ATDM with nonindependent sources

This paper presents a study of the queueing behaviour of an Asynchronous Time Division Multiplexing (ATDM) system. The mathematical model chosen to describe this system differs from prior models in that the data sources to be multiplexed may be, in some sense, correlated. More specifically, it is assumed that the number of active users of the ATDM system evolves from slot to slot according to a first order Markov chain. Under certain restrictions for the transition probabilities of this Markov chain, an explicit expression is derived for the probability generating function of the number of data packets in the ATDM-buffer. The results of the analysis are illustrated by means of an example, which shows the possibly substantial influence of the correlation among the users on the queueing behaviour of the system.