An effective algorithm to calculate the distribution of the buffer contents and the packet delay in a multiplexer with bursty sources

A statistical multiplexer with a finite number of independent and identical bursty traffic sources (users) is considered. The burstiness of the sources is modeled by describing both the active periods (during which a user generates one packet per slot) and the passive periods (during which a user does not generate any data) as geometric random variables. As a result, a correlated-arrivals queuing model for the multiplexer buffer is obtained, and it is analyzed by numerical means. Specifically, algorithms are given for the explicit derivation of the probability mass functions of the buffer contents (in packets) and the packet delay (in slots). The results indicate a very strong influence of the burstiness of the required buffer space in the multiplexer and the possible values of the packet delay, even for a given mean arrival rate per slot