Simple formulas for multiplexing delay for independent regenerative sources

Simple expressions are given for the mean delay, mean waiting time, and mean busy period length in a multiplexer. A large class of possible data streams is considered. For example, data streams with active periods having a general distribution are permitted, and the traffic rate during the active periods can be random. Data can also arrive in batches. The output stream of the multiplexer again falls into the class. The exact formulas allow evaluation of the error in approximations such as a heavy traffic diffusion approximation. Both continuous-time and discrete-time models are considered. The discrete-time model includes that studied by A. M. Viterbi and subsequently generalized by M. Neuts. The Pollaczek-Khinchine formula for the mean amount of work in an M/G/1 queue is retrieved as a limiting case.