A large-deviations analysis of the GI/GI/1 SRPT queue

We consider a GI/GI/1 queue with the shortest remaining processing time discipline (SRPT) and light-tailed service times. Our interest is focused on the tail behavior of the sojourn-time distribution. We obtain a general expression for its large-deviations decay rate. The value of this decay rate critically depends on whether there is mass in the endpoint of the service-time distribution or not. An auxiliary priority queue, for which we obtain some new results, plays an important role in our analysis. We apply our SRPT-results to compare SRPT with FIFO from a large-deviations point of view.Comment: 22 page

Fractal time random walk and subrecoil laser cooling considered as renewal processes with infinite mean waiting times

There exist important stochastic physical processes involving infinite mean waiting times. The mean divergence has dramatic consequences on the process dynamics. Fractal time random walks, a diffusion process, and subrecoil laser cooling, a concentration process, are two such processes that look qualitatively dissimilar. Yet, a unifying treatment of these two processes, which is the topic of this pedagogic paper, can be developed by combining renewal theory with the generalized central limit theorem. This approach enables to derive without technical difficulties the key physical properties and it emphasizes the role of the behaviour of sums with infinite means.Comment: 9 pages, 7 figures, to appear in the Proceedings of Cargese Summer School on "Chaotic dynamics and transport in classical and quantum systems

Queueing Systems with Heavy Tails

VI+227hlm.;24c