Lexicographically Maximum Contraflow Problem with Vertex Capacities

The contraflow approach has been extensively considered in the literature for modeling evacuations and has been claimed, due to its lane-direction-reversal capability, as an efficient idea to speed up the evacuation process. This paper considers the contraflow evacuation model on network with prioritized capacitated vertices that allows evacuees to be held at intermediate spots too, respecting their capacities and priority order. In particular, it studies the maximum flow evacuation planning problem and proposes polynomial and pseudo-polynomial time solution algorithms for static network and dynamic multinetwork, respectively. A real dataset of Kathmandu road network with evacuation spaces is considered to implement the algorithm designed for dynamic multinetwork and to observe its computational performance.

RESOURCE NETWORKS WITH LIMITATIONS ON VERTEX CAPACITIES

Work is continuation of studies whose results are published in the monograph "Theory of resource networks" — M.: RIOR: INFRA-M, 2017. The resource network is a dynamic graph model in which vertices at discrete time homogeneous resource exchange through channels with limited bandwidth capabilities. At each step, the vertices give the resource to one of the two rules with the threshold switch, depending on its quantity. In the original model all the vertices have an unlimited capacity. Ie can take and store an arbitrary amount of the resource. In the model proposed in the present work, the vertices, the storage resource (attractors) have limitations on capacity. This creates the possibility of accumulation of the resource in the set of vertices, called secondary attractors. Investigated the inhomogeneous Markov chain generated by the process of redistribution of the resource. The book is intended for specialists in graph theory and operations research, students, masters and post-graduate students studying in various areas of discrete mathematics and computer science.