1. ADVANTAGES OF SIMULATION
Most complex, real-world systems with stochastic elements cannot be accurately described by a mathematical model that can be evaluated analytically. Thus, a simulation is often the only type of investigation possible.
Simulation allows one to estimate the performance of an existing system under some projected set of operating conditions.
Alternative proposed system designs (or alternative operating policies for a single system) can be compared via simulation to see which best meets a specified requirement.
In a simulation we can maintain much better control over experimental conditions than would generally be possible when experimenting with the system itself.
Simulation allows us to study a system with a long time frame---e.g., an economic system---in compressed time, or alternatively to study the detailed workings of a system in expanded time.

2. DISADVANTAGES OF SIMULATION
Each run of a stochastic simulation model produces only estimates of a model’s true characteristics for a particular set of input parameters. If a “valid” analytic model is available or can be easily de developed, it will generally be preferable to a simulation model.
Simulation models are often expensive and time-consuming to develop.
If a model is not a “valid” representation of a system under study, the simulation results, no matter how impressive they appear, will provide little useful information about the actual system.

3. DISADVANTAGES OF SIMULATION
Each simulation model is unique
In some studies both simulation and analytic models might be useful. In particular, simulation can be used to check the validity of assumptions needed in an analytic model. On the other hand, an analytic model can suggest reasonable alternatives to investigate in a simulation study.

4. Pitfalls to the successful completion of a simulation study
Failure to have a well-defined set of objectives at the beginning of the simulation study
Inappropriate level of model detail
Failure to communicate with management throughout the course of the simulation study
Misunderstanding of simulation by management
Treating a simulation study as if it were primarily an exercise in computer programming
Failure to have people with a knowledge of simulation methodology and statistics on the modeling team
Failure to collect good system data
Inappropriate simulation software
Obliviously using simulation software products whose complex marco statement may not be well documented and may not implement the desired modeling logic

5. Pitfalls to the successful completion of a simulation study
Belief that easy-to-use simulation packages, which require little or no programming, require a significantly lower level of technical competence
Misuse of animation
Failure to account correctly for sources of randomness in the actual system
Using arbitrary distributions (e.g., normal, uniform, or triangular) as input to the simulation
Analyzing the output data from one simulation run (replication) using formulas that assume independence
Making a single replication of a particular system design and treating the output statistics as the “true answers”
Comparing alternative system design on the basis of one replication for each design
Using the wrong performance measures

6. Discrete-Event Simulation continued…

7. State Variables State:
queue
customer
server
State:
InTheAir: number of aircraft either landing or waiting to land
OnTheGround: number of landed aircraft
RunwayFree: Boolean, true if runway available

8. Time Step Implementation
/* ignore aircraft departures */ Float InTheAir: # aircraft landing or waiting to land Float OnTheGround: # landed aircraft Boolean RunwayFree: True if runway available Float NextArrivalTime: Time the next aircraft arrives Float NextLanding: Time next aircraft lands (if one is landing) For (Now = 1 to EndTime) { /* time step size is 1.0 */ if (Now >= NextArrivalTime) { /* if aircraft just arrived */ InTheAir := InTheAir + 1; NextArrivalTime := NextArrivalTime + RandExp(A); if (RunwayFree) { RunwayFree := False; NextLanding := Now + RandExp(L); } if (Now >= NextLanding) { /* if aircraft just landed */ InTheAir := InTheAir - 1; OnTheGround := OnTheGround + 1; if (InTheAir > 0) NextLanding := Now + RandExp(L) else {RunWayFree := True; NextLanding := EndTime+1;}

9. Problems With Time Step Approach
State changes may occur between time steps
Use small time steps to minimize error
Multiple state changes within the same time step may be processed in the wrong order
Solvable by ordering state changes within time step (this imposes more work)
Inefficient
Many time steps no state changes occur, especially if small time steps

10. Discrete Event Simulation
Discrete Event Simulation: computer model for a system where changes in the state of the system occur at discrete points in simulation time.
Fundamental concepts:
System state (state variables)
State transitions (events)
Each event has a timestamp indicating when it occurs.
A DES computation can be viewed as a sequence of event computations, with each event computation is assigned a (simulation time) time stamp
Each event computation can
Modify state variables
Schedule new events

11. Discrete Event Simulation Computation
Example: air traffic at an airport
Events: aircraft arrival, landing, departure
arrival
8:00
schedules
processed event
current event
unprocessed event
departure
9:15
arrival
9:30
landed
8:05
schedules
simulation time
Events that have been scheduled, but have not been simulated (processed) yet are stored in a pending event list
Events are processed in time stamp order; why?

12. Events
An event must be associated with any change in the state of the system
Airport example:
Event 1: Aircraft Arrival (InTheAir, RunwayFree)
Event 2: Aircraft Landing (InTheAir, OnTheGround, RunwayFree)
Event 3: Aircraft Departure (OnTheGround)

13. Event-Oriented World View
state variables
Integer: InTheAir;
Integer: OnTheGround;
Boolean: RunwayFree;
Event handler procedures
Simulation Application
Arrival Event { … }
Landed Event
Departure Event
Pending Event List (PEL)
9:00
9:16
10:10
Now = 8:45
Simulation Engine
Event processing loop
While (simulation not finished)
E = smallest time stamp event in PEL
Remove E from PEL
Now := time stamp of E
call event handler procedure

14. Example: Air traffic at an Airport
Model aircraft arrivals and departures, arrival queuing
Single runway for incoming aircraft, ignore departure queuing
L = mean time runway used for each landing aircraft (exponential distrib.)
G = mean time on the ground before departing (exponential distribution)
A = mean inter-arrival time of incoming aircraft (exponential distribution)
States
Now: current simulation time
InTheAir: number of aircraft landing or waiting to land
OnTheGround: number of landed aircraft
RunwayFree: Boolean, true if runway available
Events
Arrival: denotes aircraft arriving in air space of airport
Landed: denotes aircraft landing
Departure: denotes aircraft leaving

15. Arrival Events Arrival Process: New aircraft arrives at airport.
If the runway is free, it will begin to land.
Otherwise, the aircraft must circle, and wait to land.
A: mean interarrival time of incoming aircraft
Now: current simulation time
InTheAir: number of aircraft landing or waiting to land
OnTheGround: number of landed aircraft
RunwayFree: Boolean, true if runway available
Arrival Event: InTheAir := InTheAir+1; Schedule Arrival Now + RandExp(A); If (RunwayFree) { RunwayFree:=FALSE; Schedule Landed Now + RandExp(L); }

16. Landed Event Landing Process: An aircraft has completed its landing.
L = mean time runway is used for each landing aircraft
G = mean time required on the ground before departing
Now: current simulation time
InTheAir: number of aircraft landing or waiting to land
OnTheGround: number of landed aircraft
RunwayFree: Boolean, true if runway available
Landed Event: InTheAir:=InTheAir-1; OnTheGround:=OnTheGround+1; Schedule Departure Now + RandExp(G); If (InTheAir>0) Schedule Landed Now + RandExp(L); Else RunwayFree := TRUE;

17. Departure Event
Departure Process: An aircraft now on the ground departs for a new destination.
Now: current simulation time
InTheAir: number of aircraft landing or waiting to land
OnTheGround: number of landed aircraft
RunwayFree: Boolean, true if runway available
Departure Event: OnTheGround := OnTheGround - 1;

18. Execution Example L=3 G=4 State Variables InTheAir OnTheGround
Simulation Time
State Variables
RunwayFree
InTheAir 1 2 3 4 5 6 7 8 9 10 11
true
L=3 G=4
Time
Event
1 Arrival F1
3 Arrival F2
Now=0
Processing:
false 1
Time
Event
4 Landed F1
3 Arrival F2
Arrival F1
Now=1 2
Time
Event
4 Landed F1
Arrival F2
Now=3 1
Time
Event
11 Depart F2
Depart F1
Now=8 2
true
Time
Event
8 Depart F1
11 Depart F2
Landed F2
Now=7 1
Landed F1
Now=4
Time
Event
8 Depart F1
7 Landed F2
Time
Event
Depart F2
Now=11