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Lecture10 (1)

# Lecture10 (1) - Lecture 10 Mariana Olvera-Cravioto Columbia...

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Lecture 10 Mariana Olvera-Cravioto Columbia University [email protected] February 20th, 2012 IEOR 4404, Simulation Lecture 10 1/14

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Discrete Event Simulation Variables: I Time variable t : amount of (simulated) time that has elapsed. I Counter variables: variables that keep a count of the number of times that certain events have occurred by time t . I System state variable: describes the “state of the system” at time t . Note: the system state variable must contain “all” the information we need to determine how the system evolves in time. Events: whatever makes the system change from one state to another. Event List: it tells us which event occurs next. Output data: information we need to collect to answer the questions of interest. IEOR 4404, Simulation Lecture 10 2/14
A Single-Server Queueing System I Customers arrive according to a non homogeneous Poisson process with intensity function λ ( t ) , t 0 . I One server providing service to customers in the order in which they arrive (FIFO). I When the server completes the service of a customer it immediately begins serving the customer who has been waiting the longest; if no customer is waiting then the server remains free until the next customer arrives. I Customers are not allowed to enter the system after time T , but those who were already in the system by time T do receive service. I The service time of a customer is a random variable (independent of all other service times and of the arrival process) having CDF G . IEOR 4404, Simulation Lecture 10 3/14

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I We want to determine: I the average time a customer spends in the system I the average time past T that the last customer departs I What are the variables in this system? IEOR 4404, Simulation Lecture 10 4/14
I We want to determine: I the average time a customer spends in the system I the average time past T that the last customer departs I What are the variables in this system? I Answer: Time variable: t Counter variables: N A = number of arrivals (by time t ) N D = number of departures (by time t ) System state: n = number of customers in the system (at time t ) . IEOR 4404, Simulation Lecture 10 4/14

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I We want to determine: I the average time a customer spends in the system I the average time past T that the last customer departs I What are the variables in this system? I Answer: Time variable: t Counter variables: N A = number of arrivals (by time t ) N D = number of departures (by time t ) System state: n = number of customers in the system (at time t ) . I What are the events? IEOR 4404, Simulation Lecture 10 4/14
I We want to determine: I the average time a customer spends in the system I the average time past T that the last customer departs I What are the variables in this system?

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