On functioning of resource networks

I. M. Erusalimskyi ; H. N. Abdulrahman ; V. A. Skorokhodov ; V. A. Babintsev

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 2, Tome 236 (2024), pp. 13-21

Résumé

Resource networks are dynamic graph models introduced by O. P. Kuznetsov and L. Yu. Zhilyakova. These models are based on their functioning rules. The paper proposes a general approach to determining the functioning of resource networks, which consists of specifying a priority function on arcs of the resource network. Such a function determines the rules for the functioning of the resource network. Kuznetsov–Zhilyakova resource networks are a special case of resource networks with priorities on the arcs, where all arcs have the same priorities. We show by examples that resource networks of the same topology with different priority functions operates differently. Criteria for the emergence of stationary functioning of a resource network with priorities on arcs are obtained; the main criterion is the condition of flow balance. Also, we propose a more general extension of the concept of a resource network, namely, the definition of a resource network with dynamic priorities on arcs. In this case, the priority function specified on the network arcs is a function of discrete time in which the network operates.

Détail

Keywords: graph, resource network, resource allocation, flow, priorities on arcs