results and Observations Number of Stations/ Buffer size Vehicles 0 1 2 3 4 5 2 3 4 5 6 7 This system has slightly reduced throughput Comparison with Erlang-2 production line (Papadopoulos et al., 1990) (Throughput).7273.6404.5977.5723.5553.5433.8214.7613.7307.7120.6993.8682.8219.7978.7829.8957.8580.8380.9137.8819.9264.7273.6389.5951.5689.5515.5390.8214.7607.7297.7108.6980.8957.8579.8379.9137.8818.8682.8217.7974.7825.9264 Erlang-2 This system
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Zakynthos Island, Greece May 23, 2005 Results and Observations Likelihood of Vehicles Waiting SystemT'put#ItemsSojrn1st2nd3rd 3 0,5 1,6,3,5,4,2.78201.7132.191.2809.00220 3 1,4 1,6,3,5,4,2.83432.0172.418.0828.01530 3 2,3 1,6,3,5,4,2.84822.1272.508.0294.04500 3 3,2 1,6,3,5,4,2.85162.1692.547.0156.10210 3 4,1 1,6,3,5,4,2.85202.2242.611.0134.21760 3 5,0 1,6,3,5,4,2.84842.5102.958.0212.47480 A buffer allocation problem…
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Zakynthos Island, Greece May 23, 2005 Conclusions Existing methodology was used to investigate a new kind of material handling system New numerical results regarding system performance were obtained Numerical results agree with intuition and with previously obtained results for other systems
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Zakynthos Island, Greece May 23, 2005 Further Research Compare theoretical results to simulation trials on systems with less variable vehicle travel times Consider more complicated systems Consider buffer allocation problems
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Zakynthos Island, Greece May 23, 2005 Questions?
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Zakynthos Island, Greece May 23, 2005 The Double Trolley Quay Crane
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Zakynthos Island, Greece May 23, 2005 Generating the List of States
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Recursive Method
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Recursive Method Find the list of states and transitions for successively larger subsystems of original system
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Recursive Method Find the list of states and transitions for successively larger subsystems of original system
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Recursive Method Find the list of states and transitions for successively larger subsystems of original system
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Recursive Method Find the list of states and transitions for successively larger subsystems of original system
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Zakynthos Island, Greece May 23, 2005 Generating the List of States
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Zakynthos Island, Greece May 23, 2005 Generating the List of States L B = list of states for the B-buffer subsystem First construct L 1 Recursive method successively constructs L 2, L 3, …, L N
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Zakynthos Island, Greece May 23, 2005 Generating the List of States
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example:
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: 3 Vehicles Rates of travel: R 1 +/-, R 2 +/-, R 3 +/- 2 Intermediate Buffers Buffer capacities: C 1 = 1, C 2 = 1
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: 3 Vehicles Rates of travel: R 1 +/-, R 2 +/-, R 3 +/- 2 Intermediate Buffers Buffer capacities: C 1 = 1, C 2 = 1
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: 3 Vehicles Rates of travel: R 1 +/-, R 2 +/-, R 3 +/- 2 Intermediate Buffers Buffer capacities: C 1 = 1, C 2 = 1 start by making list of states for the 1-buffer subsystem:
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: 3 Vehicles Rates of travel: R 1 +/-, R 2 +/-, R 3 +/- 2 Intermediate Buffers Buffer capacities: C 1 = 1, C 2 = 1 start by making list of states for the 1-buffer subsystem:
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- Example: the 1-buffer subsystem:
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) Example: the 1-buffer subsystem:
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 - L 1 =
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- ( I -, 0, I - ) ( I -, 0, M - ) ( I -, 0, M + ) ( I -, 1, M - ) ( I -, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- ( I -, 0, I - ) ( I -, 0, M - ) ( I -, 0, M + ) ( I -, 1, M - ) ( I -, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1 Rates of travel: R 2 +/-, R 3 +/- ( I -, 0, I - ) ( I -, 0, M - ) ( I -, 0, M + ) ( I -, 1, M - ) ( I -, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) the 1-buffer subsystem: Example: R 2 + R 2 - R 3 + R 3 - Z 1 =
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: Going from L 1 to L 2 :
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ” “ (M -, 1 ) + L 1 ” “ ( I +, 1) + L 1 ” “ (M +, 0) + Z 1 ” “ (M +, 0) + L 1 ” “ (M +, 1) + L 1 ” = L 2 Going from L 1 to L 2 : Make initial list of states with inherited transitions
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ” “ (M -, 1 ) + L 1 ” “ ( I +, 1) + L 1 ” “ (M +, 0) + Z 1 ” “ (M +, 0) + L 1 ” “ (M +, 1) + L 1 ” = L 2 Going from L 1 to L 2 : Make initial list of states with inherited transitions Adjust inherited transitions with rate R 2 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ” “ (M -, 1 ) + L 1 ” “ ( I +, 1) + L 1 ” “ (M +, 0) + Z 1 ” “ (M +, 0) + L 1 ” “ (M +, 1) + L 1 ” = L 2 R 1 + R 1 - Going from L 1 to L 2 : Make initial list of states with inherited transitions Adjust inherited transitions with rate R 2 - Add new transitions with rates R 1 + and R 1 -
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Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ” “ (M -, 1 ) + L 1 ” “ ( I +, 1) + L 1 ” “ (M +, 0) + Z 1 ” “ (M +, 0) + L 1 ” “ (M +, 1) + L 1 ” 3 Vehicles Rates of travel: R 1 +/-, R 2 +/-, R 3 +/- 2 Intermediate Buffers Buffer capacities: C 1 = 1, C 2 = 1 = L 2 R 1 + R 1 - Going from L 1 to L 2 : Make initial list of states with inherited transitions Adjust inherited transitions with rate R 2 - Add new transitions with rates R 1 + and R 1 -
91
Zakynthos Island, Greece May 23, 2005 Generating the List of States The entire list L 2 : Example:
92
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M +, 0, I - ) (M +, 1, M +, 0, M - ) (M +, 1, M +, 0, M + ) (M +, 1, M +, 1, M - ) (M +, 1, M +, 1, M + ) (M +, 1, M -, 0, I - ) (M +, 1, M -, 0, M - ) (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) The entire list L 2 :
93
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M +, 0, I - ) (M +, 1, M +, 0, M - ) (M +, 1, M +, 0, M + ) (M +, 1, M +, 1, M - ) (M +, 1, M +, 1, M + ) (M +, 1, M -, 0, I - ) (M +, 1, M -, 0, M - ) (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) The entire list L 2 :
94
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M +, 0, I - ) (M +, 1, M +, 0, M - ) (M +, 1, M +, 0, M + ) (M +, 1, M +, 1, M - ) (M +, 1, M +, 1, M + ) (M +, 1, M -, 0, I - ) (M +, 1, M -, 0, M - ) (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) The entire list L 2 :
95
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M +, 0, M - ) (M +, 1, M +, 0, M + ) (M +, 1, M +, 1, M - ) (M +, 1, M +, 1, M + ) (M +, 1, M -, 0, I - ) (M +, 1, M -, 0, M - ) (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) … The entire list L 2 :
96
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M +, 0, M + ) (M +, 1, M +, 1, M - ) (M +, 1, M +, 1, M + ) (M +, 1, M -, 0, I - ) (M +, 1, M -, 0, M - ) (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) … The entire list L 2 :
97
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M +, 1, M - ) (M +, 1, M +, 1, M + ) (M +, 1, M -, 0, I - ) (M +, 1, M -, 0, M - ) (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) … The entire list L 2 :
98
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M +, 1, M + ) (M +, 1, M -, 0, I - ) (M +, 1, M -, 0, M - ) (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) …
99
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M -, 0, I - ) (M +, 1, M -, 0, M - ) (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) …
100
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M -, 0, M - ) (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) …
101
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M -, 0, M + ) (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) …
102
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M -, 1, M - ) (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) …
103
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, M -, 1, M + ) (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) …
104
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, I +, 1, M - ) (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) …
105
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 1) + L 1 ” “ (M +, 0) + L 1 ” (M +, 1, I +, 1, M + ) (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) … “ (M +, 0) + Z 1 ”
106
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) … “ (M +, 0) + Z 1 ”
107
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) … “ (M +, 0) + Z 1 ”
108
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) … “ (M +, 0) + Z 1 ”
109
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M +, 0, I - ) (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) … “ (M +, 0) + Z 1 ”
110
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M +, 0, M - ) (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) … “ (M +, 0) + Z 1 ”
111
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M +, 0, M + ) (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) … “ (M +, 0) + Z 1 ”
112
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M +, 1, M - ) (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) … “ (M +, 0) + Z 1 ”
113
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M +, 1, M + ) (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
114
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M -, 0, I - ) (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
115
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M -, 0, M - ) (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
116
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M -, 0, M + ) (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
117
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M -, 1, M - ) (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
118
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, M -, 1, M + ) (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
119
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, I +, 1, M - ) (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
120
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - “ (M +, 0) + L 1 ” (M +, 0, I +, 1, M + ) (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
121
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
122
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
123
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
124
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M +, 0, I -, 0, I - ) (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
125
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M +, 0, I -, 0, M - ) (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
126
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M +, 0, I -, 0, M + ) (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
127
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M +, 0, I -, 1, M - ) (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ”
128
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M +, 0, I -, 1, M + ) ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) … “ (M +, 0) + Z 1 ” “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
129
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
130
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
131
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
132
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M +, 0, I - ) ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
133
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M +, 0, M - ) ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
134
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M +, 0, M + ) ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
135
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M +, 1, M - ) ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
136
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M +, 1, M + ) ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
137
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M -, 0, I - ) ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
138
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M -, 0, M - ) ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
139
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M -, 0, M + ) ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
140
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M -, 1, M - ) ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
141
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, M -, 1, M + ) ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
142
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, I +, 1, M - ) ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ”
143
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - ( I +, 1, I +, 1, M + ) (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) … “ ( I +, 1) + L 1 ” “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
144
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
145
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
146
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
147
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M +, 0, I - ) (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
148
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M +, 0, M - ) (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
149
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M +, 0, M + ) (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
150
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M +, 1, M - ) (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
151
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M +, 1, M + ) (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
152
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M -, 0, I - ) (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
153
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M -, 0, M - ) (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
154
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M -, 0, M + ) (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
155
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M -, 1, M - ) (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
156
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, M -, 1, M + ) (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
157
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, I +, 1, M - ) (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ”
158
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 1, I +, 1, M + ) (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) (M -, 0, I -, 0, I - ) … “ (M -, 1 ) + L 1 ” “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ”
159
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) (M -, 0, I -, 0, I - ) (M -, 0, I -, 0, M - ) … “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ”
160
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) (M -, 0, I -, 0, I - ) (M -, 0, I -, 0, M - ) … “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ”
161
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) (M -, 0, I -, 0, I - ) (M -, 0, I -, 0, M - ) … “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ”
162
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 0, M +, 0, I - ) (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) (M -, 0, I -, 0, I - ) (M -, 0, I -, 0, M - ) … “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ”
163
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 0, M +, 0, M - ) (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) (M -, 0, I -, 0, I - ) (M -, 0, I -, 0, M - ) (M -, 0, I -, 0, M + ) … “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ”
164
Zakynthos Island, Greece May 23, 2005 Generating the List of States (M +, 0, I - ) (M +, 0, M - ) (M +, 0, M + ) (M +, 1, M - ) (M +, 1, M + ) (M -, 0, I - ) (M -, 0, M - ) (M -, 0, M + ) (M -, 1, M - ) (M -, 1, M + ) (I +, 1, M - ) (I +, 1, M + ) (M +, 0, I - ) (M +, 0, M - ) … Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 0, M +, 0, M + ) (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) (M -, 0, I -, 0, I - ) (M -, 0, I -, 0, M - ) (M -, 0, I -, 0, M + ) (M -, 0, I -, 1, M - ) … “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ”
165
Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) (M -, 0, I -, 0, I - ) (M -, 0, I -, 0, M - ) (M -, 0, I -, 0, M + ) (M -, 0, I -, 1, M - ) (M -, 0, I -, 1, M + ) … “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ”
166
Zakynthos Island, Greece May 23, 2005 Generating the List of States Example: (M +, 1, (M +, 0, R 2 + R 2 - R 3 + R 3 - (M -, 0, M +, 1, M - ) (M -, 0, M +, 1, M + ) (M -, 0, M -, 0, I - ) (M -, 0, M -, 0, M - ) (M -, 0, M -, 0, M + ) (M -, 0, M -, 1, M - ) (M -, 0, M -, 1, M + ) (M -, 0, I +, 1, M - ) (M -, 0, I +, 1, M + ) (M -, 0, I -, 0, I - ) (M -, 0, I -, 0, M - ) (M -, 0, I -, 0, M + ) (M -, 0, I -, 1, M - ) (M -, 0, I -, 1, M + ) … “ (M -, 0 ) + L 1 ” “ (M -, 0 ) + Z 1 ”
167
Zakynthos Island, Greece May 23, 2005 Generating the List of States L B = list of states for the B-buffer subsystem First construct L 1 Recursive method successively constructs L 2, L 3, …, L N
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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Zakynthos Island, Greece May 23, 2005 Example of System Behavior 2 Vehicles 1 Intermediate Buffer Buffer capacity = 1
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