1. Discrete Event Simulation

2. Building blocks
Entities
Activities
Events

3. Discrete Event Model
Changes of system state only occur at discrete points in time

4. Concepts in DES (1) System Model
A collection of entities that interact together over time to accomplish one or more goals
Model
An abstract representation of a system

5. Concepts in DES (2) System state Entity
A collection of variables that contain all information necessary to describe the system at any time
Entity
Any object or component in the system which requires representation in the model

6. Concepts in DES (3) Attribute List Event
The properties of a given entity
List
A collection of associated entities
Event
An instantaneous occurrence that changes the state of a system

7. Concepts in DES (4) Event notice Event list
A record of an event: event time stamp, event type, associated data, …
Event list
A list of event notices for future events. Also known as future event list (FEL)

8. Concepts in DES (5) Activity Delay Clock
A duration of time of specified length, which is known when it begins (e.g. service time,inter-arrival time)
Delay
A duration of time of unspecified length, which is unknown until it ends (delay in last-in, first-out system)
Clock
A variable representing simulated time

9. Activities Represents time whose duration is defined by the modeler
Deterministic
Statistical
A function depending on system variables or entity attributes
Loading time of cargo depends on the number of items

10. Example:The Able Baker Carhop Problem
One Queue with Two Servers
Two Carhops:
Able and Baker
Able is faster
Able gets the customer if both carhops are idle

11. Example Interval distribution of cars 1 min 25% 2 min 40% 3 min 20%

12. Example Service Distribution for Able 2 min 30% 3 min 28% 4 min 25%

13. Example Service Distribution for Baker 3 min 35% 4 min 25% 5 min 20%

14. System state Q(t): The number of cars waiting to be served at time t
A(t): 0 or 1 indicate Able being idle or busy at time t
B(t): 0 or 1 indicate Baker being idle or busy at time t

15. Entities and Attributes
Server
Total service time
Total idle time
Customers
Waiting
In service

16. Events Arrival Event Service completion by Able
Service completion by Baker

17. Activities Inter-arrival time Service time by Able
Service time by Baker

18. Event-scheduling/time-advance algorithm
Put all the events into future event list (FEL) by time order
Pick the smallest time stamped event and execute, put new event into FEL
Executing the events changes the system state, attribute of entities
Simulation ends when
No more events

19. Example: Manual Simulation of Single-channel Queue
A small grocery store has only one checkout counter
Customers arrive randomly from 1 to 8 minutes
Service time varies randomly from 1 to 6 minutes

20. System state Q(t) S(t) Number of customers in line
Status of server: 0 1 (idle busy)

21. Events Arrival (A) Departure (D)
Stopping event (E), scheduled to occur at time 60

22. Event Notices
(A,t), representing an arrival event to occur at future time t
(D,t), representing an departure event to occur at future time t
(E,60), representing a simulation stop event to occur at future time 60

23. Activities and Delays Activities: Delay Inter arrival time 1 to 8 min
Service time 1 to 6 min
Delay
Customer time spent in waiting line

24. Simulation Table Clock System State Entities and attributes FEL
Statistics