Bound analysis of closed queueing networks with workload burstiness

Abstract

Burstiness and temporal dependence in service processes are often found in multi-tier architectures and storage devices and must be captured accurately in capacity planning models as these features are responsible of significant performance degradations. However, existing models and approximations for networks of first-come first-served (FCFS) queues with general independent (GI) service are unable to predict performance of systems with temporal dependence in workloads. To overcome this difficulty, we define and study a class of closed queueing networks where service times are represented by Markovian Arrival Processes (MAPs), a class of point processes that can model general distributions, but also temporal dependent features such as burstiness in service times. We call these models MAP queueing networks. We introduce provable upper and lower bounds for arbitrary performance indexes (e.g., throughput, response time, utilization) that we call Linear Reduction (LR) bounds. Numerical experiments indicate that LR bounds achieve a mean accuracy error of 2 percent. The result promotes LR bounds as a versatile and reliable bounding methodology of the performance of modern computer systems.