A queuing model for a hybrid data multiplexer

There are several instances in a data network where a communication line is shared by two or more types of data. In this paper, we analyze the performance of a buffer used to multiplex two types of data. Sporadic short messages, like inquiries from terminals, share the same channel as relatively steady synchronous data, like trunk traffic or long messages from computer data bases. To the authors' knowledge, previous studies have been limited to an ad hoc approximation to the probability distribution of interest. We solve for the equilibrium distribution of number of units of data in the buffer. The delay distribution easily follows. Numerical results are also presented which can be used as a guide to determining how much of each type of traffic can be sustained simultaneously.