1. Lab 01 Fundamentals SE 405 Discrete Event Simulation
Last update September 7, 1999

2. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Lab Objectives
Introduction to Simulation
Needs
Uses … etc.
Understanding Manual Simulation
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

3. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Introduction
Background
Here the process or facility under consideration is called system
Simulation is imitating the (dynamic behavior of) real world system (as compared to static models) using computer programs to study the behavior of the system under study
In order to study it there are set of assumptions on how a system works
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

4. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Introduction
Background
These assumptions take the form of mathematical or logical relationships which constitutes simulation model
Simulation models are numeric (Not analytic) in order to estimates (presents error or approximation)
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

5. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Introduction
Applications
Designing and analyzing manufacturing system
Determining ordering policies for an inventory system
Evaluating designs for service operations e.g., Banks, post office and hospital customer in-service-out operations
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

6. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Introduction
Definitions
System: Collection of entities interacting to achieve a common objective or logical end
State (of a system): collection of variables within a system to describe a system at a particular time. (Number of customer in bank queue)
Discrete / Continues systems
Model: Representation of actual system
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

7. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Introduction
Definitions
Analytic Solution vs Simulation (Numeric)
Static Models vs Dynamic Simulation
Deterministic (output determined) vs Stochastic Simulations (output unknown or random)
Events (ei= Time of occurrence of the ith event): Any change in system (Part arrival, service complete etc.)
Events Lists (e0, e1, e2, …)
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

8. Manual Simulation What We’ll Do ...
Understanding simulation through example
Software-independent …
Centered around an example of a simple processing system
Decompose the problem
Terminology
Simulation by hand
Some basic statistical issues
Overview of a simulation study
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

9. The System: A Simple Single server Queuing Model
Machine
(Server)
Arriving
Blank Parts
Departing
Finished Parts 8 7 6 5 4
Queue (FIFO)
Part in Process
General intent:
Estimate expected production
Time in queue, queue length, proportion of time machine is busy
Time units: arbitrary, but …
Be consistent (simulation doesn’t know)
Be reasonable (interpretation, roundoff error)
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

10. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Model Specifics
Initially (time 0) empty and idle
Time units: minutes
Interarrival times An (n=1,2,3…): 6.84, 2.4, 2.7, …
Service times Sn (n=1,2,3…): 4.58, 2.96, 5.86, …
Stop Criteria:
Stop when customer/part number = 10
Stop when 15 minutes of (simulated) time have passed
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

11. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Model Specifics
Si = time that a server actually spend serving ith customer
Di = delay in queue of the ith customer
ti = time of arrival of the ith customer t0=??
ci = ti+ Di + Si = time that ith customer completes service and departs
Stop Criteria:
Stop when customer/part number 10 has
Stop when 15 minutes of (simulated) time have passed
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

12. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Model Specifics
e e e e e4
t t c c2
A A A3
S S2
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

13. Goals of the Study: Output Performance Measures
*Total production of parts over the run (P)
Average waiting time (or delay) of parts in queue:
Maximum waiting time of parts in queue:
N = no. of parts completing queue wait
Di = waiting time in queue of ith part
Know: D1 = 0 (why?)
N > 1 (why?)
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

14. Goals of the Study: Output Performance Measures (cont’d.)
Time-average number of parts in queue:
Maximum number of parts in queue:
Average and maximum flowtime of parts (time in system, a.k.a. cycle time): t
Q(t) = number of parts in queue
at time t t
Fi = flowtime of ith part
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

15. Goals of the Study: Output Performance Measures (cont’d.)
Utilization of the machine (proportion of time busy)
Many others possible (information overload?) t t
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

16. Simulation Dynamics: The Event-Scheduling World View
Identify characteristic events — change state
Decide on logic to: effect state changes for each event type, observe statistics
Keep a simulation clock, future event calendar
Jump from one event to the next, process, observe statistics, update event calendar
Stopping rule
Usually done with general-purpose programming language (C, FORTRAN, etc.)
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

17. Events for Simple Processing System
Arrival of new part to the system
Update time-persistent statistical accumulators (from last event to now)
Area under Q(t)
Max of Q(t)
Area under B(t)
“Mark” arriving part with current time (use later)
If machine is idle:
Start processing (schedule departure), Make machine busy, Tally time in queue (0)
Else (machine is busy):
Put part at end of queue, Increase queue-length variable
Schedule the next arrival event
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

18. Events for Simple Processing System (cont’d.)
Departure (when a service is completed)
Increment number-produced stat accumulator
Compute & tally flowtime (now - time of arrival)
Update time-persistent statistics
If queue is non-empty:
Take first part out of queue, compute & tally its time in queue, begin service (schedule departure event)
Else (queue is empty):
Make the machine idle (Note: there will be no departure event scheduled on the future events calendar)
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

19. Events for Simple Processing System (cont’d.)
The End
Update time-persistent statistics (to end of the simulation)
Compute final output performance measures using current values of statistical accumulators
After each event, the event calendar’s top record is removed to see what time it is, what to do
Also must initialize everything
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

20. Specifics for Simple Processing System
Simulation clock (internal in Arena)
Event calendar: List of event records:
[Entity No., Event Time, Event Type]
Keep ranked in increasing order on Event Time
Next event always in top record
Initially, schedule first Arrival, The End (Dep.?)
State variables: describe current status
Server status B(t) = 1 for busy, 0 for idle
Number of customers in queue Q(t)
Times of arrival of each customer now in queue (a list of random length)
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

21. Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts
Simulation by Hand
Manually track state variables, statistical accumulators
Use “given” interarrival, service times
Keep track of event calendar
“Lurch” clock from one event to the next
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

22. Simulation by Hand: Setup1 t 1 2 3
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

23. Simulation by Hand: Initialize at t = 0.001 3 2 1 t
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

24. Simulation by Hand: Arrival of Part 1 at t = 0.001 t 1 2 3
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

25. Simulation by Hand: Departure of Part 1 at t = 4.581 t 1 2 3
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

26. Simulation by Hand: Arrival of Part 2 at t = 6.841 t 1 2 3
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

27. Simulation by Hand: Arrival of Part 3 at t = 9.241 t 1 2 3
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

28. Simulation by Hand: Departure of Part 2 at t = 9.803 t 1 t 1 2 3
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

29. Simulation by Hand: Arrival of Part 4 at t = 11.943 t 1 t 1 2 3
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

30. Simulation by Hand: Arrival of Part 5 at t = 14.531 t 1 2 3
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

31. Simulation by Hand: The End at t = 15.003 4 5 t 1 t 1 2 3
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

32. Simulation by Hand: Finishing Up
Time-average number in queue:
Server utilization
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts

33. Complete Record of the Hand Simulation
Simulation with Arena — Chapter 2 — Fundamental Simulation Concepts