Simulation Examples

Contents
• Simulation using Tables
• Simulation of Queueing Systems
• Examples
• A Grocery
• Call Center
• Inventory System
• Appendix: Random Digits


Simulation using a Table
• Introducing simulation by manually simulating on a table
• Can be done via pen-and-paper or by using a spreadsheet

Simulation of Queueing Systems
• Single server queue
• Calling population is infinite
?? Arrival rate does not change
• Units are served according FIFO
• Arrivals are defined by the
distribution of the time between
arrivals ?? inter-arrival time
• Service times are according to a
distribution
• Arrival rate must be less than
service rate ?? stable system
• Otherwise waiting line will grow
unbounded ?? unstable system
• Queueing system state
• System
• Server
• Units (in queue or being served)
• Clock
• State of the system
• Number of units in the system
• Status of server (idle, busy)
• Events
• Arrival of a unit
• Departure of a unit

• Arrival Event
• If server idle unit gets service, otherwise unit enters queue.
• Departure Event
• If queue is not empty begin servicing next unit, otherwise server will be idle

• How do events occur?
• Events occur randomly
• Interarrival times ? {1,...,6}
• Service times ? {1,...,4}

Clock
Time
Customer
Number
Event
Type
Number of
customers
0 1 Arrival 1
2 1 Departure 0
2 2 Arrival 1
3 2 Departure 0
6 3 Arrival 1
7 4 Arrival 2
9 3 Departure 1
9 5 Arrival 2
11 4 Departure 1
12 5 Departure 0
15 6 Arrival 1
19 6 Departure 0