A statistical multiplexer for integrated service in the customer-premise equipment is analyzed. The integrated service is generally assumed to contain both wideband (WB) and narrowband (NB) services. The arrival process for the former is modeled as a discrete birth-death Markov chain and that for the latter is modeled as an independent Poisson. Each customer of WB arrival requires more than one channels (servers) for service, while each customer of NB arrival requires a single channel, and the service times of channels are the same and constant. These two types of customers are assumed to be delayed in a finite waiting room if blocked. Also, a cutoff parameter specifying the maximum number of WB customers that can receive service in one slot is provided for protection of NB. The performance measures include queue length distribution, blocking probability, and mean waiting time. Simulation results are also provided to help verify the validity of the analysis.
Computer Networks and ISDN Systems / Volume 25, Issue 2, 17 August 1992, Pages 191–201, doi:10.1016/0169-7552(92)90070-7