BANK2.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

BANK2.MOD represents tellers at a bank as several identical servers operating in parallel on a single waiting line of customers. The main difference between this model and BANK1.MOD is that BANK2.MOD models transient entities using parameters. BANK2.MOD tracks the time for each customer to get through the system.

State Variables

**State Variables in BANK2.MOD**
Variable Name	Abbreviation	Variable Description	Size	Type
QUEUE	Q	Number of customers in line	1	Integer
SERVERS	S	Number of available tellers	1	Integer
W	W	Array of customer waiting times	100	Real
MST	MST	Mean service time	1	Real
IAT	IAT	Mean Interarrival time	1	Real
ID	ID	Customer identification number	1	Integer
IN	IN	I.D. number of customer in service	1	Integer
NEXT	NEXT	I.D. of customer next in line	1	Integer

Vertices

**Vertices in BANK2.MOD**
Vertex Name	Vertex Description	State Changes
RUN	The simulation is started	None
ENTER	Arrival of a customer	ID=ID+1, Q=Q+1, W[ID]=CLK
START	Start of Service	S=S-1, Q=Q-1, NEXT=NEXT+1
LEAVE	End of Service	S=S+1, W[IN]=CLK-W[IN]

Initialization Conditions

**Initialization Conditions in BANK2.MOD**
Variable	Description
SERVERS	Initial number of tellers

Event Relationship Graph

BANK2.MOD

English Translation

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

The SIGMA Model, BANK2.MOD, is a discrete event simulation. 
It models A BANK USING TRANSIENT ENTITIES .

I. STATE VARIABLE DEFINITIONS.

For this simulation, the following state variables are defined:

QUEUE: NUMBER OF CUSTOMERS WAITING IN LINE   (integer valued)
SERVERS: NUMBER OF FREE SERVERS   (integer valued)
W[100]: ARRAY OF CUSTOMER WAITING TIMES  (real valued)
ID: CUSTOMER IDENTIFICATION NUMBER   (integer valued)
IN: I.D. NUMBER OF CUSTOMER IN SERVICE   (integer valued)
NEXT: I.D. OF CUSTOMER NEXT IN LINE   (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(SERVERS,IAT,MST) event occurs when INITIALIZATION OF THE RUN with number of SERVERS, 
   interarrival time, IAT, and mean service time, MST.
   Initial values for, SERVERS,IAT,MST, are needed for each run.
   After every occurrence of the RUN event:
   Unconditionally, INITIATE THE FIRST CUSTOMER ARRIVAL;
   that is, schedule the ENTER() event to occur without delay.

2. The ENTER() event occurs when ARRIVAL OF CUSTOMERS.
   This event causes the following state change(s):
   ID=ID+1
   QUEUE=QUEUE+1
   W[ID]=CLK
   After every occurrence of the ENTER event:
   If SERVERS>0, then START SERVICE WITH AN IDLE SERVER;
   that is, schedule the START(IN) event to occur without delay...using the parameter value(s) of ID.
   Unconditionally, SCHEDULE THE NEXT CUSTOMER ARRIVAL;
   that is, schedule the ENTER() event to occur in IAT*ERL{1} time units.
   (Time ties are broken by an execution priority of 6.)

3. The START(IN) event occurs when START OF SERVICE.
   This event causes the following state change(s):
   QUEUE=QUEUE-1
   SERVERS=SERVERS-1
   NEXT=NEXT+1
   After every occurrence of the START event:
   Unconditionally, SCHEDULE END OF SERVICE FOR CUSTOMER=IN;
   that is, schedule the LEAVE(IN) event to occur in MST*ERL{1} time units...
   using the parameter value(s) of IN.
   (Time ties are broken by an execution priority of 6.)

4. The LEAVE(IN) event occurs when END OF SERVICE.
   This event causes the following state change(s):
   SERVERS=SERVERS+1
   W[IN]=CLK-W[IN]
   After every occurrence of the LEAVE event:
   If QUEUE>0, then START SERVICE OF THE NEXT WAITING CUSTOMER;
   that is, schedule the START(IN) event to occur without delay...
   using the parameter value(s) of NEXT.