A simple algorithm for reliability evaluation in dynamic networks with stochastic transit times

Abstract

In a network flow, transit time of an arc is the time span that a unit of flow takes to travel through this arc. In most real-world systems, such as road traffic, communication networks, pipeline systems, transit time of an arc is not constant and may take a value, randomly, from among several possible values. In such systems, reliability is the main concern. Given a demand d, time threshold T, and budget B, we define the reliability as the probability that d units of flow can be sent from the source to the sink under time horizon T and budget B. In this paper, we propose a simple algorithm to evaluate the reliability of networks in which the transition times are stochastic variable.

Minimum parametric flow over time

“…Moreover, in many applications of graph algorithms, including communication networks, graphics, assembly planning, and scheduling, graphs are subject to discrete changes, such as additions or deletions of arcs or nodes. In the last decade there has been a growing interest for such dynamically changing graphs, and a whole body of algorithms and data structures for dynamic graphs has been discovered: Fathabadi et al (2015), He et al (2015), Nassir et al (2014), Rashidi and Tsang (2015) or . Further on, the next section presents some basic discrete-time dynamic networks terminology and notations and Section 3 introduces the parametric minimum flow over time problem.…”