Asst. Prof. Dr. Mongkut Piantanakulchai CES 341:Transportation Engineering and Planning Chapter 8 Traffic Analysis Techniques Asst. Prof. Dr. Mongkut Piantanakulchai Email: mongkut@siit.tu.ac.th

8.1 Space-Time Relationships Figure 8.1 Space-time diagram CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.1 Space-Time Relationships Note: Assume vehicle’s length is negligible CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8. 1. 1 Direct Graphical Solution Fig. 8 8.1.1 Direct Graphical Solution Fig. 8.2 Location and size of double-track sections Transit system Single track 15 km long Train 10 min interval dispatched from each end (W-E) 5 min layovers Neglect stop time at stations Uniform speed 45 km/h both directions Determine number and location of double-track sections, and the minimum length required for such sections in order for trains running as much as 2 min behind schedule to pass one another without delay CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.1.1 Direct Graphical Solution Fig. 8.3 Train dispatch problem Rail line 90 km long 7.5 km long double-track section located between 60-67.5 km from W end A train leaves W end at 1:00 p.m. and travel E at constant speed of 45 km/h The second train leaves from the E end at 1:30 p.m. and may travel at any speed up to 90 km/h 1) Determine earliest time the W-bound train can arrive at the W end of the line 2) Determine the latest dispatch time (after 1:00 p.m.) that will allow the W-bound train to reach its destination without unnecessary delay CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.1.2 Development of Analytical Solutions Complicated space-time problems Space-time diagrams are used to derive analytical solutions CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Example: Runway Capacity Analysis Fig. 8.5 Time separation at runway threshold, vi ≥ vj Fig. 8.4 Time separation at runway threshold, vi ≤ vj CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Example: Runway Capacity Analysis Capacity is expressed by Weighted average of interarrival time (10.1) (10.2) where pij = probability of arrival pair i-j If arrivals are independent (10.3) Note: Assume arrivals only, no departures More details in CES 446 Port and Airport Engineering CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.1.3 Development of Simulation Models More complicated problems Space-time diagrams are used to develop simulation models Behavior of system in a step-by-step manner CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Example: Block Signal Control System for Rail Line Objective: To protect train collisions and other hazards such as broken rails System consists of Electronically insulated section of tracks = blocks Train detection system: to determine if a train is in a particular block (the block is occupied) Signal system (warn or control) System of blocks and aspects (combination of signal lights) CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Example: Block Signal Control System for Rail Line Fig. 8.6 Block signal control systems CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Example: Block Signal Control System 0.75 km long blocks Three-block, four aspect system RR –stop and proceed at 7.5 km/h prepared to stop RY – proceed at 30 km/h, prepare to stop at next signal GY – proceed at 60 km/h GG – proceed at full speed CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Example: Block Signal Control System A train traveling at 45 km/h, passes a point A, which is located at a block boundary, at 11:00 a.m. Five min and 30 s later, a second train passes this point traveling at 90 km/h in the same direction Both trains are 0.375 km long Describe the motion of the second train, determine the time that the rear of second train passes point B, located 4.875 km beyond point A CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Time-space diagram of the first train CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Signal indication after the first train CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Trajectory of the second train according to block signals CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Trajectory of the second train (front) according to block signals CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Trajectory of the second train (front&rear) according to block signals CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.14 Non-trajectory Space-Time Diagrams Display information about traffic states (speed, flow rate, density) as well as vehicle trajectories Contour diagram can be used to display region with similar traffic state values CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.14 Non-trajectory Space-Time Diagrams Figure 8.11 Speed contours CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.2 Queuing Analysis Figure 8.12 Queuing System CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.2.1 Queuing Theory Fundamentals Figure 8.13 Arrival function for airport runway Figure 8.14 Arrival and departure functions for airport runway CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.2.1 Queuing Theory Fundamentals Figure 8.14 Queuing diagram, smooth curve approximation Figure 8.14 Queuing diagram features CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.2.2 Queue Discipline First-in, first-out (FIFO) Last-in, first-out (LIFO) Random service Priority service CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Relationship of Delay (w(t)) and Queue Length (Q(t)) of Individual at Time t W(t) = Waiting time (Delay) of an individual at time t Q(t) = Queue length at time t CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.2.3 Stochastic Queuing Models Deterministic queuing models – arrival and service rate are deterministic (known as some function) Stochastic queuing models constant long term arrival and service rates short-term random fluctuations around the average rates arrival rate may exceed service rate for short time intervals and queues will form CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Stochastic Queuing Models M/D/1 M/M/1 One Channel Arrivals Exponentially Distributed Service Deterministic (No random variation) Inter-arrival times follow Negative Exponential Distribution CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

M/D/1 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

M/M/1 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

General relationships CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.2.4 Transportation Applications of Queuing Theory Server opens after arrivals begin Arrival rate temporary exceeds constant service rate Service rate varies Server temporarily shut down CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.2.5 Queue Density, Storage, and Spillback Density (vehicles per unit distance) Occupancy – fraction of time vehicles are over the detector Objectives of studying queue density Locating queues and bottlenecks in traffic Determine the length of the queue and space needed for queue storage, control the queue spillback to upstream section CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Example Problem 8.1 Morning peak traffic upstream of a toll booth is given in the table The toll plaza consists of three booths, each of which can handle an average of one vehicle every 6 s. Using queuing diagram, determine the maximum queue, the longest delay to an individual vehicle, and the total delay CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Example Problem 8.1 7:00-7:10 200 7:10-7:20 400 600 7:20-7:30 500 1100 Time period 10 min volume Cumulative volume 7:00-7:10 200 7:10-7:20 400 600 7:20-7:30 500 1100 7:30-7:40 250 1350 7:40-7:50 1550 7:50-8:00 150 1700 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8-21 Cumulative volume, A(t) 300 veh/min, D(t) D(t)>A(t) {Show A(t), No queues} 8-21 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8.3 Network Analysis Network Link characteristics Nodes : Usually points of facilities intersect Origins or destinations of trips (source or sink nodes) Decision points Links : Usually road or railway segments Link characteristics Link costs: Distance, travel time, generalized costs (weighted sum of several costs) CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Network Elements 8-23 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Minimum path algorithm, step 1 Example network Minimum path algorithm, step 1 8-25 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Minimum path algorithm, step 2 8-26 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Minimum path algorithm, step 3 8-27 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Minimum path algorithm, step 4 8-28 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Minimum path algorithm, step 5 8-29 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Minimum path algorithm, step 6 8-30 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

Table 8.1 Link-cost array Node 1 2 3 4 5 6 -1 8 10 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8-31 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8-32 CES 341 Transportation Engineering and Planning Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 8-32 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8-33 CES 341 Transportation Engineering and Planning Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 8-33 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques

8-34 CES 341 Transportation Engineering and Planning Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 8-34 CES 341 Transportation Engineering and Planning Chapter8: Traffic Analysis Techniques