Question: 2. (15 points): (from past cram} Consider an M {'M f 1 queue with arrival rate A and the service rate a with A

2. (15 points): (from past cram} Consider an M {'M f 1 queue with arrival rate A and the service rate a with A <: pt. prove that1 in the steadystate interdeparture time between two consecutive departure instants is exponentially distributed with rate a. note: this could he a partial proof for famous result saying that process of an m f l queue equilibrium also poisson hints: let d be and n number customers system. find distribution using cdf or laplace transform via conditioning on i: le whether system empty not. under each these cases you should able to express terms other known random variables exponential p1 then remove>

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