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Lecture 12

# Lecture 12 - Lecture 12 Waiting Time Problems o Learning...

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Lecture 12 - Waiting Time Problems o Learning Objectives Analyze stationary arrival queues Predict waiting times and quantify performance metrics Redesign service systems to reduce variability o Waiting time in a stationary queue Assumptions - stationary queuing system o Arrival On average, a flow unit arrives every a time units, or 1/a flow units arrives per unit of time . The standard deviation of the inter-arrival time is σ a . The coefficient of variation is CV a = σ a /a . o Process There are m servers (resource) in the system It takes an average of p units of time to serve a flow unit, or 1/p flow units can be processed per unit of time. The standard deviation of the processing time is σ p . The coefficient of variation is CV p = σ p /p . o Reducing Variability Pool resources - Pooling Independent Resource (Economies of Scale) Pooling does not change utilization à because it’s an average measure! Pooling can reduce customer waiting time without investing extra resource Pooling can reduce resource requirement while maintaining the same responsiveness to the customer. The benefit of pooling becomes more significant when the utilization is higher.

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