Lecture12 (1)

Lecture12 (1) - Lecture 12 Mariana Olvera-Cravioto Columbia...

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Unformatted text preview: Lecture 12 Mariana Olvera-Cravioto Columbia University [email protected] February 27th, 2012 IEOR 4404, Simulation Lecture 12 1/15 A call center I A call center for United Airlines has s people answering the phones. I Calls arrive according to a nonhomogeneous Poisson process with intensity function λ ( t ) . I Calls are answered in the order in which they arrive. I Service times of customers are iid random variables with distribution F . I If a customer calls when all s servers are busy, it joins a queue. I The system can only hold up to B calls at any given time, excluding those being served ( B + s calls in total). I A call that arrives when there are B calls in the holding system will be automatically be lost. I Each customer put on hold will wait for an exponential amount of time with mean 1 /μ ; once this time is up the customer will hang up (abandon). I We want to estimate the average number of calls that are lost and the average number of abandoned calls during the time [0 ,T ] . IEOR 4404, Simulation Lecture 12 2/15 I What are the variables in the system? IEOR 4404, Simulation Lecture 12 3/15 I What are the variables in the system? I Answer: Time variable: t System state: n, where n is the number of calls in the system at time t IEOR 4404, Simulation Lecture 12 3/15 I What are the variables in the system? I Answer: Time variable: t System state: n, where n is the number of calls in the system at time t I What are the events? IEOR 4404, Simulation Lecture 12 3/15 I What are the variables in the system? I Answer: Time variable: t System state: n, where n is the number of calls in the system at time t I What are the events? I Answer: arrival times of calls, abandonment times, and service completion times. IEOR 4404, Simulation Lecture 12 3/15 I What are the variables in the system? I Answer: Time variable: t System state: n, where n is the number of calls in the system at time t I What are the events? I Answer: arrival times of calls, abandonment times, and service completion times. I What output data do we need to collect? IEOR 4404, Simulation Lecture 12 3/15 I What are the variables in the system? I Answer: Time variable: t System state: n, where n is the number of calls in the system at time t I What are the events? I Answer: arrival times of calls, abandonment times, and service completion times. I What output data do we need to collect? I Answer: L ( T ) , the number of lost calls, A ( T ) , the number of abandoned calls, and N ( T ) , the total number of calls, during the period [0 ,T ] . IEOR 4404, Simulation Lecture 12 3/15 Nonhomogeneous Poisson process in Arena I Arena can only handle intensity functions λ ( t ) that are piecewise constant....
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This note was uploaded on 03/18/2012 for the course IEOR 4404 taught by Professor C during the Spring '10 term at Columbia.

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Lecture12 (1) - Lecture 12 Mariana Olvera-Cravioto Columbia...

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