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Problem 4 [15 points = 5 -l- 5 l 5] Consider a queuing system M /M /00 with unlimited number of servers that is functioning under stationary distribution. Sojourn and service times below are measured in minutes. Customer arrivals form a Poisson process having exponentially distributed sojourn times, {33; : j 2 1} with E [33;] = 2. Service times are independent exponentially distributed with average = ,u_1 = 5. 1. Derive stationary distribution for X (t) and present it as probabilities Tl'k = lim P [X(t) = k] ti-oo for each integer k 2 0 2. Evaluate average queue length, L = E [X(t)] under stationary distribution 3. Find expected waiting time (W) in minutes. Solution