Cell delay and queue length characteristics in ATM buffers with multiple output lines

A lot of effort has been invested into solving all kinds of Markov modulated discrete-time queueing models, which occur, almost in a natural way, in the performance analysis of slotted systems. A vast amount of results has been derived as far as the buffer contents is concerned. Analytic results for the cell delay however, are mostly limited to the mean value, which is easily calculated by Little's theorem. Nevertheless, other performance measures related to the cell delay, such as variance and tail distribution, may be equally important in the system design of ATM-based B-ISDN networks, especially for those applications that are sensitive to large delays or delay variations. We focus attention on deriving these cell delay performance characteristics in a buffer with multiple output links, which, due to some results derived before, can be reduced to deriving the corresponding quantities concerning the buffer contents. Since the tail distribution, of the buffer contents for a general heterogeneous Markovian arrival process was already extensively treated in some previous work (in addition to some accurate approximation techniques), attention is mainly focused on calculating the moments of this quantity.