Traffic multiplexing networks: queueing analysis

Summary form only given. The multiplexer of independent inputs, each being regenerative ON-OFF, i.e. memoryless OFF and generally distributed ON has been recently resurrected in the limit M/G/∞ and subexponentially tailed ON for the purpose of understanding the long range dependence and the self-similarity of the aggregation of heterogeneous high speed traffic. We remark that for the purpose of computing the tail distribution, the M/G/∞ subexponentially tailed ON reduces to one subexponentially tailed ON multiplexed with compound Poisson input and that furthermore, it is possible to obtain a complete analysis for a multiplexing network. A unidirectional bus is a special case (tandem concentrating network). A single multiplexer is a further specialized case (concentrating station). We assume that the service rate is nondecreasing in the direction of the traffic flow (in particular all the stations may have the same service rate). We point out that for input/output purposes the network is equivalent to a single multiplexer and that under these assumptions the network becomes a distributed multiplexer for which the multidimensional queueing process sampled at particular epochs along a tandem path decomposes in stationarity into independent one dimensional processes. We discuss the network queueing analysis for several service disciplines (FCFS, priority), searching for the distribution of the buffer content at each station and for the joint queueing distribution encountered by each source at all the stations along its tandem path