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. 1
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 timeconsuming 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. 2
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. 3
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 4
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 5
Discrete-Event Simulation continued 6
State Variables server queue customer State: InTheAir: number of aircraft either landing or waiting to land OnTheGround: number of landed aircraft RunwayFree: Boolean, true if runway available 7
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;} } } 8
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 9
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 10
Discrete Event Simulation Computation Example: air traffic at an airport Events: aircraft arrival, landing, departure arrival schedules 8:00 departure landed schedules 9:15 8:05 arrival 9:30 processed event current event unprocessed event 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? 11
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) 12
Event-Oriented World View state variables Integer: InTheAir; Integer: OnTheGround; Boolean: RunwayFree; Arrival Event { } Event handler procedures Landed Event { } Departure Event { } Simulation Application Simulation Engine Event processing loop Now = 8:45 Pending Event List (PEL) 9:00 10:10 9:16 While (simulation not finished) E = smallest time stamp event in PEL Remove E from PEL Now := time stamp of E call event handler procedure 13
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 14
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 event @ Now + RandExp(A); If (RunwayFree) { RunwayFree:=FALSE; Schedule Landed event @ Now + RandExp(L); } 15
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 event @ Now + RandExp(G); If (InTheAir>0) Schedule Landed event @ Now + RandExp(L); Else RunwayFree := TRUE; 16
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; 17
Execution Example State Variables L=3 G=4 InTheAir 0 1 2 1 0 OnTheGround 0 1 2 1 0 RunwayFree truefalse true Processing: Time Event 1 Arrival F1 3 Arrival F2 Time 0 1 2 3 4 5 6 7 8 9 10 11 Simulation Time Arrival F1 Event 3 Arrival F2 4 Landed F1 Arrival F2 Time Event 4 Landed F1 Landed F1 Time Event 7 Landed F2 8 Depart F1 Landed F2 Time Event 8 Depart F1 11 Depart F2 Depart F1 Time Event 11 Depart F2 Depart F2 Time Event Now=0 Now=1 Now=3 Now=4 Now=7 Now=8 Now=11 18