Lagrangian relaxation for maximum service in multicast routing with QoS constraints

Abstract

In this paper, we propose a new variant of the Multicast Routing Problem called Maximum Service in Multicast Routing with Quality of Service constraints applied in the context of vehicular ad hoc networks, for which data must be sent from a root node to a set of terminal nodes. The use of all nodes is not mandatory and each connection between the root and a terminal aims to satisfy the quality of service according to the limits established for each metric. The objective is to maximize the number of serviced terminals according to the network's quality of service metrics. We present an integer programming formulation and four Lagrangian relaxations, to obtain good primal and dual bounds. We also develop a local search applied during the resolution of the Lagrangian relaxations. These methodologies were subjected to computational experiments with a set of 40 instances generated with characteristics of vehicular ad hoc networks. Statistical analyses were performed to compare the performance between methodologies, where the model achieved optimal values for 29 instances, and the Lagrangian relaxations rendered competitive bounds, especially for large instances.

Multicast Routing Based on Data Envelopment Analysis and Markovian Decision Processes for Multimodal Transportation

“…Consequently, in the subsequent experiments, we explored an extension of our proposed approach wherein the overall weight of a multicast tree must also conform to a budget constraint. This problem is commonly identified as a constrained Steiner tree problem, well-known for its NP-hard nature [31]. A specific manifestation of this model is widely acknowledged as a constrained shortest path problem, a crucial challenge in optimization domains such as transportation, crew scheduling, network routing, and communication networks [32].…”