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hmwk10_11 - ISyE 3232 Stochastic Manufacturing and Service...

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Unformatted text preview: ISyE 3232 Stochastic Manufacturing and Service Systems Fall 2011 H. Ayhan Homework 10 November 16, 2011 (For your practice only) 1. Suppose there are two tellers taking customers in a bank. Service times at a teller are independent, exponentially distributed random variables, but the first teller has a mean service time of 3 minutes while the second teller has a mean of 6 minutes. There is a single queue for customers awaiting service. Suppose at noon, 3 customers enter the system. Customer A goes to the first teller, B to the second teller, and C queues. To standardize the answers, let us assume that T A is the length of time in minutes starting from noon until Customer A departs, and similarly define T B and T C . (a) What is the probability that Customer A will still be in service at time 12:05? (b) What is the expected length of time that A is in the system? (c) What is the expected length of time that A is in the system if A is still in the system at 12:05?...
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