The numerical solution of a birth–death process arising in multimedia synchronization

One of the most important features of multimedia applications is the integration of multiple media streams that have to be presented in a synchronized fashion. In this paper, we consider a distributed multimedia system where the communication between two nodes involves two media. Arrivals consist of two types of media packets, and the packets are processed for pairs of one packet from each medium. We view this model as a two-dimensional finite birth–death process by considering the arrivals of the packets, following Poisson distribution, as births and the departures of the impatient packets, after waiting in the network for an exponential period, as deaths. We analyze the time-dependent behaviour of our model numerically. We study the various system characteristics like, time-dependent probabilities of the number of packets in each medium, their averages, variances and the busy period. They are illustrated through tables and graphs.