STOCHASTIC COMPARISONS FOR FORK-JOIN QUEUES WITH EXPONENTIAL PROCESSING TIMES

Consider a fork-join queue, where each job upon arrival splits into k tasks and each joins a separate queue that is attended by a single ser ver. Service times are independent, exponentially distributed random v ariables. Server i works at rate mu(i), Sigma(i=1)(k), mu(i) = mu wher e mu is constant. We prove that the departure process becomes stochast ically faster as the service rates become more homogeneous in the sens e of stochastic majorization. Consequently, when all k servers work wi th equal rates the departure process is stochastically maximized.