ON MULTI-CHANNEL QUEUEING SYSTEMS WITH FLUCTUATING PARAMETERS.

The authors deal with a generalization of the classical M/M/K and M/M/ infinity queuing models, where the arrival and service rates fluctuate concurrently, based on the mode of the queuing system. The queuing system can be either in a heavy traffic mode (mode 1) or in a light traffic mode (mode 0). The expectation and variance of the queue size steady-state distribution are derived for both models. The performance of both queuing systems under traffic activity limiting (extreme) conditions is demonstrated. It is shown that for the case where the traffic intensity of one mode is greater than one (even if the average traffic intensity is arbitrarily small) the average queue size approaches infinity as the fluctuations between modes get more and more infrequent. However, for the case where the traffic intensity is less than one for both modes (including the case involving an infinite number of servers) the queue size is not as dependent on the rate of fluctuation between modes.