# Chapter6 - Chapter 6 Queueing Models Banks Carson Nelson...

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Chapter 6 Queueing Models Banks, Carson, Nelson & Nicol Discrete-Event System Simulation ٢ 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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٣ 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. ٤ 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.
٥ Calling Population [Characteristics of Queueing System] ± 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, e.g., model of one corporate jet, if it is being repaired, the repair arrival rate becomes zero. 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. ٦ System Capacity [Characteristics of Queueing System] ± 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.

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٧ Arrival Process [Characteristics of Queueing System] ± For infinite-population models: ² In terms of interarrival times of successive customers. ² Random arrivals: interarrival times usually characterized by a probability distribution. ± Most important model: Poisson arrival process (with rate λ ), where A n represents the interarrival time between customer n-1 and customer n , and is exponentially distributed (with mean 1/ ). ² Scheduled arrivals: interarrival times can be constant or constant plus or minus a small random amount to represent early or late arrivals. ± e.g., patients to a physician or scheduled airline flight arrivals to an airport.
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## This note was uploaded on 11/13/2011 for the course IE 230 taught by Professor Akbari during the Spring '11 term at Amirkabir University of Technology.

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Chapter6 - Chapter 6 Queueing Models Banks Carson Nelson...

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