This paper addresses the issue of Quality of Service (QoS) routing for supporting multimedia applications. The authors highlight that QoS routing is a critical but missing component in many network architectures. They examine the problem of finding a path that satisfies multiple constraints and discuss the implications for routing metric selection. Three path computation algorithms are presented for both source routing and hop-by-hop routing. The paper discusses the complexity of finding paths under multiple constraints and the selection of metrics for QoS routing. It argues that a single metric may not be sufficient to support all QoS requirements, and that multiple metrics are needed. The authors analyze the composition rules of different metrics and show that finding a path subject to multiple constraints is NP-complete. They propose that bandwidth and propagation delay are the most suitable metrics for QoS routing, as they reflect fundamental characteristics of a path. The paper presents three path computation algorithms for source routing and hop-by-hop routing. The source routing algorithm is centralized and finds a path that satisfies both bandwidth and delay constraints. The hop-by-hop routing algorithms are distributed and find the shortest-widest path, which is defined as the path with maximum bottleneck bandwidth and, in case of ties, the shortest propagation delay. The authors show that these algorithms are scalable and have similar time complexity to traditional shortest path algorithms. The paper also discusses future research directions, including integrating QoS routing with resource management systems, studying the convergence speed of algorithms after link or node failures, and investigating approximation algorithms for NP-complete search problems. The authors conclude that QoS routing is an important aspect of network design and that further research is needed to improve the efficiency and effectiveness of routing protocols.This paper addresses the issue of Quality of Service (QoS) routing for supporting multimedia applications. The authors highlight that QoS routing is a critical but missing component in many network architectures. They examine the problem of finding a path that satisfies multiple constraints and discuss the implications for routing metric selection. Three path computation algorithms are presented for both source routing and hop-by-hop routing. The paper discusses the complexity of finding paths under multiple constraints and the selection of metrics for QoS routing. It argues that a single metric may not be sufficient to support all QoS requirements, and that multiple metrics are needed. The authors analyze the composition rules of different metrics and show that finding a path subject to multiple constraints is NP-complete. They propose that bandwidth and propagation delay are the most suitable metrics for QoS routing, as they reflect fundamental characteristics of a path. The paper presents three path computation algorithms for source routing and hop-by-hop routing. The source routing algorithm is centralized and finds a path that satisfies both bandwidth and delay constraints. The hop-by-hop routing algorithms are distributed and find the shortest-widest path, which is defined as the path with maximum bottleneck bandwidth and, in case of ties, the shortest propagation delay. The authors show that these algorithms are scalable and have similar time complexity to traditional shortest path algorithms. The paper also discusses future research directions, including integrating QoS routing with resource management systems, studying the convergence speed of algorithms after link or node failures, and investigating approximation algorithms for NP-complete search problems. The authors conclude that QoS routing is an important aspect of network design and that further research is needed to improve the efficiency and effectiveness of routing protocols.