Approximate Analytical Models for Networked Servers Subject to MMPP Arrival Processes

Abstract

Input characterization to describe the flow of incoming traffic in network systems, such as the GRID and the WWW, is often performed by using Markov modulated Poisson processes (MMPP). Therefore, to enact capacity planning and quality-of-service (QoS) oriented design, the model of the hosts that receive the incoming traffic is often described as a MMPP/M/1 queue. The drawback of this model is that no closed form for its solution has been derived. This means that evaluating even the simplest output statistics of the model, such as the average response times of the queue, is a computationally intensive task and its usage in the above contexts is often unadvisable. In this paper we discuss the possibility to approximate the behavior of a MMPP/M/1 queue with a computational effective analytical approximation, thus saving the large amount of calculations required to evaluate the same data by other means. The employed method consists in approximating the MMPP/M/1 queue as a weighted superposition of different M/M/1 queues. The analysis is validated by comparing the results of a discrete event simulator with those obtained from the proposed approximations, in the context of a real case study involving a GRID networked server.