Accuracy versus efficiency of hyper-exponential approximations of the response time distribution of MMPP/M/1 queues

Abstract

The Markov-Modulated Poisson Process (MMPP) has been shown to well describe the flow of incoming traffic in networked systems, such as the Grid and the WWW. This makes the MMPP/M/1 queue a valuable instrument to evaluate and predict the service level of networked servers. In a recent work, we have provided an approximate solution for the response time distribution of the MMPP/M/1 queue, based on a weighted superposition of M/M/1 queues (i.e. a hyper-exponential process). In this article, we address the tradeoff between the accuracy of this approximation and its computational cost. By jointly considering both accuracy and cost, we identify the scenarios where such approximate solution could be effectively used in support of network servers (dynamic) configuration and evaluation strategies aimed at ensuring agreed dependability levels in case of, e.g. request redirection due to faults. Finally, the effectiveness of the proposed approximate solution method is evaluated for a real-world case study relying on a trace-based traffic characterisation of a Grid server.

Keywords:

• performability evaluation
• Markov-modulated Poisson process
• queuing theory
• hyper-exponential approximation

Notes