QUEUE.MOD

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See also: How to read .MOD pages

1 Description
2 State Variables
3 Vertices
4 Initialization Conditions
5 Event Relationship Graph
6 English Translation
7 Comments

Description

QUEUE.MOD models an exponential (M/M/1) queue, so the arrival and service times have an exponential distribution. It is similar to CARWASH.MOD in structure, the only difference being that CARWASH.MOD is a G/G/1 queue.

State Variables

**State Variables in QUEUE.MOD**
Variable Name	Abbreviation	Variable Description	Size	Type
QUEUE	Q	The number of jobs waiting in line	1	Integer
SERVER	S	Server is available/busy/broken=1/0/-1	1	Integer
IAT	IAT	Mean interarrival time	1,1	Real
MST	MST	Mean service time	1,1	Real

Vertices

**Vertices in QUEUE.MOD**
Vertex Name	Vertex Description	State Changes
RUN	Initialization of the queue and the server	S=1
ENTER	Arrival of a job	Q=Q+1
START	Start of service	S=0, Q=Q-1
LEAVE	End of service	S=1

Initialization Conditions

**Initialization Conditions in QUEUE.MOD**
Variable	Description
QUEUE	The number of jobs waiting in line
IAT	Mean interarrival time
MST	Mean service time

Event Relationship Graph

QUEUE.MOD

English Translation

An English translation is a verbal description of a model, automatically generated by SIGMA.

The SIGMA Model, QUEUE.MOD, is a discrete event simulation. 
It models AN EXPONENTIAL (M/M/1) QUEUE.

I. STATE VARIABLE DEFINITIONS.

For this simulation, the following state variables are defined:

QUEUE: THE NUMBER OF JOBS WAITING IN LINE   (integer valued)
SERVER: SERVER IS AVAIL/BUSY/BROKEN=1/0/-1   (integer valued)
IAT: MEAN INTERARRIVAL TIME  (real valued)
MST: MEAN SERVICE TIME  (real valued)

II. EVENT DEFINITIONS.

Simulation state changes are represented by event vertices (nodes or balls) in a SIGMA graph.  
Event vertex parameters, if any, are given in parentheses. Logical and dynamic relationships 
between pairs of events are represented in a SIGMA graph by edges (arrows) between event vertices.  
Unless otherwise stated, vertex execution priorities, to break time ties, are equal to 5.

1. The RUN(QUEUE,IAT,MST) event occurs when INITIALIZATION OF THE QUEUE AND THE SERVER.
   Initial values for, QUEUE,IAT,MST, are needed for each run.
   This event causes the following state change(s):
   SERVER=1
   After every occurrence of the RUN event:
   Unconditionally, INITIATE THE FIRST JOB ARRIVAL;
   that is, schedule the ENTER() event to occur without delay.
   (Time ties are broken by an execution priority of 6.)

2. The ENTER() event occurs when ARRIVAL OF A JOB.
   This event causes the following state change(s):
   QUEUE=QUEUE+1
   After every occurrence of the ENTER event:
   Unconditionally, SCHEDULE THE NEXT ARRIVAL;
   that is, schedule the ENTER() event to occur in IAT*ERL{1} time units.
   If SERVER==1, then START SERVICE;
   that is, schedule the START() event to occur without delay.

3. The START() event occurs when START OF SERVICE.
   This event causes the following state change(s):
   SERVER=0
   QUEUE=QUEUE-1
   After every occurrence of the START event:
   Unconditionally, THE JOB IS PLACED IN SERVICE FOR 5 MINUTES;
   that is, schedule the LEAVE() event to occur in MST*ERL{1} time units.

4. The LEAVE() event occurs when END OF SERVICE.
   This event causes the following state change(s):
   SERVER=1
   After every occurrence of the LEAVE event:
   If QUEUE>0, then START SERVICING THE WAITING JOB;
   that is, schedule the START() event to occur without delay.
   (Time ties are broken by an execution priority of 4.)