11.07.Fall - ISyE 3232 Stochastic Manufacturing and Service...

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ISyE 3232 Stochastic Manufacturing and Service Systems Fall 2007 Professors Hayriye Ayhan and Jim Dai November 9, 2007 Homework 11 (Due not hand in; finish this assignment before the 2nd test) 1. Consider a CTMC X = { X ( t ) , t 0 } on S = { A, B, C } with generator G given by G = - 12 4 8 5 - 6 1 2 0 - 2 (a) Draw the rate diagram. (b) Use a computer software like matlab or a good calculator to directly compute the transition probability matrix P ( t ) at t = 0 . 20 minutes. (In matlab, the command to exponentiate a matrix A is expm(A).) (c) Do the previous part for t = 1 . 0 minute. (d) Using the results from parts (b) and (c), but without using a software package or calculator, find P { X (1 . 2) = C | X (0) = A } and P { X (3) = A | X (1) = B } . (e) Do part (b) for t = 5 minutes. What phenomenon have you observed? 2. Suppose we have a small call center staffed by two operators A and B handling three telephone lines. A only handles line 1, and B only handles only line 2 and 3. Calls arrive according to a Poisson process with rate λ = 100 calls per hour. All arrivals prefer line 1. Arrivals find all lines are busy will go away.
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  • Fall '07
  • Billings
  • Markov chain, Continuous-time Markov process, Continuous Time Markov, Stochastic Manufacturing, time Markov chain, Hayriye Ayhan

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