수 25 5월 2016

Q. Consider a queuing system with one server, where the customers arrive according to Poisson process with rate \(\lambda\) and the queue size is unlimited. In addition, the service time of a customer is determined in the following manner. Before a customer is served, a biased coin whose probability of head is \(p\) is flipped. If it comes up head, the service time is exponentially distributed with mean \(1/u\). If it comes up tail, the service time is constant at \(d\). Calculate the mean sojourn time of a customer in the system.

[ Refer to \(\int x^2 \mathrm{e}^{ax} \mathrm{d}x = \mathrm{e}^{ax}(x^2-2x/a+2/a^2)/a\). ]

A.

Category: quiz Tagged: system analysis quiz markov chain transition probability diagram