6-queueing_systems

# 6-queueing_systems - SYSC4005/5001 Winter 2010 Queueing...

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Professor John Lambadaris SYSC4005/5001 Winter 2010 1 Queueing Models in Simulation Winter 2010 Slides are based on the texts: -Discrete Event System Simulation, by Banks et al -Discrete Event Simulation: A first Course, by Leemis and Park

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Professor John Lambadaris SYSC4005/5001 Winter 2010 2 Outline ± Discuss some well-known models (not development of queueing theories): ² General characteristics of queues, ² Meanings and relationships of important performance measures, ² Estimation of mean measures of performance. ² Effect of varying input parameters, ² Mathematical solution of some basic queueing models.
Professor John Lambadaris SYSC4005/5001 Winter 2010 3 Purpose ± Simulation is often used in the analysis of queueing models. ± A simple but typical queueing model: ± Queueing models provide the analyst with a powerful tool for designing and evaluating the performance of queueing systems. ± Typical measures of system performance: ² Server utilization, length of waiting lines, and delays of customers ² For relatively simple systems, compute mathematically ² For realistic models of complex systems, simulation is usually required .

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Professor John Lambadaris SYSC4005/5001 Winter 2010 4 Characteristics of Queueing Systems ± Key elements of queueing systems: ² Customer: refers to anything that arrives at a facility and requires service, e.g., people, machines, trucks, emails. ² Server: refers to any resource that provides the requested service, e.g., repairpersons, retrieval machines, runways at airport.
Professor John Lambadaris SYSC4005/5001 Winter 2010 5 Calling Population ± Calling population: the population of potential customers, may be assumed to be finite or infinite. ² Finite population model: if arrival rate depends on the number of customers being served and waiting ² Infinite population model: if arrival rate is not affected by the number of customers being served and waiting, e.g., systems with large population of potential customers.

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Professor John Lambadaris SYSC4005/5001 Winter 2010 6 System Capacity ± System Capacity: a limit on the number of customers that may be in the waiting line or system. ² Limited capacity, e.g., an automatic car wash only has room for 10 cars to wait in line to enter the mechanism. ² Unlimited capacity, e.g., concert ticket sales with no limit on the number of people allowed to wait to purchase tickets.
Professor John Lambadaris SYSC4005/5001 Winter 2010 7 Arrival Process ± For infinite-population models: ² In terms of inter-arrival times of successive customers. ² Random arrivals: inter-arrival times usually characterized by a probability distribution. ± Most important model: Poisson arrival process (with rate λ ), where A n represents the inter-arrival time between customer n-1 and customer n , and is exponentially distributed (with mean 1/ ).

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6-queueing_systems - SYSC4005/5001 Winter 2010 Queueing...

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