Insensitivity of the Mean Field of Loss Systems Under Randomized SQ(d) Algorithms

Speaker: 

Ravi Mazumdar

Affiliation: 

University of Waterloo
Dept. of Electrical and Computer Engineering
Waterloo, ON N2L 3G1
Canada

Time: 

Tuesday, 2 May 2017, 16:00 to 17:00

Venue: 

Organisers: 

In many applications such as cloud computing, managing server farm resources etc. an incoming task or job has to be matched with an appropriate server in order to minimise the latency or blocking associated with the processing. Ideally the best choice would be to match a job to the fastest available server. However when there are thousands of servers requiring the information on all server tasks is an overkill.

Pioneered in the 1990's the idea of randomised sampling of a few servers was proposed by Vvedenskaya and Dobrushin in Russia and Mitzmenmacher in the US and popularised as the "power of two" schemes which basically means that sampling two servers randomly and sending the job to the "better" server (i.e. with the shortest queue, or most resources) provides most of the benets of sampling all the servers.

In the talk I will discuss multi-server loss models under power-of-d routing scheme when service time distributions are general with nite mean. Previous works on these models assume that the service times are exponentially distributed and insensitivity was suggested through simulations. Showing insensitivity to service time distributions has remained an open problem. The diculty is that for general service times the underlying Markovian model is more complex. Using a measure valued process approach we rst derive the mean eld equation (MFE) for the empirical measure. The MFE is now characterized by a pde whose stationary point coincides with the xed point in the case with exponential service times. This establishes the insensitivity of the xed point. The techniques developed in this paper are applicable to study mean eld limits for Markov processes on general state spaces and insensitivity properties of other queueing models.

Bio: 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. He is a D.J. Gandhi Distinguished Visiting Professor at the Indian Institute of Technology, Bombay. He is a Fellow of the IEEE and the Royal Statistical Society. He is a recipient of the Best Paper Awards at INFOCOM 2006, the International Teletrac Congress 2015, Performance 2015, 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.