# Operations Research and Reliability-Queuing Models (ISS (Statistical Services) 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

### Describe in Detail

(d) Show that for M/M/1/∞ queue model

where λ_{n} and µ_{n} 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:

If there are no