A Note on the M/M/∞ Queue in Random Environment
نویسندگان
چکیده
We show that, for the M/M/∞ queue in a Markovian random environment, the joint probability distribution function (pdf) of the two variables: random phase and number of customers in the system, is equal to the product of the corresponding marginal pdfs if and only if the ratio of arrival rate to service rate is the same for all phases. We explicitly derive this joint pdf. Furthermore, for the general case, we calculate the conditional and overall mean queue lengths.
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