Find steady-state probability p of state i in embedded chain

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Reference no: EM13908868

Consider an M/G/1 queueing system with Poisson arrivals of rate λ and expected service time E [X]. Let ρ = λE [X] and assume ρ 1. Consider a semi-Markov process model of the M/G/1 queueing system in which transitions occur on depar- tures from the queueing system and the state is the number of customers immediately following a departure.

(a) Suppose a colleague has calculated the steady-state probabilities {pi} of being in state i for each i ≥ 0. For each i ≥ 0, find the steady-state probability π of state i in the embedded Markov chain. Give your solution as a function of ρ, Πi, and p0.

(b) Calculate p0 as a function of ρ.

(d) Is pi the same as the steady-state probability that the queueing system contains i customers at a given time? Explain carefully.

Reference no: EM13908868

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