Queueing analysis of an integrated services TDM system using a matrix-analytic method

A matrix-analytic method is used to analyze the queueing behavior of small time division multiplexing (TDM) integrated services systems. Such systems have priority services for time-critical traffics in which adjacent packets exhibit a strong interdependency. The TDM frame with a capacity of M packets is used to transmit the high-priority packets at every time step. Any unused capacity is utilized to transmit low-priority packets. The system can be modeled as a discrete-time system with a fluctuating number of servers for the low-priority packets. Because the number of servers is small and adjacent packets are dependent, the birth-and-death analysis is not appropriate. An algorithm, based on a modification of Neuts´ method, is used to determine the boundary points required in the queuing analysis. Numerical results for two integrated services systems, each with different characteristics, are presented to demonstrate the feasibility of the analysis method and the computational algorithm