Minimum Clearance Time on the Prioritized Integrated Evacuation Network

Abstract

The evacuation planning problem can be viewed as different variants of dynamic flow maximization and time minimization problems. An optimal solution to the latter problem sends a given amount of flow from disaster zones to safe zones in minimum time. We solve this problem on an embedded integrated network of a prioritized primary and a bus-routed secondary sub-networks. For a lexicographically maximum (lex-max) dynamic flow problem, we are given a time horizon and a prioritized network, where we need a feasible dynamic flow that lexicographically maximizes the flow amount leaving each terminal respecting the priority. Here, we use the quickest transshipment partial arc reversal strategy to collect the evacuees in minimum time from the disaster zones to the pickup locations of the primary sub-network. By treating such pickup locations as sources, the available set of transit-buses is assigned in the secondary sub-network to shift the evacuees finally to the sinks on the first-come-first-serve basis. This novel approach proposed here is better suited for the simultaneous flow of evacuees with minimum waiting delay at such pickup locations in the integrated evacuation network topology. The lane reversal strategy significantly reduces the evacuation time, whereas reversing them only partially has an additional benefit that the unused road capacities can be used for supplying emergency logistics and allocating facilities as well.

Quickest Transshipment in the Prioritized Evacuation Network

“…Transit buses are assigned in 𝑁𝑁 " from 𝑑𝑑, which are sufficiently closer to it, on a first-come-first-serve basis, i.e., the evacuees collected earlier will be assigned earlier to the appropriate sink and will be continued till the supply is available at Y respecting the capacity of the sink. For details, we refer to [7][8].…”

“…It demands a minimum time limit such that all supplies can be sent to the sinks (safe places) from the sources (disastrous zones). There has been a fair amount of work regarding its different aspects, including the quickest transshipment, as referred by [3][4][5][6][7][8][9]. These problems are handled from different perspectives: transit-based, car-based, and pedestrian movements.…”

Quickest Transshipment in an Evacuation Network Topology

“…In a prioritized evacuation system as in [11,12], evacuees are collected from the disaster zone to the prioritized pickup locations of the primary sub-network in the minimum time as the quickest transshipment by using the lex-max flow approach [13]. Considering such pickup locations as the sources, the available set of transit buses are also assigned in the network to evacuate the evacuees safely to the sinks on a first-come-first-serve basis and is better suited for the simultaneous flow of evacuees.…”

Quickest Flow Algorithms with Time-Varying Attributes

“…Saho and Shigino (2017) also proved that a strongly polynomial bound is possible by making use of a different cost scaling minimum cost flow algorithms: Cancel-and-Tighten of Goldberg and Tarjan (1989). These works can be useful in evacuation planning (Nath et al, 2020;Pyakurel et al, 2018;Adhikari & Dhamala, 2020). A contra-flow approach can be used to solve evacuation planning problem in a continuous time dynamic network (Pyakurel & Dhamala, 2016).…”