A unifying product form framework for queueing models
The discovery of queueing systems with product form stationary distribution is probably one of the fundamental contributions in queueing theory. In fact, the work on product form distribution for Jackson networks was considered among the 10 most influential titles in INFORMS Management Science journal. 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 such systems tohave 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 includes applications that are not covered by the other. Anatural question that arises is whether the two approaches can be generalized while preserving product-form. In this talk, we will see that the answer tothis question is in the affirmative. I will introduce a token based centralqueue framework that not only offers a unifying product form analysis for thetwo models, but also covers applications that are not subsumed by them. In thistalk, we will also see an application of this new framework to redundancy basedqueueing systems that have become increasingly popular in recent times. Thistalk is based on a joint work with U. Ayesta and Maaike Verloop from theUniversity of Toulouse and J.L. Dorsman from the University of Amsterdam andwas recently accepted for publication in INFORMS Operations Research.
Tejas is currently an Assistant Professor at the department of Electricalengineering at IIT Dharwad from January 2020. Prior to this, he was a C.V.Raman postdoc in the ECE department at IISc. He has also been a short-termpostdoc at the University of Antwerp in Belgium, a full time postdoc from 2016to 2018 at LAAS, CNRS Toulouse in France and a visiting fellow at TIFR, Mumbai.He received his M.Tech and Ph.D (dual degree) from IIT Bombay in 2016. Hisresearch interests are in Stochastic processes, Queueing theory, Game theory,Markov decision processes and Reinforcement learning.