BANK1.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

BANK1.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 CARWASH.MOD is the number of servers: CARWASH.MOD has 1 server, and BANK1.MOD has multiple servers.

State Variables

**State Variables in BANK1.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

Vertices

**Vertices in BANK1.MOD**
Vertex Name	Vertex Description	State Changes
RUN	The simulation is started	None
ENTER	Arrival of a customer	Q=Q+1
START	Start of Service	S=S-1, Q=Q-1
LEAVE	End of Service	S=S+1

Initialization Conditions

**Initialization Conditions in BANK1.MOD**
Variable	Description
QUEUE	Initial number of customers in line
SERVERS	Initial number of tellers

Event Relationship Graph

BANK1.MOD

English Translation

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

The SIGMA Model, BANK1.MOD, is a discrete event simulation. 
It models A BANK WITH ONE LINE AND SEVERAL TELLERS.

I. STATE VARIABLE DEFINITIONS.

For this simulation, the following state variables are defined:

QUEUE: NUMBER OF CUSTOMERS IN LINE (INITIALLY=0)   (integer valued)
SERVERS: NUMBER OF AVAILABLE TELLERS   (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) event occurs when INITIALIZATION OF THE RUN.
   Initial values for, SERVERS, 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 A CUSTOMER.
   This event causes the following state change(s):
   QUEUE=QUEUE+1
   After every occurrence of the ENTER event:
   Unconditionally, SCHEDULE THE NEXT ARRIVAL;
   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 START SERVICE WITH THE IDLE SERVER;
   that is, schedule the START() event to occur without delay.

3. The START() event occurs when START OF SERVICE.
   This event causes the following state change(s):
   SERVERS=SERVERS-1
   QUEUE=QUEUE-1
   After every occurrence of the START event:
   Unconditionally, THE CUSTOMER WILL BE IN SERVICE ABOUT 4 MINUTES;
   that is, schedule the LEAVE() event to occur in 2+4*RND time units.
   (Time ties are broken by an execution priority of 6.)

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