SLOFAST0.MOD

From Support

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

SLOFAST0.MOD represents two servers with different average processing speeds, such as a grocery store with an express checkout lane and a regular check out lane. The main difference between this model and CARWASH.MOD is that a CHECK vertex and a second pair of START and LEAVE vertices for the second server have been added, see Event Relationship Graph.

SLOFAST1.MOD and SLOFAST2.MOD are variations of SLOFAST0.MOD.

State Variables

**State Variables in SLOFAST0.MOD**
Variable Name	Abbreviation	Variable Description	Size	Type
QUEUE	Q	Number of parts in line	1	Integer
SERVER	S[i]	Number of available servers of type i	2	Integer

Vertices

**Vertices in SLOFAST0.MOD**
Vertex Name	Vertex Description	State Changes
RUN	The simulation is started	S[0]=1,S[1]=1
ARRIVE	Arrival of a part	Q=Q+1
CHECK	Checking of server 0 and of server 1 if 0 is busy	None
STRT0	Start of Service with Server 0	S[0]=S[0]-1, Q=Q-1
LEAV0	End of Service with Server 0	S[0]=S[0]+1
STRT1	Start of Service with Server 1	S[1]=S[1]-1, Q=Q-1
LEAV1	End of Service with Server 1	S[1]=S[1]+1

Initialization Conditions

This model has no initialization conditions.

Event Relationship Graph

SLOFAST0.MOD

English Translation

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

The SIGMA Model, SLOFAST0.MOD, is a discrete event simulation. 
It models ONE SLOW AND ONE FAST SERVER.

I. STATE VARIABLE DEFINITIONS.

For this simulation, the following state variables are defined:

  QUEUE: THE NUMBER OF PARTS WAITING IN LINE   (integer valued)
  SERVER[2]: SERVER STATUS (IDLE/BUSY=1/0)   (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() event occurs when INITIALIZATION OF THE SERVERS.
   This event causes the following state change(s):
   SERVER[0]=1
   SERVER[1]=1
   After every occurrence of the RUN event:
   Unconditionally, INITIATE THE FIRST PART ARRIVAL;
   that is, schedule the ARRIV() event to occur without delay.

2. The ARRIV() event occurs when ARRIVAL OF A PART.
   This event causes the following state change(s):
   QUEUE=QUEUE+1
   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, schedule the CHECK() event to occur without delay.

3. The STRT0() event occurs when START OF SERVICE WITH SERVER 0.
   This event causes the following state change(s):
   SERVER[0]=SERVER[0]-1
   QUEUE=QUEUE-1
   After every occurrence of the STRT0 event:
   Unconditionally, THE PART IS PLACED IN SERVICE FOR 3 MINUTES;
   that is, schedule the LEAV0() event to occur in 3 time units.
   (Time ties are broken by an execution priority of 6.)

4. The LEAV0() event occurs when END OF SERVICE WITH SERVER 0.
   This event causes the following state change(s):
   SERVER[0]=SERVER[0]+1
   After every occurrence of the LEAV0 event:
   If QUEUE>0, then START SERVICING THE WAITING PART;
   that is, schedule the STRT0() event to occur without delay.

5. The CHECK() event occurs when CHECKING OF SERVER 0 AND OF SERVER 1 IF 0 BUSY.
   After every occurrence of the CHECK event:
   If SERVER[0]>0, then START SERVICE;
   that is, schedule the STRT0() event to occur without delay.
   If SERVER[0]<=0 and SERVER[1]>0, then schedule the STRT1() event to occur without delay.

6. The STRT1() event occurs when START OF SERVICE WITH SERVER 1.
   This event causes the following state change(s):
   SERVER[1]=SERVER[1]-1
   QUEUE=QUEUE-1
   After every occurrence of the STRT1 event:
   Unconditionally, THE PART IS PLACED IN SERVICE FOR 5 MINUTES;
   that is, schedule the LEAV1() event to occur in 5 time units.
   (Time ties are broken by an execution priority of 6.)

7. The LEAV1() event occurs when END OF SERVICE WITH SERVER 1.
   This event causes the following state change(s):
   SERVER[1]=SERVER[1]+1
   After every occurrence of the LEAV1 event:
   If QUEUE>0, then START SERVICING THE WAITING PART;
   that is, schedule the STRT1() event to occur without delay.