On probabilistic model of the statistical multiplexing and queueing buffer in ATM switch system

Broadband integrated services digital network (B-ISDN) is a telecommunications technology that is designed to integrate all kinds of services (e.g., voice, data, image and video) into a universal all-purpose digital network. Asynchronous transfer mode (ATM) is a packet-oriented switching and multiplexing technique which is believed to have the technical capability to handle many types of services encompassed by B-ISDNs. At an ATM switch, ATM cells coming from heterogeneous sources are multiplexed together and stored temporarily in the multiplexer buffer before they are transmitted to their designated output ports through the switching fabric. Our works are interested in modeling performance measures such as the throughput of the ATM switch, buffer overflow probability, cell loss ratio, average delay of ATM cells, variation in the delay, etc. Although the performance analysis of ATM switches depends significantly on the switch architectures and could be very complex, the modeling and evaluation of the statistical multiplexer and multiplexer buffers in an ATM switch system is useful for understanding whether the switching system is practical for some applications, and if so, what multiplexing efficiency and cell-loss regimes may be expected in such systems. We will focus on the modeling of the statistical multiplexer and multiplexer buffer overflow probability as an approach to probabilistic model throughout this paper.