Find the steady steady probability distribution

Reference no: EM131162866

We consider an M/M/1=∞ queue. The mean service time of the exponential server is μ-1 and the customers arrive according to a Poisson process with mean rate λ where λAn arrived customer may leave the system directly with a probability of

(i/ (i+1) )
i=0,1,....

when they find there are already i customers in the system.
(a) Find the steady-steady probability distribution of the queueing system in terms of λ and μ.

(b) Assuming that the queueing system is in steady-state, find the loss probability (probability that an arrived customer chooses not to join the queueing system).

(c) If the mean service time μ^-1 can be assigned as fast as possible (λ μ), recommend the service rate μ if the loss probability has to be less than 1 %.

Reference no: EM131162866

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