FAILURE.MOD

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Contents

Description

FAILURE.MOD models a system with resources that periodically fail without using canceling edges.

See BRKDN.MOD for modeling failures with canceling edges.

Most simulators have the ability to model resources becoming unavailable, such as a machine going off-line or a worker going on a break. However, these simulators tend to have one or more of four major shortcomings, see Periodic Resource Unavailability.

State Variables

State Variables in FAILURE.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
TTF TTF Time to failure (Assumed since end of process!) 1 Real
PT PT Time until current job is finished 1 Real
FAIL FAIL A failure will occur during processing 1 Integer
TTR TTR Time to repair resource 1 Integer
TP TP Raw job processing time 1 Real

Vertices

Vertices in FAILURE.MOD
Vertex Name Vertex Description State Changes
RUN The simulation is started None
ENTER Arrival of a job Q=Q+1
START Start of Service S=0, Q=Q-1,PT=30*RND,FAIL=(TTF<=PT),TTR=200+200*RND,PT=(FAIL==0)*PT+(FAIL==1)*(PT+TTR),TTF=(FAIL==0)*(TTF-PT)+(FAIL==1)*(700+200*RND-PT+TTF)
FINISH End of Service S=1

Initialization Conditions

This model has no initialization conditions.

Event Relationship Graph

FAILURE.MOD
FAILURE.MOD

English Translation

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

The SIGMA Model, FAILURE.MOD, is a discrete event simulation. 
It models Parallel resources with failures.
I. STATE VARIABLE DEFINITIONS.
For this simulation, the following state variables are defined:
S: Resource I status (1=available, 0=unavailable   (integer valued)
TTF: Time to failure (Assumed since end of process!)  (real valued)
Q: The number of jobs waiting in line   (integer valued)
PT: Time until current job is finished  (real valued)
FAIL: A failure will occur during processing   (integer valued)
TTR: Time to repair resource   (integer valued)
TP: Raw job processing time  (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() event occurs when the simulation is started, set the job disposition flag (FR=1=rework 2=restart 3=resuem 4=reject).
   This event causes the following state change(s):
   S=1
   TTF=700+200*RND
   After every occurrence of the Run event:
   Unconditionally, schedule the Enter() event to occur without delay.
2. The Enter() event occurs when a job enters the queue.
   This event causes the following state change(s):
   Q=Q+1
   After every occurrence of the Enter event:
   Unconditionally, the next job enters after a delay;
   that is, schedule the Enter() event to occur in 20+20*RND time units.
   If S>0, then if the resource is available, start processing the job;
   that is, schedule the Start() event to occur without delay.
3. The Start() event occurs when processing is started with job I.
   This event causes the following state change(s):
   S=0
   Q=Q-1
   PT=30*RND
   FAIL=(TTF<=PT)
   TTR=200+200*RND
   PT=(FAIL==0)*PT+(FAIL==1)*(PT+TTR)
   TTF=(FAIL==0)*(TTF-PT)+(FAIL==1)*(700+200*RND-PT+TTF)
   After every occurrence of the Start event:
   Unconditionally, the job is scheduled to finish (with or without a repair occuring);
   that is, schedule the Finish() event to occur in PT time units.
4. The Finish() event occurs when the job is finished.
   This event causes the following state change(s):
   S=1
   After every occurrence of the Finish event:
   If Q>0, then schedule the Start() event to occur without delay.

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