A paradox in optimal flow control of M/M/m queues

Optimal flow control problems of multiple-server (M/M/m) queueing systems are studied. Due to enhanced flexibility of the decision making, intuitively, we expect that grouping together separated systems into one system provides improved performance over the previously separated systems. This paper presents a counter-intuitive result. We consider a noncooperative optimal flow control problem of M/M/m queueing systems where each player strives to optimize unilaterally its own power where the power of a player is the quotient of the throughput divided by the mean response time for the player. We report a counter-intuitive case where the power of every user degrades after grouping together K(> 1) separated M/M/N systems into a single M/M(K×N) system. Some numerical results are presented.