ops mgt 7_8_queuing_spring3501-2

ops mgt 7_8_queuing_spring3501-2 - Waiting Line Management...

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Unformatted text preview: Waiting Line Management Queuing systems: basic framework & key metrics Customer Population Arrival Queue Service Exit 1. Average utilization (% time server busy) 2. Average queuing time 3. Average queue length (# of customers in line) 4. Average system time (queuing + service) 5. Average # of customers in the system (in line + being served) Life without variability Customer Population Arrival Queue Service Exit Arrival stream: 1 every 5 minutes Service time: Exactly 5 minutes Average utilization Average queuing time Average queue length Average system time Average no. in system 50% 5 0.5 100% 5 1 1 every 10 minutes Exactly 5 minutes Queuing Models Arrival rate Service rate Single queue, single server (M/M/1) Assume Time between arrivals is Exp() Time between services is Exp( ) Queuing Models: Arrivals T = time between arrivals Assume T is an exponential random variable with rate 1 ] [ = T E Expected time between arrivals: , ) ( =- t e t f t T Probability density function for the exponential distribution: Queuing Models: Arrivals If we want to know how many customers arrive in a given time period, we can use the Poisson distribution. , ! ) ( ) ( ) ( =- n n e T n P T n T N PN(T)(n) is the probability that the number of arriving customers in any period of length T is exactly n Time between arrivals is Exp( ) Poisson arrivals at rate N(T) = number of arrivals in T time units Examples:...
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This note was uploaded on 01/25/2011 for the course MGT 3501 taught by Professor Chang during the Spring '10 term at Georgia Institute of Technology.

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ops mgt 7_8_queuing_spring3501-2 - Waiting Line Management...

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