Markovian Arrival and Service Communication Systems: Spectral Expansions, Separability and Kronecker-Product Forms

In packet-switched communication networks information generation is bursty, resulting in traffic at multiplexers, switches and transmission channels which fluctuates randomly, often with a high correlation in time. Accurate models and efficient analytical techniques are needed to study these networks. We consider typical statistical multiplexing systems where traffic from many bursty sources is buffered if necessary and transmitted over channels (servers). We focus on models in which the traffic from each source is a Markov-modulated Poisson process and information units (packets) contain exponentially distributed number of bits. The capacity of the channels (servers) may be constant or Markov-modulated to reflect capacity sharing among systems.