Pricing and admission control for shared computer services using the token bucket mechanism

Abstract

This dissertation presents and analyzes token-bucket pricing schemes for shared resources. This research is motivated by the computer services industry, where services are provided mostly on a dedicated basis. However, leading computer companies such as HP and IBM forecast that external service providers will share resources between customers, in order to realize economies of scale. Two of the challenges faced by providers and consumers of shared services are admission control and pricing. In order to allow sellers to guarantee service levels, we recommend that pricing schemes for shared resources include admission controls. The implementation of such schemes requires understanding of buyers' and sellers' actions and a characterization of the admission control. This dissertation reviews the computer services supply-chain and proposes a five-step procedure for analyzing the pricing of shared services. Then it extends the usage of token-bucket and token-bucket-with-rate-control admission controls to pricing schemes. We show that for the token-bucket (token-bucket-with-rate-control) mechanism the bucket level behaves as a two- (one-) sided regulated random walk. Thus, the performance analysis (loss sales or backlog) is identical to the analysis of threshold crossing probabilities of regulated random walks. This dissertation's main contribution is an upper bound on the probability of a two-sided regulated random walk being on its "rare" boundary. Using the bounds developed, we solve constrained or relaxed versions of the buyer's problem. For the token-bucket-with-rate-control pricing scheme and exponential demand the buyer's problem can be solved in closed form.

(cont.) Moreover, numerical experiments show that the approximate solutions for the normal demand case are within 1% of optimal. Similar results hold for the token-bucket mechanism. Finally, we characterize the output stream of these admission controls (the jumps of one- or two-sided regulated random walks). We use a Brownian motion approximation for the bucket level process, but still consider the actual demand and arrival processes. Moreover, we enhance the performance of this approach by relating fill rates with the percentage of periods with losses. Numerical results show that in both mechanisms, when demand is exponential or normal, the approximated first two moments of the output stream are, typically, within the 99% confidence intervals.