Transient solution of a link with finite capacity supporting multiple streams

Most of the real-time applications involve connection establishment in point-to-point (unicast) communication in computer networks that can be modelled as a problem of resource allocation and resource sharing. These applications have different streams, such as video, voice, graphics, etc., each having different arrival rates. A stream (call) will be admitted into the network only if the network guarantees the `Quality of Service' (QoS) parameters of the call such as bandwidth, delay, jitter and loss probability. Otherwise, the call is rejected. Hence, the study of call blocking probabilities in such communication networks is a problem of growing importance. Application of queueing theory to solve these problems has received considerable attention in the research community. Due to the real-time nature of the applications, it is pertinent to study the time-dependent behaviour of such systems. In this paper, a real-time unicast communication has been modelled as a multi-dimensional Markov process to obtain the time-dependent blocking probabilities. The time-dependent system size probabilities, means, variances and correlation coefficients of different streams are also obtained.