Design differentiated service multicast with selfish agents

Differentiated service (DiffServ) is a mechanism to provide the quality-of-service (QoS) with a certain performance guarantee. In this paper, we study how to design DiffServ multicast when every relay link is an independent selfish agent. We assume that each link e/sub i/ is associated with a (privately known) cost coefficient c/sub i/ such that the cost of e/sub i/ to provide a transmission service with bandwidth demand x is c/sub i//spl middot/x. Further, we assume that there is a fixed source node s and a set R of receivers, each of which requires from s data with a minimum bandwidth demand. The DiffServ multicast problem is to compute a link-weighted tree rooted at s and spanning R such that the receivers' demands are met. This generalizes the traditional link-weighted Steiner tree problem. We first show that a previous approximation algorithm does not directly induce a strategyproof mechanism. We then give a new polynomial time algorithm to construct a DiffServ multicast tree whose total cost is no more than eight times the optimal total cost when the cost coefficient of each link is known. Based on this tree, we design a truthful mechanism for DiffServ multicast, i.e., we give a polynomial-time computable payment scheme to compensate all chosen relay links such that each link maximizes its profit when it declares its cost coefficient truthfully.