Bandwidth Tiered Service: Deterministic Demands

Consider a network operator providing a service characterized strictly by the amount of bandwidth allocated to each user, e.g., as is the case for many residential and business Internet access services. The service provider is interested in making available only a small number p of distinct bandwidth levels (tiers) to which users may subscribe. In offering such a tiered bandwidth service, the operator must determine the number of tiers and the amount of bandwidth for each tier, as well as provision suffcient capacity within the network. Assuming that the provider has some information regarding the users' bandwidth requirements, it must balance two objectives in dimensioning its network for the tiered service: on the one hand, it must ensure that each user's bandwidth needs are adequately satisfied, while on the other hand it must minimize its own cost for providing the service.

In this chapter we make the assumption that the service provider has complete knowledge of the exact bandwidth requirements of its customers; we address the problem of stochastic bandwidth demands in Chapter 5. We show that the problem of dimensioning the network for tiered bandwidth service with deterministic demands can be expressed as a directional p-median problem on the real line (DPM1). We address two variants of the problem, one in which the number p of tiers is provided as an input parameter, and one in which the number of tiers is a variable to be optimized, and we present efficient optimal algorithms for both. We also quantify the impact of this .bandwidth quantization. on the amount of network resources to be provisioned for the tiered service.