A unifying product form framework for queueing models

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The discovery of queueing systems with product form stationary distribution is probably one of the fundamental contributions in queueing theory. Recent years have witnessed a surge of interest in parallel server models with multi-class jobs. In two recent studies by Visschers et al. (Multi-type job and server model, Queueing Systems 2012) and Krzesinski (Order Independent queues, Queueing Networks, 2011), sufficient conditions have been obtained for a multi-server system to have a product form. These two results differ in their Markovian descriptor for the underlying system and have led to two separate streams of research, where each approach covers applications that are not covered by the other. A natural question that arises is whether the two approaches can be generalized while preserving product-form. In this talk, we will see that the answer to this question is in the affirmative. I will introduce a token based central queue framework that not only offers a unifying product form analysis for the above two models, but also covers applications that are not subsumed by them. We will also see an application of this new framework to redundancy based queueing systems that have become increasingly popular in recent times. This talk is based on a joint work with U. Ayesta and Maaike Verloop from the University of Toulouse and J.L. Dorsman from the University of Amsterdam.

Tejas Bodas

Tejas is currently a Raman postdoc in the ECE department. Prior to this, he was a short-term postdoc at the University of Antwerp in Belgium, a postdoc at LAAS, CNRS Toulouse in France and a visiting fellow at TIFR, Mumbai. He received his M.Tech and Ph.D (dual degree) in Electrical Engineering from IIT Bombay in 2016.