Path-vector contracting: Profit maximization and risk management

Abstract

We consider an Internet Service Provider’s (ISP’s) problem of providing end-to-end (e2e) services with bandwidth guarantees, using a path-vector based approach. In this approach, an ISP uses its edge-to-edge (g2g) single-domain contracts and vector of contracts purchased from neighboring ISPs as the building blocks to construct, or participate in constructing, an end-to-end “contract path”. We develop a spot-pricing framework for the e2e bandwidth guaranteed services utilizing this path contracting strategy, by formulating it as a stochastic optimization problem with the objective of maximizing expected profit subject to risk constraints. In particular, we present time-invariant path contracting strategies that offer high expected profit at low risks, and can be implemented in a fully distributed manner. Simulation analysis is employed to evaluate the contracting and pricing framework under different network and market conditions. An admission control policy based on the path contracting strategy is developed and its performance is analyzed using simulations.

Introduction

The Internet consists of several network domains owned and administered by independently operated ISPs. Today’s end-to-end (e2e) Internet services are mostly best-effort without any explicit QoS guarantee mainly due to the fact that “all bets are off” once the traffic crosses into another ISP’s domain. Significant amount of research has been carried out to provide QoS-assured Internet services, most of them focusing on intra-domain QoS guarantees. Though e2e QoS contracts are currently possible via virtual private networks, such possibilities only work with static and long-term contracts. Customers often demand services that require more dynamism and crossing of multiple ISPs, which cannot be realistically accommodated via rigid and static inter-ISP service level agreements (SLAs) in the current Internet architecture. The problem of end-to-end (e2e) QoS provisioning is further complicated due to the size and heterogeneity of users and providers in the Internet. Towards this end, we believe that using path-vector routing principles to construct end-to-end QoS-enabled services hold promise, as it provides a scalable and flexible mechanism for solving the e2e QoS provisioning problem.

In this work, we consider a path-vector based bandwidth contracting framework as a possible future architecture for Internet routing, and attempt to answer if such an inter-domain routing architecture is economically viable from an ISP’s perspective. We develop the necessary tools and techniques that can help ISPs maximize their profitability while meeting their contractual obligations, and thereby satisfying the e2e demands. In particular, we develop a spot-contracting and non-linear pricing framework for e2e services over the Internet for time durations finer than the existing SLAs. An ISP constructs or participates in constructing a set of “contract paths” to destination networks (ISPs) in order to serve its customer base. A customer (which can be an end user or an upstream ISP) can then enter into spot-contracts in order to get a flexible-duration of QoS guaranteed services from itself to the destination networks (ISPs). The QoS metric that we consider in this paper is data rate that can be supported between different source–destination pairs by the ISP. Most of the SLAs involve some form of delay or even loss guarantees. However, such guarantees are typically defined as additional parameters on top of a baseline average and/or maximum traffic rate or bandwidth. The average and maximum rates are more realistic at a more aggregate level, such as peering SLAs. Because of these reasons, we have focused our efforts on formulating the optimization problem just on the bandwidth. It is, however, possible to extend our formulation with other metrics. We could, for example, define utility functions for the provider that depends on the experienced delay. With some changes to our formulation, these can then be incorporated in the objective function to provide delay guarantees. However, the problem of reserving enough bandwidth along the paths would still be the major bottom line. Therefore, we consider only bandwidth as the QoS metric in this paper. Our framework allows the ISP both temporal (by tuning the duration of the contracts it advertises) and spatial (by advertising different prices for contracts crossing its different ingress and egress points) flexibility in contracting. Note that in general, an ISP’s strategy for constructing the contract paths determines its profitability and customer satisfaction.

We consider a path-vector contracting framework in which an ISP can announce different contract paths and prices for different destinations. This can be realized using a contract-switched Internet architecture proposed in our earlier work [1], where each ISP is abstracted as a set of edge-to-edge (g2g) contracts (which we call intra-domain “contract links”) as shown in Fig. 1. In such an architecture, an ISP can compose e2e contract paths in a path-vector style by using its g2g single-domain contracts and the vector of service contracts purchased from the neighboring ISPs. This framework is scalable since it is based on path-vector style of contracting and is directly compatible with the existing inter-domain routing protocols such as BGP [2]. In our framework, an ISP would receive advertisements for contract paths to a destination from its neighboring ISPs through its egress points. These contract paths (hereafter referred as extra-domain paths) ensure guaranteed service for traffic starting from a neighboring ISP to the destination. Therefore, the ISP can construct end-to-end contract paths to a destination by choosing some of these extra-domain paths and prepending them with its edge-to-edge contract links.

A key component in our inter-ISP architecture is the g2g contract links which provide guaranteed service between two end points of an ISP’s domain. We illustrate this using the contract-switching Internet abstraction shown in Fig. 1. Traditionally, for inter-domain routing, ISPs in the Internet are abstracted as nodes as shown in Fig. 1(b). Now, consider the path-vector contract-switched model [1], shown in Fig. 1(a) and let us suppose that the ISP A wants to setup end-to-end contracts between point (router/network) 1 located within its domain and point (router/network) 9 located in ISP D. The links 1-2, 1-3, 3-5 are g2g contract links belonging to ISP A. Similarly 3-6 and 2-8 are g2g contract links belonging to ISP B. Now, the ISP A would look for advertisements for extra-domain paths to point 9 from its neighboring ISPs B and C. Examples of extra-domain paths from the neighbor ISP B include 2-8-9 (involves the g2g links 2-8, 8-9), and 3-6-10-9 (involves links 3-6, 6-10, and 10-9). ISP A then provides one or more of its available intra-domain contract links, and enters into contract with its neighboring ISPs (B and C) to carry the traffic forward from 1 up to 9. The idea of path formation using negotiation and contracting has been proposed earlier in [3], [4], [5], although these approaches still use the node level ISP abstraction. The focus of this paper, however, is not on the protocol design and policy issues of how a path-vector (i.e. extra-domain contract path) gets constructed, but on developing a profit maximizing risk management strategy to help ISPs select which contract paths to participate.

Since dynamic, end-to-end provisioning for bandwidth and other QoS metrics is largely absent from the current Internet, limited-term services that require end-to-end QoS guarantees are not readily enabled. On-demand high-quality video-conferencing/streaming is one such example – even though such applications are run over the current Internet, they are not associated with any QoS guarantees, and often do not scale well to high quality/resolution. The path-vector contracting framework that we consider is well suited for this purpose, as it can concatenate several guaranteed but single-domain contracts into end-to-end reliable and QoS-guaranteed services.

Viewed from the perspective of an ISP participating in path-vector style contracting as described above, the end-to-end (e2e) contracting problem boils down to establishing contract paths between the ISP’s customers (end users or other ISPs) and specific destinations that the customers want to send traffic to. In the following, our reference to the e2e contracting problem, e2e contract paths or e2e traffic (service) demands must thus be viewed from a perspective of a single ISP. Note that the e2e contract paths are not set up dynamically for each arriving incoming request, which may happen on the seconds to minutes time-scale. Instead, we obtain a relatively longer-term e2e contracting strategy covering hours to days, wherein the contract paths are set up based on past data on the demand for intra-domain and extra-domain (inter-domain) services.

Typically, the demand for e2e services and network conditions can be dynamic and stochastic. Therefore, provisioning of e2e contract paths becomes risky due to uncertainties caused by competing traffic in the Internet. In such situations, an ISP cannot determine the exact amount of capacity to contract along each of the links/paths, since traffic is inherently stochastic. A time-invariant contracting strategy developed for the entire planning period can lead to capacity deficit or under-utilization of resources at certain times. Moreover, time-varying demands or router failures within any other Internet domains can potentially cause changes in the prices of the contract paths offered by the neighboring ISPs, premature termination of contract by neighboring ISPs, etc. Therefore, the ISP’s cost of providing or participating in creating the e2e service can increase or decrease, due to which the provider may or may not deliver the e2e service at the promised quality level. In this paper, the marginal cost of extra-domain service is modeled as mean-reverting random walk process. We consider two models for the demand process, namely, the mean-reverting process and the time-of-day process, described in Section 3.2.1.

For pricing links and paths, we use the Ramsey pricing model with a reasonable choice of demand profile for the ISP’s customer base. Due to uncertainty in the customer demand as well as the cost of the e2e service, any contracting and pricing strategy would lead to fluctuations in the ISP’s profit. Therefore, risk management becomes a critical issue while providing e2e services. In this paper, we assume that the average e2e user demand and cost can be determined using historical data. We show that the ISP can achieve significantly higher expected profit, at a given risk level, by reserving capacities along the links and paths that target supporting the average e2e demands inflated by a certain factor.

The major contributions of this paper can be outlined as follows.

• We introduce an architectural framework for scalable construction of e2e contracts by using the edge-to-edge single-domain contracts and the vector of contract paths obtained from other ISPs using a path-vector approach.

• The e2e path contracting and pricing strategy for a participating ISP is formulated as a stochastic optimization problem with the objective of maximizing expected profit subject to risk constraints.

• We obtain a solution to the problem in the space of time-invariant contracting strategies. The path contracting solution achieves maximum expected profit, for a given constraint on the risk (standard deviation) of profit.

• The optimal time-invariant contracting strategy is assessed for the effect of input volatility, path failures, and path correlation properties.

• We use the Rocketfuel dataset [6] and the GTITM models [7] to evaluate the performance of the proposed path contracting solution.

• Finally, we develop and evaluate an admission control policy that can be combined with the contracting strategy to obtain implementable solutions for e2e service provisioning.

The rest of the paper is organized as follows. Section 2 provides a brief review of state-of-the-art for QoS support and pricing. In Section 3, we develop the models and formulate the e2e pricing and risk management problem as a stochastic optimization problem, and present an approximation solution to the problem. Section 4 presents a detailed discussion of simulation results including the study of the effects of input volatility, failures, and correlation on the contracting strategy. Section 5 addresses the challenges involved while implementing the long-term strategy in practice. We conclude the paper and provide prospects for future research in Section 6.