Travel and Sojourn Times in Stochastic Networks

Using Stochastic-Dominance Relationships for Bounding Travel Times in Stochastic Networks

We consider stochastic networks in which link travel times are dependent, discrete random variables. We present methods for computing bounds on path travel times using stochastic dominance relationships among link travel times, and discuss techniques for controlling tightness of the bounds. We apply these methods to shortest-path problems, show that the proposed algorithm can provide bounds on ...

Stochastic Vehicle Routing with Random Travel Times

We consider stochastic vehicle routing problems on a network with random travel and service times. A fleet of one or more vehicles is available to be routed through the network to service each node. Two versions of the model are developed based on alternative objective functions. We provide bounds on optimal objective function values and conditions under which reductions to simpler models can b...

Quantiles of sojourn times

Fast response times and the satisfaction of response time quantile targets are important performance criteria for almost all transaction processing and computer-communication systems. However, they tend to be difficult to obtain in stochastic models, even when the mean value of the response time has a relatively simple mathematical expression. Expressions have been obtained for the Laplace tran...

Sojourn Times of Brownian Sheet

In a canonical way, one can think of B as “two-parameter Brownian motion”. In this article, we address the following question: “Given a measurable function υ : R → R+, what can be said about the distribution of ∫ [0,1]2 υ(Bs) ds?” The one-parameter variant of this question is both easy-to-state and well understood. Indeed, if b designates standard Brownian motion, the Laplace transform of ∫ 1 0...

The Vehicle Routing Problem with Stochastic and Correlated Travel Times