Algorithms for the quickest path problem and the reliable quickest path problem

Abstract

The quickest path problem consists of finding a path in a directed network to transmit a given amount of items from an origin node to a destination node with minimal transmission time, when the transmission time depends on both the traversal times of the arcs, or lead time, and the rates of flow along arcs, or capacity. In telecommunications networks, arcs often also have an associated operational probability of the transmission being fault free. The reliability of a path is defined as the product of the operational probabilities of its arcs. The reliability as well as the transmission time are of interest. In this paper, algorithms are proposed to solve the quickest path problem as well as the problem of identifying the quickest path whose reliability is not lower than a given threshold. The algorithms rely on both the properties of a network which turns the computation of a quickest path into the computation of a shortest path and the fact that the reliability of a path can be evaluated through the reliability of the ordered sequence of its arcs. Other constraints on resources consumed, on the number of arcs of the path, etc. can also be managed with the same algorithms.

An efficient algorithm for the multi-state two separate minimal paths reliability problem with budget constraint

“…However, in an optical network, there are some time thresholds and when the transmission time exceeds the threshold, the transmission will be canceled, and so the transmission time is an important issue to be considered. Attending to transmission time, several studies have been made in terms of minimal paths Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ress according to the quickest path problem [23][24][25][26][27][33][34][35][36][37][38]. Quickest path problem is a version of shortest path problem in a network flow with arcs having two attributes, capacity and lead time [23][24][25][26][27][33][34][35][36][37][38].Although the inception of the problem may be attributed to the work by Moore [23], however, the notion of quickest path problem in our context has been introduced by Chen and Chin [33].…”

“…Attending to transmission time, several studies have been made in terms of minimal paths Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ress according to the quickest path problem [23][24][25][26][27][33][34][35][36][37][38]. Quickest path problem is a version of shortest path problem in a network flow with arcs having two attributes, capacity and lead time [23][24][25][26][27][33][34][35][36][37][38].Although the inception of the problem may be attributed to the work by Moore [23], however, the notion of quickest path problem in our context has been introduced by Chen and Chin [33]. The problem is finding a path to transmit d units of flow from a source node to a sink node within a minimal transmission time [23][24][25][26][27][33][34][35][36][37][38].…”

“…Quickest path problem is a version of shortest path problem in a network flow with arcs having two attributes, capacity and lead time [23][24][25][26][27][33][34][35][36][37][38].Although the inception of the problem may be attributed to the work by Moore [23], however, the notion of quickest path problem in our context has been introduced by Chen and Chin [33]. The problem is finding a path to transmit d units of flow from a source node to a sink node within a minimal transmission time [23][24][25][26][27][33][34][35][36][37][38]. Mentioning and rectifying two existing disadvantages of the previous works, Park et al [34] proposed a labelsetting algorithm to recognize the quickest path.…”

The energy-constrained quickest path problem

“…They are based on solving a shortest path problem in an enlarged network [2,5], solving a sequence of shortest path problems with respect to the delay time on networks where the minimum capacity increases [10,11,16,19], using a label-setting algorithm [12] or taking into account that a quickest path is a supported efficient solution of the aforementioned bi-objective problem [20].…”

“…The problem of determining the transmission process when data are transmitted in batches of variable size but with required limits has been considered in [1]. The problem of computing the quickest path whose reliability is not lower than a given threshold has been analyzed in [2]. Pascoal et al [14] provide a survey on the subject.…”