Consider an M/M/1 system with parameters ? and µin which customers are impatient. Specifically, a…

Consider an M/M/1 system with parameters λ and µin which customers are impatient. Specifically, a customer that finds k other customers already in the system joins the queue with probability exp(−αk/µ) or leaves with complementary probability 1 − exp(−αk/µ), where α ≥ 0:

a) Find the asymptotic probability px(k) in terms of px(0).

b) Give an expression for px(0) in terms of the system parameters. c) Find the stability condition assuming µ > 0 and α > 0. d) Find the asymptotic distribution of x and its mean when α → ∞.

 

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