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Lecture11 (1)

# Lecture11 (1) - Lecture 11 Mariana Olvera-Cravioto Columbia...

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Lecture 11 Mariana Olvera-Cravioto Columbia University [email protected] February 22nd, 2012 IEOR 4404, Simulation Lecture 11 1/16

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A Queueing System with s Parallel Servers I Customers arrive at a system having s servers and a single queue. I Upon arrival customers join the queue if all s servers are busy, or enter service with an available server otherwise. I When a customer completes service with any of the s servers, the customer departs the system and the customer who has been waiting the longest enters service. I The service distribution at all s servers is G , and service times are all independent. I We number the customers in the order in which they arrive. I We want to collect information that will allow us to analyze the distribution of the time a customer spends in the system. IEOR 4404, Simulation Lecture 11 2/16
I What are the variables in the system? IEOR 4404, Simulation Lecture 11 3/16

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I What are the variables in the system? I Answer: Time variable: t Counter variables: N A = number of arrivals by time t C i = number of customers served by server i , i = 1 , . . . , s , by time t System state: ( n, i 1 , . . . , i s ) where n is the number of customers in the system, and i k is the “identity” of the customer currently being served by server k , k = 1 , . . . , s . IEOR 4404, Simulation Lecture 11 3/16
I What are the variables in the system? I Answer: Time variable: t Counter variables: N A = number of arrivals by time t C i = number of customers served by server i , i = 1 , . . . , s , by time t System state: ( n, i 1 , . . . , i s ) where n is the number of customers in the system, and i k is the “identity” of the customer currently being served by server k , k = 1 , . . . , s . I What are the events? IEOR 4404, Simulation Lecture 11 3/16

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I What are the variables in the system? I Answer: Time variable: t Counter variables: N A = number of arrivals by time t C i = number of customers served by server i , i = 1 , . . . , s , by time t System state: ( n, i 1 , . . . , i s ) where n is the number of customers in the system, and i k is the “identity” of the customer currently being served by server k , k = 1 , . . . , s . I What are the events? I Answer: Arrivals to the system, departures from each of the servers. IEOR 4404, Simulation Lecture 11 3/16
I What output data do we need to collect? IEOR 4404, Simulation Lecture 11 4/16

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I What output data do we need to collect? I Answer: A ( n ) = arrival time of customer n D ( n ) = departure time of customer n IEOR 4404, Simulation Lecture 11 4/16
I What output data do we need to collect? I Answer: A ( n ) = arrival time of customer n D ( n ) = departure time of customer n I What should the event list tell us? IEOR 4404, Simulation Lecture 11 4/16

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I What output data do we need to collect?
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