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Processor sharing models occur in a wide variety of situations for example in models of internet bottlenecks. They are good models for bandwidth sharing as well as being solutions to NUM for logarithmic utilities. In addition they possess the desirable stochastic property of the stationary distribution being insensitive to the service time distribution. In this talk I will discuss new advances in understanding and characterizing the behavior of randomized routing to PS servers that are heterogeneous in terms of their server speeds.
We will rst discuss the so-called Power-of-two rule in the homogeneous case of identical servers where routing to the least occupied server amongst two randomly chosen servers results in a very low server occupancy and a so-called propagation of chaos or asymptotic independence. There were no known characterizations about the heterogeneous case. In the heterogeneous case we will see that the stability region for randomized routing is strictly included in the maximal stability region that can be achieved by state independent routing. Therefore the average sojourn of tasks can be longer in randomized routing in heterogeneous systems. When the system is stable we completely characterize the steady-state behavior of the server occupancies and show that it exhibits super-exponential decay and asymptotic independence among servers. To overcome the reduction in the stability region we show that a combination of state independent routing (biased sampling) to a server class combined with JSQ within the class recovers the stability region as well as the benets of small server occupancies.
The techniques are based on a mean eld analysis and an ansatz based on propagation of chaos that then establishes the asymptotic independence between servers (joint work with Arpan Mukhopadhyay (Waterloo).
Biography: The speaker was educated at the Indian Institute of Technology, Bombay (B.Tech, 1977), Imperial College, London (MSc, DIC, 1978) and obtained his PhD under A. V. Balakrishnan at UCLA in 1983. He is currently a University Research Chair Professor in the Dept. of ECE at the University of Waterloo, Ont., Canada where he has been since September 2004. Prior to this he was Professor of ECE at Purdue University, West Lafayette, USA. Since 2012 he is a D.J. Gandhi Distinguished Visiting Professor at the Indian Institute of Technology, Bombay, India. He is a Fellow of the IEEE and the Royal Statistical Society. He is a recipient of the INFOCOM 2006 Best Paper Award and was runner-up for the Best Paper Award at INFOCOM 1998. His research interests are in modeling, control, and performance analysis of both wireline and wireless networks, and in applied probability and stochastic analysis with applications to queueing, ltering, and optimization.
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