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Week09-Lecture (20101021)

# Week09-Lecture (20101021) - Simulation Modeling and...

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1 Simulation Modeling and Analysis (ORIE 4580/5580) Week 9: Introduction to Discrete-Event Simulation and Single-Server Queue (10/21/10)

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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 mid-semester 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 confidential, 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 4-5 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 mid-November 2
Introduction: Single-Server Queue Discrete-Event Simulation (DES) is used for modeling systems where events happen sequentially over time. We will use an example of the single-server queue to illustrate the basic concepts of discrete-event simulation 3 server Single-Server Queue: queue Assume that the queue (or waiting room) has infinite capacity Queueing discipline is first-come-first-serve (FCFS) Interarrival times of each job are i.i.d. random variables with a cumulative distribution function F A ( ) Service times of each job are i.i.d. random variables with a cumulative distribution F S ( ) Assume that the interarrival and service times are independent

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Building Blocks of DES: Simulation Clock We need to keep track of the simulated time. The variable in a simulation model that keeps track of the simulated time is called the simulation clock. Two basic methods for advancing the simulation clock Method 1: Next-event time advance The clock moves when an event happens This will be our focus! Method 2: Fixed-increment time advance Typically used for applications of a “continuous” nature” Example: If you’re simulating a Yacht’s race, you might want to increment your clock in a 5-second increments This is a special case of the next-event time advance. 4
Building Block of DES: System State System state is a collection of variables necessary to describe the status of the system at a particular point in time. This is the FIRST step in building DES models. Single-Server Queue: System State is the number of customers in the system, that is, the number of customers in the queue and in the service area Let X(t) denote the number of customers in the system at time t 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 Two-Server Queue: System state is the number of customers in the system, and which servers are busy.

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