1. Simulation Examples And General Principles Part 2
Chapter 2 & 3
Simulation Examples
And General Principles
Part 2

2. General Principles in Discrete-Event Simulation
Goal: Dynamic & stochastic systems change in discrete manner.
Definitions:
System
A collection of entities (people and machines..) that interact together over time for one or more goals
Model
An abstract representation of a system, usually containing structural, logical or mathematical relationship that describe a system in term of state, entities and their attributes , sets, processes,…
System state
A collection of variables in any time that describe the system

3. General Principles in Discrete-Event Simulation
Entity
Any object or component in system that require explicit representation (server, customer,...)
Attributes
The properties of a given customer
List
A collection of associated entities , ordered in some logical fashion (FIFO, priority,…)
Event
An instantaneous occurrence that changes the state of a system
Event Notice
A record of a event to occur at the current or future time (type and time)

4. General Principles in Discrete-Event Simulation
Event List
FEL (future event list)
Activity (unconditional wait)
A duration time of specified length (service time or interarrival time,… )
Deterministic, Statistical and functional
Delay (conditional wait)
A duration of time of unspecified indefinite length, which is not known until it ends (customer delay in waiting line)
Clock
A variable representing simulated time

5. Example (Able and Baker)
What are the simulation components?
System state
Entities
Events
Activities
Delay
Components are static. Need also to model system dynamics – relationships & interactions between components.
How does an event affect/trigger other system components?
How are activities defined?
What are the initial and termination system states?

6. Example (Able and Baker)

7. Simulation Process
A sequence of system snapshots representing the evolution of the system through time.
A snapshot at a given time includes:
System state
List of activities and status of components when each activity ends.
Cumulative statistics.

8. Event Scheduling / Time Advance Algorithm
The sequence of actions which a simulator must perform to advance the clock and build a new system snapshot.
Future event list (FEL): a key element
Contains all event notices for events that have been scheduled to occur at a future time.
Advances simulation time and guarantees that all events occur in correct order.
What does scheduling a future event mean?

9. Event Scheduling
The essential idea: move along the time scale until an event occurs and then, depending on the event, modify the system state and possibly schedule new events.
Based on this, it is a trivial exercise to run through a simulation of the system. The events are stored in an event queue, which lists all events in order.
The first event in the queue is taken off, and other events may then be added (assuming that an event only triggers other events in the future).

10. Event Scheduling cont’d
Arrival Event:
1. Check the status of the server(s) (idle or busy)
If there is an idle server
Update idle status; Start serving the customer.
Generate a new departure event at t + s* for this customer.
If all busy, place customer in queue & update LQ(t)
2. Generate new arrival event t + a* for next customer.
3. Collect stats; Return control to time-advance routine

11. Simple diagram

12. Detailed diagram

13. Event Scheduling cont’d
Departure Event
1. Check queue (empty or not)
If empty, set server to idle.
If not empty then do
Choose a waiting customer, start serving the customer
Generate a new departure event at time t + s* for this customer
2. Collect stats; Return control to time-advance routine

14. Simple diagram

15. Detailed diagram

16. Single server example using event scheduling

19. Dump-Truck example using event scheduling

20. Components, assumptions ad objectives
System contains
Six trucks
Two loaders
One scale
Assumptions
FCFS waiting lines for loading and scaling
Travel time from loading to scaling negligible
After scaling, the truck start traveling time during which it will unload all its loads
Purpose: estimate loaders and scale utilization

23. Simulation starts with one truck at the scale and the others loading (i.e. two loading and 3 waiting to load)
Generated times for loading, weighting, and traveling are:

31. Simulation can be simplified by not considering the trucks in the event notices.
i.e. (EL, t, DTi) can be simplified to (EL, t)
However, for other objectives rather than computing the loaders and the scale utilization, like computing the system response time, this details is required.
System response time: how long the truck spends from the time of arrival at loading until it leaves scaling.