The talk introduces two new classes of ultra-sharp bounds in queueing systems. The first is specific to the G/G/1 queue, with possibly correlated inter-arrivals; the main result is an exact expression for the distribution of the delay in terms of a series, whose terms are subject to elementary integration. Remarkably, the first few terms are sufficient to render ultra-sharp bounds improving upon state-of-the-art bounds by orders of magnitude. The second new class of bounds is specific to a tandem queueing network with general (i.e., not necessarily Poisson) arrivals and light-tailed service times. Besides showing for the first time that the end-to-end delay distribution is subject to a polynomial-exponential structure, explicit bounds computed in some special cases are shown to improve upon state-of-the-art results by many orders of magnitude.
Florin Ciucu is a Professor in the CS Department at the University of Warwick. His research interests are stochastic analysis of communication networks and non-asymptotic analysis of stochastic bandits. He co-chaired ACM Sigmetrics 2024 and served on the Technical Program Committees of several other top conferences; currently he is on the Editorial Boards of the Performance Evaluation Journal and IEEE Transactions on Networking. Florin is a recipient of the ACM Sigmetrics 2005 Best Student Paper Award and IFIP Performance 2014 Best Paper Award.