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311_session_7_waiting_line_theory_hiroshi

311_session_7_waiting_line_theory_hiroshi - Waiting Line...

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1 Waiting Line Theory BUAD311 Session 7 Hiroshi Ochiumi
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2 Objectives Classification of waiting line systems Formula/macro for waiting line calculation
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3 Classification of Waiting Lines The characteristics of a queuing system is captured by five parameters: Arrival pattern Service pattern Number of server Restriction on queue capacity The queue discipline
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4 We are interested to evaluate.. Average waiting time in line and in the system The average number of orders (customers) waiting in line and in the system The utilization of server(s).
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5 What are the Key Information? You are managing a local GAP store. Customers are complaining about long waits. It may be difficult to gather waiting time data.
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6 Waiting Line Performance Evaluation Notation: Arrival rate: λ (10 cust. per hour) Average interarrival time: 1/ λ (1/10 hr = 6 min 29 Service rate: μ (12 cust. per hour) Average service time: 1/ μ (1/12 hr = 5 min)
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7 What are the Key Information? Arrival rate: λ Average interarrival time: m a = 1/ λ Standard deviation of interarrival time: S a Coefficient of variation for arrivals : C a = S a / m a Service rate: μ Average service time: m s = 1/ μ Standard deviation of service time: S s Coefficient of variation for services: C = S /
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8 Formulae ρ ρ ρ μ λ ρ S L L system in waiting customers of number Average C C L line in waiting customers of number Average S n Utilizatio q s s a S q + = + - = = + 2 1 2 2 ) 1 ( 2
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9 Formulae WIP = TR * TT L q = λ * W q 2 1 2 2 ) 1 ( 2 s a S a q C C m W line in time
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