Parallel queueing networks with Markov-modulated service speeds in heavy traffic

Authors:
Jan-Pieter Dorsman;Maria Vlasiou;Bert Zwart
Affiliations:
Eindhoven University of Technology, Centrum Wiskunde & Informatica;Eindhoven University of Technology, Centrum Wiskunde & Informatica;Centrum Wiskunde & Informatica, VU University Amsterdam, Eindhoven University of Technology, Georgia Institute of Technology
Venue:
ACM SIGMETRICS Performance Evaluation Review - Special issue on the 31st international symposium on computer performance, modeling, measurements and evaluation (IFIPWG 7.3 Performance 2013)
Year:
2013

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Abstract

We study a network of parallel single-server queues, where the service speeds are governed by a continuous-time Markov chain. This generic model finds applications in many areas such as communication systems, computer systems and manufacturing systems. We obtain heavy-traffic approximations for the joint workload, delay and queue length processes by combining a functional central limit theorem approach with matrix-analytic methods. In addition, we numerically compute the joint distributions by viewing the limit processes as semi-martingale reflected Brownian motions.