TWOTYPES.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

TWOTYPES.MOD models a queuing system with two types of jobs and two types of technicians.

State Variables

**State Variables in TWOTYPES.MOD**
Variable Name	Abbreviation	Variable Description	Size	Type
QUEUE	Q	Number of waiting jobs in queue [TYPE+2*TECH]	4	Integer
FREE	FREE	Number of idle technicians of each type	2	Integer
TYPE	TYPE	Type of job (0=SHORT, 1=LONG)	1	Integer
TECH	TECH	Type of technician (0=TRAINEE;1=EXPERIENCED)	1,1	Integer
TIME	TIME	Processing times by type and tech	2,2	Integer

Vertices

**Vertices in TWOTYPES.MOD**
VERTEX NAME	Vertex Description	State Changes
RUN	Run initialization	None
ARRIV	Arrival of a job	TYPE=(RND<.3), TECH=(TYPE==0&RND<.3) or (TYPE==1&RND<.8)
ENTER	Job joining the queue	Q[TYPE+2TECH]=Q[TYPE+2TECH]+1
START	Start of service	FREE[TECH]=FREE[TECH]-1, Q[TYPE+2TECH]=Q[TYPE+2TECH]-1
LEAVE	End of service	FREE[TECH]=FREE[TECH]+1
INPUT	Read input data	TIME[TYPE;TECH]=DISK{TWOTYPES.DAT;0}

Initialization Conditions

**Initialization Conditions in TWOTYPES.MOD**
Variable	Description
FREE[i]	Number of idle technicians of each type

Event Relationship Graph

There is no Event Relationship Graph available for this model.

TWOTYPES.MOD as seen in SIGMA

English Translation

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

The SIGMA Model, TWOTYPES.MOD, is a discrete event simulation. 
It models TWO JOB TYPES AND TWO TYPES OF TECHNICIANS.

I. STATE VARIABLE DEFINITIONS.

For this simulation, the following state variables are defined:

Q[4]: NUMBER OF WAITING JOBS IN QUEUE[TYPE+2*TECH]   (integer valued)
FREE[2]: NUMBER OF IDLE TECHNICIANS OF EACH TYPE   (integer valued)
TYPE: TYPE OF JOB (0=SHORT, 1=LONG)   (integer valued)
TECH: TYPE OF TECHNICIAN (0=TRAINEE;1=EXPERIENCED)   (integer valued)
TIME[2,2]: PROCESSING TIMES BY TYPE AND TECH   (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(FREE[0],FREE[1]) event occurs when RUN INITIALIZATION.
   Initial values for, FREE[0],FREE[1], are needed for each run.
   After every occurrence of the RUN event:
   Unconditionally, INITIATE THE FIRST JOB ARRIVAL;
   that is, schedule the ARRIV() event to occur without delay.
   Unconditionally, schedule the INPUT(TYPE,TECH) event to occur without delay...
   using the parameter value(s) of 0,0.
   (Time ties are broken by an execution priority of 4.)

2. The INPUT(TYPE,TECH) event occurs when READ INPUT DATA.
   This event causes the following state change(s):
   TIME[TYPE;TECH]=DISK{TWOTYPES.DAT;0}
   After every occurrence of the INPUT event:
   If TYPE<1 and TECH<=1, then schedule the INPUT(TYPE,TECH) event to occur without delay...
   using the parameter value(s) of TYPE+1,TECH.
   (Time ties are broken by an execution priority of 4.)
   If TYPE==1 and TECH<1, then schedule the INPUT(TYPE,TECH) event to occur without delay...
   using the parameter value(s) of 0,TECH+1.
   (Time ties are broken by an execution priority of 4.)

3. The ARRIV() event occurs when ARRIVAL OF A JOB.
   This event causes the following state change(s):
   TYPE=(RND<.3)
   TECH=(TYPE==0&RND<.3)|(TYPE==1&RND<.8)
   After every occurrence of the ARRIV event:
   Unconditionally, SCHEDULE THE NEXT ARRIVAL;
   that is, schedule the ARRIV() event to occur in 4*ERL{1} time units.
   (Time ties are broken by an execution priority of 6.)
   Unconditionally, ENTER THE SYSTEM AND JOIN THE QUEUE;
   that is, schedule the ENTER(TYPE,TECH) event to occur without delay...
   using the parameter value(s) of TYPE,TECH.

4. The ENTER(TYPE,TECH) event occurs when JOB JOINING THE QUEUE.
   This event causes the following state change(s):
   Q[TYPE+2*TECH]=Q[TYPE+2*TECH]+1
   After every occurrence of the ENTER event:
   If FREE[TECH]>0, then START SERVICE WITH THE FREE TECHNICIAN;
   that is, schedule the START(TYPE,TECH) event to occur without delay...
   using the parameter value(s) of TYPE,TECH.
   (Time ties are broken by an execution priority of 3.)

5. The START(TYPE,TECH) event occurs when START OF SERVICE.
   This event causes the following state change(s):
   FREE[TECH]=FREE[TECH]-1
   Q[TYPE+2*TECH]=Q[TYPE+2*TECH]-1
   After every occurrence of the START event:
   Unconditionally, THE JOB CAN LEAVE AFTER ITS SERVICE TIME;
   that is, schedule the LEAVE(TYPE,TECH) event 
   to occur in TIME[TYPE;TECH]*ERL{1} time units...
   using the parameter value(s) of TYPE,TECH.
   (Time ties are broken by an execution priority of 6.)

6. The LEAVE(TYPE,TECH) event occurs when END OF SERVICE.
   This event causes the following state change(s):
   FREE[TECH]=FREE[TECH]+1
   After every occurrence of the LEAVE event:
   If TECH==0 and Q[0]>0, then SERVICE THE WAITING JOB;
   that is, schedule the START(TYPE,TECH) event to occur without delay...
   using the parameter value(s) of 0,0.
   If TECH==0 and Q[0]==0 and Q[1]>0, then SERVICE THE WAITING JOB;
   that is, schedule the START(TYPE,TECH) event to occur without delay...
   using the parameter value(s) of 1,0.
   If TECH==1 and Q[2]>0, then SERVICE THE WAITING JOB;
   that is, schedule the START(TYPE,TECH) event to occur without delay...
   using the parameter value(s) of 0,1.
   If TECH==1 and (Q[3]>0 and Q[2]==0), then SERVICE THE WAITING JOB;
   that is, schedule the START(TYPE,TECH) event to occur without delay...
   using the parameter value(s) of 1,1.