Event
Advanced Networks Colloquium: Ioannis Lambadaris, "Stability Analysis and Delay Optimality in MQMS"
Friday, August 23, 2013
2:00 p.m.
2168 A.V. Williams Bldg.
Prakash Narayan
prakash@umd.edu
The Advanced Networks Colloquium
Stability Analysis and Delay Optimality in Multi-Queue Multi-Server (MQMS) Systems
Ioannis Lambadaris
Department of Systems and Computer Engineering
Carleton University
Ottawa, Canada
Abstract
The first part of the talk presents an explicit characterization of the stability region of stationary Multi-Queue Multi-Server (MQMS) queueing systems by means of a finite set of linear inequalities. More specifically, we compute the coefficients of the linear inequalities describing the facet-defining hyperplanes of the stability region polytope. Such a characterization is useful for performance evaluation of certain scheduling algorithms such as Maximum Weight (MW) policy. Our results can be used for studying the asymptotic behavior of the MW policy and computing bounds for the average queueing delay, as well as limiting moments of the queue sizes in heavy traffic regime.
In the second part of the talk we consider symmetric MQMS systems. We study the problem of assigning K identical servers to a set of N parallel queues in a time-slotted system. The connectivity of each queue to each server is assumed to be i.i.d Bernoulli process; each server can serve at most one queue and each queue can be served by at most one server during each time slot. It has been previously proven that Maximum Weighted Matching (MWM) is a throughput optimal server assignment policy for such a system. We prove that for a symmetric system with i.i.d. Bernoulli arrivals and connectivities, MWM minimizes, in stochastic ordering sense, a range of cost functions of the queue lengths such as total queue occupancy (which implies minimization of average queueing delay).
Biography
Ioannis Lambadaris has a M.Sc. degree in Engineering from Brown University, Providence, RI (1984) and a Ph.D in Electrical Engineering from the University of Maryland, College Park, MD (1991). During his studies in Maryland he was with the Systems Research Center (currently Institute for Systems Research). He has been a faculty member of the department of Systems and Computer Engineering at Carleton University, Ottawa, Canada since 1991. At Carleton he received the Ontario Premiers Research Excellence Award (2000), and the Carleton University Research Excellence Award (2000-2001). His research interests lie in the area of applied stochastic processes, queueing theory and their application to performance analysis of communication systems
