Consider the scheme M/M/1. (a) Does the mean number of customers in the queue increase or decrease

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Consider the scheme M/M/1.

(a) Does the mean number of customers in the queue increase or decrease when ρ is increasing?

(b) Find P(Xt > k) in the stationary regime. Does this probability increase or decrease when ρ is increasing?

(c) Argue that both your answers are consistent with the significance of the characteristic ρ. So, for a larger ρ, does the system perform worse or better, and in what sense?

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