Title: Stationary Performance of Continuous Polling Models and Risk Sensitive Control of Delay Tolerant Networks
Speaker: Dr. Veeraruna Kavitha
Time and Date: 11.30am, Wed. 16/11/11
Place: Room 217, Mechanical Engg. Building
Abstract:
Polling systems are the queueing systems in which a server attends to more than one queue while taking finite amount of time to walk/rest in between the queues. Not much theory is available for calculating the stationary workload of polling systems with arrivals in a continuum, basically a system with continuum of (service) awaiting locations. We obtain the stationary performance for many
varieties of continuous polling systems, via a discretization approach, utilising the known Pseudo conservation laws of the corresponding discrete polling systems. Along with this, we obtain an integral representation for the unfinished workload, which is basically the generalisation of the well known Wald's lemma to the case with continuum of arrivals. Our results rely heavily on fixed point analysis of infinite dimensional operators.
Users demanding data transfers, can tolerate delays and this fact is utilised to design cost effective and simple wireless networks, called Delay tolerant Networks (DTNs). In one such example, a ferry (a moving base station) moves in a predetermined path continually to facilitate communication, via a wireless link, in a Local Area Network which is otherwise sparsely connected. We obtain the stationary performance of such a ferry assisted wireless LAN using the theory of continuous polling systems derived above.
In another example of DTNs, the message is spread across all the contacted (relay) users and it spreads like epidemics till it reaches the destination. The control of such dynamics has thus gained a central role in all of these areas. The classical objective function in DTNs, i.e., the successful delivery probability of a message within a given deadline, takes often the form of the expectation of the exponent of some integral cost. So far, models involving such costs have been solved by interchanging the order of expectation and the exponential function.
While reducing the problem to a standard optimal control problem, this interchange is only tight in the mean field limit obtained as the population tends to infinity. We identify a general framework from optimal control in finance, known as risk sensitive control, which let us handle the original (multiplicative) cost and obtain solutions to several novel control problems in DTNs. New optimal control problems which consider the effect of wireless propagation path loss factor and the power constraints at the source and or the destination are proposed for DTNs. The possibility of non-threshold type optimal policies is established for some of the control problems.
Speaker's brief Bio:
Dr Kavitha Veeraruna obtained her BE in Electronics from UVCE, Bangalore in 1994. She obtained her MSc(Engg) and PhD from IISc Bangalore in 2002 and 2007 respectively. Dr Kavitha was a NBHM postdoctoral fellow at TIFR, Bangalore from 2007 to 2008. From 2008, Dr Kavitha has been with MAESTRO, INRIA, Sophia Antipolis and LIA, University of Avignon, France. Her research interests include Performance analysis and modeling, Optimal control, Queuing Theory, Game theory, Wireless communications and Networking.