CLOSEIT.MOD

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Contents

Description

CLOSEIT.MOD is an expansion of the carwash model in that it adds a daily closing time. When the simulated time, CLK, reaches the value of the input variable, CLOSING_TIME, customers are no longer admitted to the system. Customers already waiting in line when we close will be served.

State Variables

State Variables in CLOSEIT.MOD
Variable Name Abbreviation Variable Description Size Type
QUEUE Q Number of customers in line 1 Integer
SERVERS S Number of servers available 1 Integer
CLOSING_TIME t_c Time the store closes 1 Real

Vertices

Vertices in CLOSEIT.MOD
Vertex Name Vertex Description State Changes
RUN The simulation is started None
ARRIVE Arrival of a customer None
ENTER Customers enter the store Q=Q+1
START Service starts S=S-1, Q=Q-1
LEAVE Customer finishes service and leaves S=S+1
CLOSE Store Closes None

Initialization Conditions

Initialization Conditions in CLOSEIT.MOD
Variable Description
QUEUE Initial number of customers in line
CLOSING_TIME Time store closes

Event Relationship Graph

CLOSEIT.MOD
CLOSEIT.MOD

English Translation

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

The SIGMA Model, CLOSEIT.MOD, is a discrete event simulation. 
It models A STORE THAT CLOSES ITS DOORS AT CLOSING_TIME.
I. STATE VARIABLE DEFINITIONS.
For this simulation, the following state variables are defined:
  QUEUE: NUMBER OF CUSTOMERS WAITING IN LINE   (integer valued)
  SERVER: SERVER STATUS (IDLE/BUSY=1/0)   (integer valued)
  CLOSING_TIME: TIME THE STORE CLOSES  (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,CLOSING_TIME) event occurs when RUN INITIALIZATION.
   Initial values for, QUEUE,CLOSING_TIME, 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 CUSTOMER ARRIVAL;
   that is, schedule the ARRIV() event to occur without delay.
   Unconditionally, AT CLOSING TIME THE STORE WILL CLOSE;
   that is, schedule the CLOSE() event to occur in CLOSING_TIME time units.
   (Time ties are broken by an execution priority of 6.)
2. The ARRIV() event occurs when ARRIVAL OF A CUSTOMER.
   After every occurrence of the ARRIV event:
   Unconditionally, SCHEDULE THE NEXT ARRIVAL IN EXP(2) MINUTES;
   that is, schedule the ARRIV() event to occur in 3+5*RND time units.
   (Time ties are broken by an execution priority of 6.)
   Unconditionally, THE CUSTOMER WILL ENTER THE STORE;
   that is, schedule the ENTER() event to occur without delay.
3. The ENTER() event occurs when CUSTOMER ENTERING THE STORE.
   This event causes the following state change(s):
   QUEUE=QUEUE+1
   After every occurrence of the ENTER event:
   If SERVER>0, then THE SERVER IS FREE, SO START SERVICE;
   that is, schedule the START() event to occur without delay.
4. The START() event occurs when START OF SERVICE.
   This event causes the following state change(s):
   SERVER=SERVER-1
   QUEUE=QUEUE-1
   After every occurrence of the START event:
   Unconditionally, SERVICE TAKES 5 MINUTES;
   that is, schedule the LEAVE() event to occur in 5 time units.
   (Time ties are broken by an execution priority of 6.)
5. The LEAVE() event occurs when CUSTOMER FINISHING SERVICE AND LEAVING.
   This event causes the following state change(s):
   SERVER=SERVER+1
   After every occurrence of the LEAVE event:
   If QUEUE>0, then CUSTOMERS ARE STILL WAITING, SO START SERVICE;
   that is, schedule the START() event to occur without delay.
   (Time ties are broken by an execution priority of 6.)
6. The CLOSE() event occurs when STORE CLOSING.
   After every occurrence of the CLOSE event:
   Unconditionally, THE STORE WILL CLOSE ITS DOORS;
   that is, immediately cancel the next scheduled occurrence of the ARRIV event.

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