We consider a fundamental pricing model in which a fixed number of units of a reusable resource are used to serve customers. Customers arrive to the system according to a stochastic process and, upon arrival, decide whether to purchase the service, depending on their willingness to pay and the current price. The service time during which the resource is used by the customer is stochastic, and the firm may incur a service cost. This model represents various markets for reusable resources, such as cloud computing, shared vehicles, rotable parts, and hotel rooms. In the present paper, we analyze this pricing problem when the firm attempts to maximize a weighted combination of three central metrics: profit, market share, and service level. Under Poisson arrivals, exponential service times, and standard assumptions on the willingness-to-pay distribution, we establish a series of results that characterize the performance of static pricing in such environments. In particular, although an optimal policy is fully dynamic in such a context, we prove that a static pricing policy simultaneously guarantees 78.9% of the profit, market share, and service level from the optimal policy. Notably, this result holds for any service rate and number of units the firm operates. Our proof technique relies on a judicious construction of a static price that is derived directly from the optimal dynamic pricing policy. In the special case in which there are two units and the induced demand is linear, we also prove that the static policy guarantees 95.5% of the profit from the optimal policy. Our numerical findings on a large test bed of instances suggest that the latter result is quite indicative of the profit obtained by the static pricing policy across all parameters.
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A price-aware congestion control protocol for cloud services
In current infrastructure-as-a service (IaaS) cloud services, customers are charged for the usage of computing/storage resources only, but not the network resource. The difficulty lies in the fact that it is nontrivial to allocate network resource to individual customers effectively, especially for short-lived flows, in terms of both performance and cost, due to highly dynamic environments by flows generated by all customers. To tackle this challenge, in this paper, we propose an end-to-end Price-Aware Congestion Control Protocol (PACCP) for cloud services. PACCP is a network utility maximization (NUM) based optimal congestion control protocol. It supports three different classes of services (CoSes), i.e., best effort service (BE), differentiated service (DS), and minimum rate guaranteed (MRG) service. In PACCP, the desired CoS or rate allocation for a given flow is enabled by properly setting a pair of control parameters, i.e., a minimum guaranteed rate and a utility weight, which in turn, determines the price paid by the user of the flow. Two pricing models, i.e., a coarse-grained VM-Based Pricing model (VBP) and a fine-grained Flow-Based Pricing model (FBP), are proposed. The optimality of PACCP is verified by both large scale simulation and small testbed implementation. The price-performance consistency of PACCP are evaluated using real datacenter workloads. The results demonstrate that PACCP provides minimum rate guarantee, high bandwidth utilization and fair rate allocation, commensurate with the pricing models.
more » « less- Award ID(s):
- 2008835
- NSF-PAR ID:
- 10360309
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Journal of Cloud Computing
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2192-113X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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