Sep 19, 2017

DERIVE THE FOLLOWING VERSION OF THE POLLACZEK-KHINTCHINE MEAN VALUE FORMULA: 2. FIND THE…

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1. Derive the following version of the Pollaczek-Khintchine mean value formula:

2. Find the expected residual service time, conditioned on the server being busy, when the service time distribution is

(a) uniformly distributed between 2 and 8 minutes;

(b) distributed according to a two-phase Erlang distribution in which the mean time spent at each phase is 2 minutes;

(c) distributed according to a two-phase hyper exponential distribution in which the mean service time at phase 1 is equal to 40 minutes and that of phase 2 is equal to 16 minutes. A customer entering service chooses phase 1 with probability α = .25.


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