Abstract
The abstract flow model deals with the flow paths (routes) that satisfy the switching property. Contraflow is a widely accepted solution approach that increases the flow and decreases the evacuation time making the traffic smooth during evacuation by reversing the required road directions from the risk areas to the safe places. In this paper, we integrate the concepts of abstract flow and contraflow, give mathematical formulations of these models and present efficient algorithms for solving the abstract contraflow problems. The efficient solution procedures are presented for maximum dynamic, lexicographically maximum and earliest arrival abstract contraflow problems. This approach maximizes the flow value in given time and seeks to eliminate the crossing conflicts.
Highlights
Due to different disasters, challenges of emergency management have been increased day by day
Based on the earlier results of earliest arrival contraflow problem with arc reversals in (Pyakurel & Dhamala, 2015) and earliest arrival abstract flow (EAAF) in (Kappmeier, 2015), we introduce earliest arrival abstract contraflow (EAACF) problem and propose Algorithm 4 to solve it. (Minieka, 1973) proved that using the successive shortest path algorithm in the original network and sending flow along the generalized temporally repeated paths leads to an earliest arrival flow
The EAACF values at these times are 12 and 25, respectively. We studied both abstract flow and contraflow models from litrature
Summary
Challenges of emergency management have been increased day by day. Authors in (Dhamala & Pyakurel, 2013; Dhungana et al, 2015; Pyakurel & Dhamala, 2015; Pyakurel & Dhamala, 2017a; Pyakurel & Dhamala, 2016) introduced the earliest arrival, quickest transshipment and lex-maximum dynamic contraflow problems in both discrete and continuous time settings The former is solved in strongly polynomial and pseudo-polynomial time on two terminal series-parallel and general networks, respectively. Authors in (Pyakurel et al, 2017) introduced the abstract contraflow approach with path reversal capability They presented a polynomial time algorithm to solve the abstract maximum dynamic contraflow in continuous time setting.
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