Versatile models of systems using map queueing networks

Abstract

Analyzing the performance impact of temporal dependent workloads on hardware and software systems is a challenging task that yet must be addressed to enhance performance of real applications. For instance, existing matrixanalytic queueing models can capture temporal dependence only in systems that can be described by one or two queues, but the capacity planning of real multi-tier architectures requires larger models with arbitrary topology.To address the lack of a proper modeling technique for systems subject to temporal dependent workloads, we introduce a class of closed queueing networks where service times can have non-exponential distribution and accurately approximate temporal dependent features such as short or long range dependence. We describe these service processes using Markovian Arrival Processes (MAPs), which include the popular Markov-Modulated Poisson Processes (MMPPs) as special cases. Using a linear programming approach, we obtain for MAP closed networks tight upper and lower bounds for arbitrary performance indexes (e.g., throughput, response time, utilization). Numerical experiments indicate that our bounds achieve a mean accuracy error of 2% and promote our modeling approach for the accurate performance analysis of real multi-tier architectures.