Many cloud systems provide dedicated resources for clients to use. When resources are finite, not all requests can be admitted and this leads to blocking. Systems like AZURE guarantee an admitted job a certain amount of resources VM (Virtual Machines) that abstract processor speed, memory, etc. This results in an Erlang type of loss system. In recent work we studied the properties of using randomized routing where the jobs are routed to least busy resources randomly chosen amongst the many resources. In particular using mean field techniques we established that such schemes are very close to the optimal blocking that can be obtained from such systems. This analysis assumed that the holding times were i.i.d exponential. Moreover we showed that the stationary point of the mean field satisfies a balance condition that suggests insensitivity that was confirmed through simulation.The case of general i.i.d service times remained open although the possibility of such a result holding was suggested in work by Bramson. In this talk I will show that the result holds when the service times are generally distributed. We establish the result by deriving the mean field equations assuming Coxian distributions that are known to be dense in the class of general distributions with rational Laplace transforms. Indeed we show that the equilibrium points of the mean field equations are identical (even though the transient solutions differ) thus establishing insensitivity of the stationary distribution corresponding to the GAS of the mean field. We can then invoke a result on the continuity of queueing models with respect to the service process to complete the proof. Joint work with Thirupathian Vasantam (Waterloo) and Arpan Mukhopadhyay (INRIA, Paris).
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 Performance 2015, ITC 27 (2015); and INFOCOM 2006 Best Paper Awards and was runner-up for the Best Paper Award at INFOCOM 1998. His research interests are in stochastic modelling and analysis applied to complex networks and systems and in issues of network science.