CARWASH.MOD

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Contents

Description

CARWASH.MOD represents a simple single server queue. Such a queuing system is often referred to as a G/G/1 queue (general arrival times, general service times, and one server).

State Variables

State Variables in CARWASH.MOD
Variable Name Abbreviation Variable Description Size Type
QUEUE Q Number of cars in line 1 Integer
SERVERS S Number of machines available 1 Integer

Vertices

Vertices in CARWASH.MOD
Vertex Name Vertex Description State Changes
RUN The simulation is started None
ENTER Cars enter the line Q=Q+1
START Service starts S=S-1, Q=Q-1
LEAVE Cars leave S=S+1

Initialization Conditions

Initialization Conditions in CARWASH.MOD
Variable Description
QUEUE Initial number of cars in line

Event Relationship Graph

CARWASH.MOD
CARWASH.MOD

English Translation

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

The SIGMA Model, CARWASH.MOD, is a discrete event simulation. It models AN AUTOMATIC CARWASH.
I. STATE VARIABLE DEFINITIONS.
For this simulation, the following state variables are defined:
  
QUEUE: NUMBER OF CARS IN LINE   (integer valued)
SERVERS: NUMBER OF AVAILABLE MACHINES   (integer 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,SERVERS) event occurs when THE SIMULATION RUN IS STARTED.
   Initial values for, QUEUE, SERVERS, are needed for each run.
   After every occurrence of the RUN event:
   Unconditionally, THE CAR WILL ENTER THE LINE;
   that is, schedule the ENTER() event to occur without delay.
2. The ENTER() event occurs when CARS ENTER THE LINE.
   This event causes the following state change(s):
   QUEUE=QUEUE+1
   After every occurrence of the ENTER event:
   Unconditionally, THE NEXT CUSTOMER ENTERS IN 3 TO 8 MINUTES;
   that is, schedule the ENTER() event to occur in 3+5*RND time units. 
   (Time ties are broken by an execution priority of 6.)
   If SERVERS>0, then THERE ARE AVAILABLE SERVERS TO START WASHING THE CAR;
   that is, schedule the START() event to occur without delay.
3. The START() event occurs when SERVICE STARTS.
   This event causes the following state change(s):
   SERVERS=SERVERS-1
   QUEUE=QUEUE-1
   After every occurrence of the START event:
   Unconditionally, THE CAR WILL BE IN SERVICE FOR AT LEAST 5 MINUTES;
   that is, schedule the LEAVE() event to occur in 5+20*RND time units.
   (Time ties are broken by an execution priority of 6.)
4. The LEAVE() event occurs when CARS LEAVE.
   This event causes the following state change(s):
   SERVERS=SERVERS+1
   After every occurrence of the LEAVE event:
   If QUEUE>0, then THERE ARE CARS IN QUEUE, START SERVICE FOR THE NEXT CAR IN LINE;
   that is, schedule the START() event to occur without delay.

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