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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
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 SINGLESERVER 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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