American Journal of Mathematics and Statistics
pISSN: 2162948X eISSN: 21628475
2021; 11(2): 2733
doi:10.5923/j.ajms.20211102.01
Received: Jan. 31, 2021; Accepted: Mar. 5, 2021; Published: Mar. 15, 2021
Shiva Prakash Gupta ^{1}, Urmila Pyakurel ^{2}, Tanka Nath Dhamala ^{2}
^{1}Tribhuvan University, TriChandra Multiple Campus, Kathmandu, Nepal
^{2}Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal
Correspondence to: Urmila Pyakurel , Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal.
Email: 
Copyright © 2021 The Author(s). Published by Scientific & Academic Publishing.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
The contraflow technique has been extensively used to evacuate people in disasters situation. By flipping the orientation of necessary road segments, the flow value increases, and the evacuation time decreases significantly. Contraflow problems with asymmetric capacity and symmetric transit time on arcs have polynomialtime solutions. But in uneven road network topology, transit time may not be symmetrical, even affected by time or flow dependency. Recently, the twoterminal maximum dynamic and earliest arrival partial contraflow problems with nonsymmetric capacity and transit time on arcs are solved polynomially. In this paper, we introduce two flow problems with asymmetric transit time. First, we present the multisource singlesink earliest arrival transshipment contraflow problem, which deals with evacuating the maximum number of people each time. Second, the singlesource multisink prioritized maximum dynamic partial contraflow problem that evacuates the people by assigning priority to critically injured people. We also provide polynomialtime algorithms to solve these problems.
Keywords: Evacuation network, Network flow, Nonsymmetric transit time, Lexicographic flow, Earliest arrival transshipment, Contraflow
Cite this paper: Shiva Prakash Gupta , Urmila Pyakurel , Tanka Nath Dhamala , Network Flows with Arc Reversals and NonSymmetric Transit Times, American Journal of Mathematics and Statistics, Vol. 11 No. 2, 2021, pp. 2733. doi: 10.5923/j.ajms.20211102.01.
Figure 1. (a) Represents a twoway road network, (b) represents the network, if arc is reversed in the direction of arc e, and (c) represents the network, if arc e is reversed in the direction of arc 
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
Figure 2. (a) Twoway road network with arc capacity and transit time (b) Transformed network of (a) 
