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

Description

BANK3.MOD is a variation on BANK2.MOD that passes fewer parameters. In BANK3.MOD only the START-LEAVE edge passes the attribute value of NEXT. Note that in BANK3.MOD the value of NEXT is not initialized to 1 but automatically started at zero. This model was simplified by assuming that customers will be served in the order in which they arrived (FIFO - First in first out).

State Variables

State Variables in BANK3.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 BANK3.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 BANK3.MOD

Variable	Description
SERVERS	Initial number of tellers

Event Relationship Graph

English Translation

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

The SIGMA Model, BANK3.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)
IAT: MEAN INTERARRIVAL TIME  (real valued)
MST: MEAN SERVICE TIME  (real 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.
   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 NEXT.
   (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.

Comments

To understand this: open two sessions of SIGMA at the same time and run BANK2.MOD in one and BANK3.MOD in the other and observe that their outputs are the same even though BANK3.MOD only has one edge passing the value an attribute, while BANK2.MOD has three such edges.

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