CLOSEIT.MOD

From Support

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

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

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.