Chapter 2 Fundamental Simulation Concepts,Slide 1 of 57,Simulation with Arena, 4th ed.,Chapter 2,Fundamental Simulation Concepts,Last revision January 22, 2007,Chapter 2 Fundamental Simulation Concepts,Slide 2 of 57,Simulation with Arena, 4th ed.,What Well Do .,Underlying ideas, methods, and issues in simulation Software-independent (setting up for Arena) Example of a simple processing system Decompose the problem Terminology Simulation by hand Some basic statistical issues Spreadsheet simulation Simple static, dynamic models Overview of a simulation study,Chapter 2 Fundamental Simulation Concepts,Slide 3 of 57,Simulation with Arena, 4th ed.,2.1 The System: A Simple Processing System,General intent: Estimate expected production Waiting time in queue, queue length, proportion of time machine is busy Time units Can use different units in different places must declare Be careful to check the units when specifying inputs Declare base time units for internal calculations, outputs Be reasonable (interpretation, roundoff error),Chapter 2 Fundamental Simulation Concepts,Slide 4 of 57,Simulation with Arena, 4th ed.,Model Specifics,Initially (time 0) empty and idle Base time units: minutes Input data (assume given for now ), in minutes:Part Number Arrival Time Interarrival Time Service Time1 0.00 1.73 2.902 1.73 1.35 1.763 3.08 0.71 3.394 3.79 0.62 4.525 4.41 14.28 4.466 18.69 0.70 4.367 19.39 15.52 2.078 34.91 3.15 3.369 38.06 1.76 2.3710 39.82 1.00 5.3811 40.82 . . . . . . . . Stop when 20 minutes of (simulated) time have passed,Chapter 2 Fundamental Simulation Concepts,Slide 5 of 57,Simulation with Arena, 4th ed.,Goals of the Study: Output Performance Measures,Total production of parts over the run (P) Average waiting time of parts in queue:Maximum waiting time of parts in queue:,N = no. of parts completing queue wait WQi = waiting time in queue of ith part Know: WQ1 = 0 (why?)N 1 (why?),Chapter 2 Fundamental Simulation Concepts,Slide 6 of 57,Simulation with Arena, 4th ed.,Goals of the Study: Output Performance Measures (contd.),Time-average number of parts in queue:Maximum number of parts in queue: Average and maximum total time in system of parts (a.k.a. cycle time):,Q(t) = number of parts in queueat time t,TSi = time in system of part i,Chapter 2 Fundamental Simulation Concepts,Slide 7 of 57,Simulation with Arena, 4th ed.,Goals of the Study: Output Performance Measures (contd.),Utilization of the machine (proportion of time busy)Many others possible (information overload?),Chapter 2 Fundamental Simulation Concepts,Slide 8 of 57,Simulation with Arena, 4th ed.,2.2 Analysis Options,Educated guessing Average interarrival time = 4.08 minutes Average service time = 3.46 minutes So (on average) parts are being processed faster than they arrive System has a chance of operating in a stable way in the long run, i.e., might not “explode” If all interarrivals and service times were exactly at their mean, there would never be a queue But the data clearly exhibit variability, so a queue could form If wed had average interarrival average service time, and this persisted, then queue would explode Truth between these extremes Guessing has its limits ,Chapter 2 Fundamental Simulation Concepts,Slide 9 of 57,Simulation with Arena, 4th ed.,Analysis Options (contd.),Queueing theory Requires additional assumptions about the model Popular, simple model: M/M/1 queue Interarrival times exponential Service times exponential, indep. of interarrivals Must have E(service) E(interarrival) Steady-state (long-run, forever) Exact analytic results; e.g., average waiting time in queue is Problems: validity, estimating means, time frame Often useful as first-cut approximation,Chapter 2 Fundamental Simulation Concepts,Slide 10 of 57,Simulation with Arena, 4th ed.,Mechanistic Simulation,Individual operations (arrivals, service times) will occur exactly as in reality Movements, changes occur at the right “time,” in the right order Different pieces interact Install “observers” to get output performance measures Concrete, “brute-force” analysis approach Nothing mysterious or subtle But a lot of details, bookkeeping Simulation software keeps track of things for you,Chapter 2 Fundamental Simulation Concepts,Slide 11 of 57,Simulation with Arena, 4th ed.,2.3 Pieces of a Simulation Model,Entities “Players” that move around, change status, affect and are affected by other entities Dynamic objects get created, move around, leave (maybe) Usually represent “real” things Our model: entities are the parts Can have “fake” entities for modeling “tricks” Breakdown demon, break angel Though Arena has built-in ways to model these examples directly Usually have multiple realizations floating around Can have different types of entities concurrently Usually, identifying the types of entities is the first thing to do in building a model,Chapter 2 Fundamental Simulation Concepts,Slide 12 of 57,Simulation with Arena, 4th ed.,