CPE 650 – Network Modeling and Analysis (1/2554) Homework III (Due July 20, 2011) 1. A group of two computers are connected to the Internet and are shared by 10 workers in an o ﬃ ce of cubicles. The workers attempt to use the computers at a rate of λ per hour per worker during the busy hour. Each computer session is distributed with a mean holding time of 1 /μ . For the Markov chain deﬁned by the number of busy computers at time t , answer the following: (a) Determine the transition rate matrix Q and draw the corresponding state transition diagram. (b) Determine the steady state probability distribution. (c) Plot the steady-state probabilities for the case of λ = 0.1 and μ = 1. 2. Consider a system with M clients served by a single server with service time exponentially distributed with mean 1 /μ . Once the client is serviced, it waits for an exponentially distributed amount of time with mean 1 /λ before sending another request to the server. (a) Model the number in the server by a CTMC. Determine the transition rate diagram and the steady
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