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

Optimal flow control problems of multiple-server (M/M/n) 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 result counter-intuitive against such an expectation. We consider a non-cooperative optimal flow control scheme M/M/n queueing systems where each of multiple players 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.