Traditional queueing theory deals mainly with one-dimensional stochastic processes like queue or orbit length, virtual or actual waiting or sojourn time, busy period, etc. Discrete or continuous time one-dimensional Markov chains and renewal theory are the main tools for their investigation. However, the increasing complexity of the modern telecommunication networks (heterogeneous bursty correl...

My main research interests lie in the applications of probability theory, with a particular focus on operations research, queueing theory, approximations and control of stochastic processes and mathematical finance. My other research interests include optimization, simulation, combinatorics and graph theory. Below, I first describe my past work and then briefly outline some directions of future...

Much that is essential in modern life would not be possible without queueing theory. All communication systems depend on the theory including the Internet. In fact, the theory was developed at the time that telephone systems were growing and requiring more and more sophistication to manage their complexity. Much of the theory was developed by Agner Krarup Erlang (1878-1929). He worked for Copen...

We propose an alternative approach for studying queues based on robust optimization. We model the uncertainty in the arrivals and services via polyhedral uncertainty sets which are inspired from the limit laws of probability. Using the generalized central limit theorem, this framework allows to model heavy-tailed behavior characterized by bursts of rapidly occurring arrivals and long service ti...

2 This book is dedicated to my wife without whom this work could have been finished much earlier. • If anything can go wrong, it will. • If you change queues, the one you have left will start to move faster than the one you are in now. • Your queue always goes the slowest. • Whatever queue you join, no matter how short it looks, it will always take the longest for you to get served.