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Unformatted text preview: 1 Waiting Line Theory BUAD311 Session 7 2 Objectives Classification of waiting line systems Formula/macro for waiting line calculation Terminology and Classification of Waiting Lines Terminology : The characteristics of a queuing system is captured by five factors: • Arrival pattern (ex. Distribution of interarrival time) • Service pattern (Distribution of service time) • Number of server • Restriction on queue capacity (ex. Capacity of the waiting room) • The queue discipline Terminology and Classification of Waiting Lines The queue discipline – The way customers are selected from the line • Define a queuing system by • Example • Poisson and exponential # of customers coming following a Poisson distribution with mean λ, interarrival time is exponentially distributed with mean 1/ λ. Terminology and Classification of Waiting Lines – M/M/2  Exponential interarrival times, exponential service times, 2 severs – M/G/8 – Exponential interarrival times, general service times, 8 servers Arrival Pattern / Service Pattern / # of Servers / Queue Capacity Notation: • M: Exponential • G: General (Any distribution) 6 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). 7 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. 8 Waiting Line Performance Evaluation Notation: Arrival rate: λ (10 cust. per hour) Average interarrival time: 1/ λ (1 /1 0 hr = 6 min 29 Service rate: μ (12 cust....
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 '07
 Vaitsos
 Management, Poisson Distribution, Mean, Queueing theory, arrival rate

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