Operations Research and Reliability-Queuing Models (ISS Statistics Paper IV): Questions 1 - 1 of 1

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Question number: 1

» Operations Research and Reliability » Queuing Models » M/M/1 Model

Appeared in Year: 2015

Essay Question▾

Describe in Detail

(d) Show that for M/M/1/∞ queue model

Pn=λ0λ1λn1μ1μ2μnP0

where λn and µn are the means of Poisson and exponential distributions respectively where there are n people in the system.

Explanation

Suppose the system is in state j at time t. There are j people in the system. In the next time interval of a very small duration Δt, the system can move to state j-1or j + 1with the following probabilities:

P{n(t+Δt)… (646 more words) …

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