Abstract
This talk features networks of coupled processor sharing queues in the Euclidean space, where customers arrive according to independent Poisson point processes at every queue, are served, and then leave the network. The coupling is through service rates. In any given queue, this rate is inversely proportional the interference seen by this queue, which is determined by the load in neighboring queues, attenuated by some distance-based path-loss function. The main focus is on the infinite grid network and translation invariant path-loss case.
The stability condition is identified. The minimal stationary regime is built using coupling from the past techniques. The mean queue size of this minimal stationary regime is determined in closed form using the rate conservation principle of Palm calculus. When the stability condition holds, for all bounded initial conditions, there is weak convergence to this minimal stationary regime; however, there exist translation invariant initial conditions for which all queue sizes converge to infinity.
Joint work with S. Foss (Edinburgh) and A. Sankararaman (Austin).
Bio:
F. Baccelli is Simons Math+X Chair in Mathematics and ECE at UT Austin. His research directions are at the interface between Applied Mathematics and Communications. He is co-author of research monographs on point processes and queues, max plus algebras and network dynamics, stationary queuing networks, and stochastic geometry and wireless networks. He received the France Télécom Prize of the French Academy of Sciences in 2002, the ACM Sigmetrics Achievement Award in 2014, the 2014 Stephen O. Rice Prize, and the 2014 Leonard G. Abraham Prize Awards of the IEEE Communications Theory Society. He is a member of the French Academy of Sciences.