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12.07.Fall

# 12.07.Fall - Version ISyE 3232 H Ayhan and J G Dai Due...

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Version:11/27/2007 ISyE 3232 H. Ayhan and J. G. Dai Due: Section B on Wednesday, 5th of December, Section C on Tuesday 4th of December. Homework 12 1. Consider a call center that is staffed by K agents with three phone lines. Call arrivals follow a Poisson process with rate 1 per minute. An arrival call that finds all lines busy is lost. Call processing times are exponentially distributed with mean 2 minutes. (a) Find the throughput and average waiting time when K = 1. (b) Find the throughput and average waiting time when K = 2. (c) Find the throughput and average waiting time when K = 3. 2. Consider a service system with a single server whose service time is exponentially distributed with rate μ and infinite capacity. The arrivals come to the system following a Poisson process of rate λ but an arrival finding i people in the system will enter the system with probability 1 / ( i + 1). For example at the time of your arrival if there are 2 people in the system you will enter with probability 1/3.
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