Optimal per-node rate allocation to provide per-flow end-to-end delay guarantees in a network of routers supporting guaranteed service class

In this paper, we investigate the problem of providing worst-case end-to-end delay guarantees to a token bucket constrained flow traversing a series of N packet schedulers. We consider a network of routers that support the guaranteed service class of the IETF Integrated Services (IntServ) Working Group; this service class is proposed to provide quality of service (QoS) in the Internet. Under this framework, a worst-case end-to-end delay bound to a flow is provided by allocating a rate at each network element on the path of the flow. We associate a cost with allocating a rate at each link. The cost is assumed to be a convex and non-decreasing function of rate. We investigate the problem of obtaining an optimal rate allocation for a flow that minimizes the total cost subject to the delay requirement and the available link capacity constraints. Allocating an identical rate at each link on the path of a flow is a widely used approach under the guaranteed service framework. We investigate the optimality of this approach and show that under certain conditions, it need not be optimal. Moreover, we investigate the optimal solution to the total cost minimization problem and give scenarios in which we can explicitly obtain the optimal solution. Based on these results, we present an algorithm for optimal rate allocation that is based on multiple rates. However, with blocking probability as the performance criterion, we find through simulations, that the optimal rate allocation algorithm is only marginally better for connections with longer path lengths at the expense of those with shorter path lengths. We also observe that the performances of both the algorithms are very close and so, in practice, the simpler identical rate algorithm may be sufficient.