An Isaac Newton Institute Workshop

First-Passage and Extreme Value Problems in Random Processes

Exact solutions for first-passage and related problems in certain classes of queueing system

29th June 2006

Author: Kearney, M (University of Surrey)

Abstract

This talk will examine discrete and continuous time queueing systems in the context of recognising the so-called busy period as the first-passage time of a random walk process. As well as identifying the queue duration (busy-period) distribution, consideration is also given to the distribution of the maximum (extreme) queue length during a busy period and, much harder, the distribution of the total waiting time (area under the curve) during a busy period. Physical examples of interest include traffic jams, Abelian sandpile (avalanche) models in the compact directed percolation universality class, and the statistics of lattice polygon models. Throughout, the emphasis is on providing exact solutions.