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3. Consider a single-server queue with Poisson rate 2 arrivals and Exponential rate u > > service times, but make the following modification: Fix some a E (1 /u, 1). When a service time is complete, with probability 1 - a the customer rejoins the end of the queue instead of leaving the system as usual. (a) By relating the modified queue to a certain M/M/1 queue, find the stationary distribution for the number of customers in the system. [2] (b) Using Little's formula, L = AW, find the long run average time spent in the queue until being served for the first time. [2]