Versatile models of systems using map queueing networks

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 matrix-analytic 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.