FACTORAL.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

FACTORAL.MOD demonstrates the use of the SET{X} function, which sets all variables (including CLK) to zero and sets the random number seed to "X." If no value is put in for "X," the original stream continues.

In FACTORAL.MOD, the carwash model is altered so that after RTIME units, the random number seed is reset to 12345 using the SET function. At this time all other variables in the model are also reset: the CLK is reset to zero, values for the other variables are read into the model using a DISK function. This process continues for NREP repetitions.

See INVENTRY.MOD for another example of using the SET function.

State Variables

**State Variables in FACTORAL.MOD**
Variable Name	Abbreviation	Variable Description	Size	Type
QUEUE	Q	Number of customers in line	1	Integer
SERVERS	S	Number of available servers	1	Integer
IAT	IAT	Mean interarrival time	1	Real
MST	MST	Mean service time	1	Real
REP	REP	Counter for replicates	1	Integer
NREP	NREP	Number of replicates in experiment	1	Integer
RTIME	RTIME	Duration of each replicate	1	Real

Vertices

**Vertices in FACTORAL.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
NEXTR	Start of the next replication	None
DONE	End of a replication	REP=REP+1

Initialization Conditions

**Initialization Conditions in FACTORAL.MOD**
Variable	Description
SERVERS	Initial number of tellers
QUEUE	Initial number of customer in line
REP	Counter for replicates
NREP	Number of replicates in experiment
RTIME	Duration of each replicate

Event Relationship Graph

FACTORAL.MOD

English Translation

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

The SIGMA Model, FACTORAL.MOD, is a discrete event simulation. 
It models REPLICATIONS OF CARWASH.MOD WITH DIFFERENT SERVERS.

I. STATE VARIABLE DEFINITIONS.

For this simulation, the following state variables are defined:

QUEUE: NUMBER OF CUSTOMERS IN LINE   (integer valued)
SERVERS: NUMBER OF FREE SERVERS   (integer valued)
IAT: MEAN INTERARRIVAL TIME  (real valued)
MST: MEAN SERVICE TIME  (real valued)
REP: COUNTER FOR REPLICATES   (integer valued)
NREP: NUMBER OF REPLICATES IN EXPERIMENT   (integer valued)
RTIME: DURATION OF EACH REPLICATE  (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(SERVERS,QUEUE,REP,RTIME,NREP) event occurs when INITIALIZATION OF THE RUN.
   Initial values for, SERVERS,QUEUE,REP,RTIME,NREP, 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 4*ERL{1} time units.
   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 FOR 5 MINUTES;
   that is, schedule the LEAVE() event to occur in 5 time units.
   If CLK==0.0 and QUEUE>0 and SERVERS>0, then TRY TO SERVICE THE INITIAL QUEUE;
   that is, schedule the START() event to occur without delay.
   (Time ties are broken by an execution priority of 2.)

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>=SERVERS, then SERVICE THE WAITING CUSTOMER;
   that is, schedule the START() event to occur without delay.
   If CLK>=RTIME, then schedule the DONE() event to occur without delay.
   (Time ties are broken by an execution priority of 4.)

5. The DONE() event occurs when END OF A REPLICATION.
   This event causes the following state change(s):
   REP=REP+1
   After every occurrence of the DONE event:
   Unconditionally, immediately cancel all scheduled occurrences of the LEAVE event.
   Unconditionally, immediately cancel the next scheduled occurrence of the ENTER event.
   Unconditionally, immediately cancel all scheduled occurrences of the START event.
   If REP<=NREP and SET{12345}, then READ THE NEXT EXPERIMENTAL DESIGN POINT ON DISKS ;
   that is, schedule the NEXTR(SERVERS,QUEUE,REP,RTIME,NREP) event to occur without delay...
   using the parameter value(s) of DISK{FACTOR1.DAT;0},DISK{FACTOR2.DAT;0},
   DISK{FACTOR3.DAT;0},DISK{FACTOR4.DAT;1},DISK{FACTOR4.DAT;2}.

6. The NEXTR(SERVERS,QUEUE,REP,RTIME,NREP) event occurs when STARTING OF THE NEXT REPLICATION.
   After every occurrence of the NEXTR event:
   Unconditionally, schedule the ENTER() event to occur without delay.