Decomposition of network of queues with self-similar traffic

Abstract

Jackson's network of queues model greatly simplifies the performance analysis of telecommunication networks with Poisson traffic arrivals and exponential service times. It reduces the analysis of a network into the analysis of individual communication links, each of which may be modeled as an M/M/m queue. Motivated by the growing significance of self-similar traffic in modeling broadband network traffic, we propose a new network of queues model for telecommunication networks. Our model resembles Jackson's model except that the arrival is self-similar and the service time is deterministic. It captures the characteristics of modern high speed cell-based networks. We hypothesize a result analogous to Jackson's Theorem, that each mode of this network model behaves as a G/D/1 queue with self-similar arrival. Based on this hypothesis, many network-wide performance measures, such as the end-to-end delay, can be evaluated in a simple fashion. Our hypothesis is strongly supported by three facts, namely, the sum of independent self-similar processes, the random splitting of self-similar processes, and the output process of a deterministic service time queue with self-similar input are all self-similar.