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1
Simulation Modeling
and Analysis
(ORIE 4580/5580)
Week 9: Introduction to DiscreteEvent
Simulation and SingleServer Queue
(10/21/10)
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View Full Document Announcement and Agenda
•
HW6 is available on Blackboard and will be due by 11am on 10/28
•
On Q4 in HW6, you’re asked to complete the midsemester course evaluation
•
The evaluation is available on Blackboard under “Assignments >
HW6”
•
Your feedback is very important to me.
•
You can be absolutely sure that your identity will be conFdential, but we
can see who participated in the evaluations.
•
Thank you very much for all of your help!
•
You should start thinking about forming a team of 45 students for the upcoming
course project.
•
Each team needs to have at least 4 students (but no more than 5)
•
The project description will be available in midNovember
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Introduction: SingleServer Queue
•
DiscreteEvent Simulation (DES) is used for modeling systems where
events happen sequentially over time.
•
We will use an example of the singleserver queue to illustrate the basic
concepts of discreteevent simulation
3
server
SingleServer Queue:
queue
•
Assume that the queue (or waiting room) has inFnite capacity
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Queueing discipline is FrstcomeFrstserve (±C±S)
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Interarrival times of each job are i.i.d.
random variables with a cumulative
distribution function ±
A
(
⋅
)
•
Service times of each job are i.i.d.
random variables with a cumulative
distribution ±
S
(
⋅
)
•
Assume that the interarrival and service times are independent
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View Full Document Building Blocks of DES:
Simulation Clock
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We need to keep track of the simulated time.
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The variable in a simulation model that keeps track of the simulated time
is called the simulation clock.
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Two basic methods for advancing the simulation clock
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Method 1:
Nextevent time advance
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The clock moves when an event happens
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This will be our focus!
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Method 2:
Fixedincrement time advance
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Typically used for applications of a “continuous” nature”
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Example:
If you’re simulating a Yacht’s race, you might want to
increment your clock in a 5second increments
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This is a special case of the nextevent time advance.
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System State
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System state is a collection of variables necessary to describe the status
of the system at a particular point in time.
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This is the FIRST step in building DES models.
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SingleServer Queue:
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System State is the number of customers in the system, that is, the
number of customers in the queue
and
in the service area
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Let X(t) denote the number of customers in the system at time t
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Note:
Since the server can only work on a single job at a time, we
do NOT have to keep track of the numbers in the service area
•
TwoServer Queue:
•
System state is the number of customers in the system,
and which
servers are busy.
5
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This note was uploaded on 10/26/2010 for the course OR&IE 5580 at Cornell University (Engineering School).
 '10
 PAAT

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