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Krajewski SN Supplement C

Krajewski SN Supplement C - Supplement C Waiting Lines A...

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Supplement C Waiting Lines A. Why Waiting Lines Form 1. Define “customers” in waiting lines. 2. Why waiting lines form? 3. When do no waiting lines form? B. Uses of Waiting-Line Theory 1. Service is the act of processing a customer (or manufacturing job). 2. Examples: C. Structure of Waiting Line Problems 1. Customer population 2. The service system SN:C-1

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SN:C-2 Waiting Lines Arrangement of service facilities Single-channel, single-phase Single-channel, multiple-phase Multiple-channel, single-phase Multiple-channel, multiple-phase Mixed arrangement Service facility 3 Service facility 4 Service facility 1 Service facility 2 Routing for : 1 : 1–2–4 Routing for : 2 : 2–4–3 Routing for : 3 Routing for : 3–2–1–4 Mixed Arrangement 3. Priority rule a. b. c.
Waiting Lines SN:C-3 D. Probability Distributions 1. Arrival distribution 2. Customer arrivals can often be described by the Poisson distribution with mean = λ T and variance also = λ T a. Arrival rate: b. Interarrival times ( 29 T n n e n T P λ λ - = ! , 2 , 1 , 0 = n for Where = n P Probability of n arrivals in T time periods = λ Average numbers of customer arrivals per period = e 7183 . 2 3. Service time distribution can be described by an exponential distribution with mean = 1/ μ and variance = (1/ μ ) 2 a. Service time: ( 29 T e T t P μ - - = 1 Where = μ Average number of customers completing service per period = t Service time of the customer = T Target service time b. The exponential distribution assumes that each service time is independent of those that preceded it.

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SN:C-4 Waiting Lines E. Using Waiting Line Models to Analyze Operations 1. Waiting line operating characteristics a.
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Krajewski SN Supplement C - Supplement C Waiting Lines A...

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