Consider a single-server queue with Poisson rate λ arrivals and Exponential rate μ>λ service times, but make the following modification: Fix some α∈(λ/μ,1).When a service time is complete, with probability 1−α the customer rejoins the end of the queue instead of leaving the system as usual
By relating the modified queue to a certain M/M/1 queue, find the stationary distribution for the number of customers in the system
Using Little’s formula, L=λW, find the long run average time spent in the queue until being served for the first time.