Analysis of multi-media traffic queues with finite buffer and overload control. I. Algorithm

A general solution methodology is provided for analysis of multi-media traffic queues. An efficient algorithm for a class of quasi-birth-death (QBD) processes, which are very versatile in formulating multi-media traffic queues, is described. Based on the Markov chain reduction principle, the algorithm exploits structural property to overcome the difficulties caused by the extraordinarily large state space of the model. It is stable, accurate and efficient for handling very large-scale problems. Applications of the algorithm to analysis of multi-media traffic queues with finite buffer and multilevel overload controls are emphasized. Two continuous time QBD models are devised for the applications. Model 1 extends the finite M/M/1 queue with Markov-modulated Poisson arrivals. Model II is the Markovian version of the continuous fluid-flow model. Both queue distribution and packet loss rate are measured. The effectiveness of the algorithm is demonstrated through analysis of various design and control issues in multi-media traffic integrations