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Chapter 18: Queuing Models. C*. Capacity decisions: a trade-off . Total cost. Cost of Service (provider). Cost . Cost of Waiting (customer). Capacity to serve. Model Nomenclature & Terms . A/B/C = arrival dist / service dist / # of servers Poisson arrivals (M)

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## Chapter 18: Queuing Models

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**C***Capacity decisions: a trade-off Total cost Cost of Service (provider) Cost Cost of Waiting (customer) Capacity to serve**Model Nomenclature & Terms**• A/B/C = arrival dist/ service dist/ # of servers • Poisson arrivals (M) • Distribution of independent arrivals over time • Exponential service (M) (time between poisson arrivals) • General service (G) (other distributions)**M/M/1**Customers waiting Customer being served • λ = average customer arrivals per hour • μ = average service rate per hour λ μ Lq = length of queue Ls =length of (# of customers in) system**M/M/1**λ μ-λ Length in System (Ls) = 1 μ-λ Time in System (Ws) = In an effort to maximize efficiency, the manager of the airport tried to get the average time per take off to equal the time between arrivals. What will happen?**Definitions**• n = number of customers in the system • ρ = mean number of customers in system (λ/μ) • N = maximum number of customers in system • c = number of servers • Pn = probability of exactly n customers in system • L = number of customers in (s=system,q=queue, b=busy system) • W= mean waiting time of a customer in (s=system,q=queue, b=busy system)

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