EAR PROC.MOD

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Contents

Description

EAR_PROC.MOD generates successive service times that are exponential autoregressive (EAR) dependent.

State Variables

State Variables in EAR_PROC.MOD
Variable Name Variable Description Size Type
X Service time 1 Real
MST Mean service time 1 Real
SCORR Serial correlation between service times 1 Real
ACORR Serial correlation between successive arrivals 1 Real

Vertices

Vertices in EAR_PROC.MOD
Vertex Name Vertex Description State Changes
RUN Initialization of the queue and the server X=MST*ERL{1}
EAR Generating service time X=SCORR*X+(RND>SCORR)*(MST*ERL{1})

Initialization Conditions

Initialization Conditions in EAR_PROC.MOD
Variable Description
MST Mean service time
SCORR Serial correlation between service times

Event Relationship Graph

EAR_PROC.MOD
EAR_PROC.MOD

English Translation

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

The SIGMA Model, EAR_PROC.MOD, is a discrete event simulation. 
It models A SINGLE-SERVER QUEUE (M/M/1) WITH EAR DEPENDENCE.
I. STATE VARIABLE DEFINITIONS.
For this simulation, the following state variables are defined:
MST: MEAN SERVICE TIME  (real valued)
SCORR: SERIAL CORRELATION BETWEEN SERVICE TIMES  (real valued)
ACORR: SERIAL CORRELATION BETWEEN SUCCESSIVE ARRIVALS  (real valued)
X:   (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(MST,SCORR) event occurs when INITIALIZATION OF THE QUEUE AND SERVER.
   Initial values for, MST,SCORR, are needed for each run.
   This event causes the following state change(s):
   X=MST*ERL{1}
   After every occurrence of the RUN event:
   Unconditionally, schedule the EAR() event to occur without delay.
2. The EAR() event:
   This event causes the following state change(s):
   X=SCORR*X+(RND>SCORR)*(MST*ERL{1})
   After every occurrence of the EAR event:
   Unconditionally, schedule the EAR() event to occur in 1 time units.

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