Optimal partition of QoS requirements for many-to-many connections

The problems related to supporting multicast connections with quality of service (QoS) requirements are studied. We investigate the problem of optimal resource allocation in the context of performance dependent costs. In this context each network element can offer several QoS guarantees, each associated with a different cost. This is a natural extension to the commonly used bi-criteria model, where each link is associated with a single delay and a single cost. This framework is simple yet strong enough to model many practical interesting networking problems. The fundamental multicast resource allocation problem under this framework is how to optimally allocate QoS requirements on the links of the multicast tree. One needs to partition the end-to-end QoS requirement along the various paths in a tree. The goal is to satisfy the end-to-end QoS requirement with minimum cost. Previous studies under this framework considered single-source multicast connections, where the end-to-end QoS requirement is specified from the source to all other multicast group members. In this paper we extend these results to the more general, and considerably harder case of multicast sessions, where the end-to-end requirement hold for every path between any two multicast group members. Our aim is to provide rigorous solutions, with proven performance guarantees, by way of algorithmic analysis. The problem under investigation is NP hard for general cost functions, thus we first present a pseudopolynomial exact solution. From this solution we derive two efficient ε-approximate solutions. One achieves optimal cost, but may violate the end-to-end delay requirement by a factor of (1 + ε), and the other strictly obeys the bounds and achieves a cost within a factor of (1+ε) of the optimum. Furthermore, we present improved results for discrete cost functions, and give a simple linear-time exact polynomial solution for a specific, and practically interesting, family of convex cost functions.