Network Reconfiguration with Orientation-Dependent Transit Times

Abstract

Motivated by applications in evacuation planning, we consider a problem of optimizing flow with arc reversals in which the transit time depends on the orientation of the arc. In the considered problems, the transit time on an arc may change when it is reversed, contrary to the problems considered in the existing literature. Extending the existing idea of auxiliary network construction to allow asymmetric transit time on arcs, we present strongly polynomial time algorithms for solving single-source-single-sink maximum dynamic contraflow problem and quickest contraflow problem. The results are substantiated by a computational experiment in a Kathmandu road network. An algorithm to solve the corresponding earliest arrival contraflow problem with a pseudo-polynomial-time complexity is also presented. The partial contraflow approach for the corresponding problems has also been discussed.

Lexicographic Maximum Flow Allowing Intermediate Storage

“…The unused arc capacities, towards the source are used by reversing the direction of the arcs towards the sink as in [22,20,3,24], where authors have considered the symmetric travel time along the arcs. Here, we assume that, the anti-parallel arcs have unequal travel time and in this work we consider the travel time along the direction of the arcs towards which it is reversed, similar to [17], as shown in Figure 2. The components along the arcs represent their capacity and required travel time.…”

“…But, the travel times may not be symmetric always. Recently, Nath et al [17] introduced arc reversal approach with asymmetric travel time along the anti-parallel arcs and considered the time along the direction of the arc towards which it is reversed. With this consideration they have introduced the maximum dynamic and quickest flow problems and presented polynomial time algorithms for the solution.…”

Maximum Multicommodity Flow with Intermediate Storage

“…For a network with asymmetric transit times, if the transit times of arcs in an auxiliary network are taken as the orientation of the arcs, then it is known as orientation-dependent transit time. Nath et al [24] considered the orientation-dependent asymmetric transit times of reversed lanes in general form and presented strongly polynomial time algorithms to solve the single source single sink maximum dynamic and quickest contraflow problems. Here, we discuss about the multicommodity contraflow problem with intermediate storage by taking orientation-dependent transit times.…”

Dynamic Multicommodity Contraflow Problem with Asymmetric Transit Times

“…(i) The capacities of auxiliary arcs is the sum of capacities of arcs e and e r , i.e., u a = u e + u e r (ii) The transit time of auxiliary arc τ a is taken as transit time of nonreversed arcs as shown in Figures 1(b) and 1(c) (iii) In the case of a single direction for each e ∈ A, there exist e r ∈ A and τ a = τ e = τ e r for contraflow configuration By modifying the algorithm of [13], Nath et al [20] solved the dynamic contraflow problems such that the reversals use asymmetric transit times that should be taken by unreserved ones. Recently, Gupta et al [21] extended the approach of Nath et al [20] in case of lexicographic flow and earliest arrival transshipment problems and presented algorithms to solve them. The same authors in [22] also introduced this approach in the case of a lossy network with τ e ≠ τ e r on arcs and provided the algorithms to solve the problem in the discrete-and continuous-time setting for single-commmodity.…”