Ariel Orda

QoS routing mechanisms and OSPF extensions

This paper presents and discusses path selection algorithms to support QoS routes in IP networks. The work is carried out in the context of extensions to the OSPF protocol, and the initial focus is on unicast flows, although some of the proposed extensions are also applicable to multicast flows. We first review the metrics required to support QoS, and then present and compare several path selection algorithms, which represent different trade-offs between accuracy and computational complexity. We also describe and discuss the associated link advertisement mechanisms, and investigate some options in balancing the requirements for accurate and timely information with the associated control overhead. The overall goal of this study is to identify a framework and possible approaches to allow deployment of QoS routing capabilities with the minimum possible impact to the existing routing infrastructure.

QoS routing in networks with inaccurate information: theory and algorithms

This paper investigates the problem of routing flows with quality-of-service (QoS) requirements through one or more networks, when the information available for making such routing decisions is inaccurate. Inaccuracy in the information used in computing QoS routes, e.g., network state such as link and node metrics, arises naturally in a number of different environments that are reviewed in the paper. The goal is to determine the impact of such inaccuracy on the ability of the path-selection process to successfully identify paths with adequate available resources. In particular, we focus on devising algorithms capable of selecting path(s) that are most likely to successfully accommodate the desired QoS, in the presence of uncertain network state information for the purpose of the analysis, we assume that this uncertainty is expressed through probabilistic models, and we briefly discuss sample cases that can give rise to such models. We establish that the impact of uncertainty is minimal for flows with only bandwidth requirements, but that it makes path selection intractable when end-to-end delay requirements are considered. For this latter case, we provide efficient solutions for special cases of interest and develop useful heuristics.

Competitive routing in multiuser communication networks

The authors consider a communication network shared by several selfish users. Each user seeks to optimize its own performance by controlling the routing of its given flow demand, giving rise to a noncooperative game. They investigate the Nash equilibrium of such systems. For a two-node multiple links system, uniqueness of the Nash equilibrium is proven under reasonable convexity conditions. It is shown that this Nash equilibrium point possesses interesting monotonicity properties. For general networks, these convexity conditions are not sufficient for guaranteeing uniqueness, and a counterexample is presented. Nonetheless, uniqueness of the Nash equilibrium for general topologies is established under various assumptions. >

Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length

In this paper the shortest-path problem in networks in which the delay (or weight) of the edges changes with time according to arbitrary functions is considered. Algorithms for finding the shortest path and minimum delay under various waiting constraints are presented and the properties of the derived path are investigated. It is shown that if departure time from the source node is unrestricted, then a shortest path can be found that is simple and achieves a delay as short as the most unrestricted path. In the case of restricted transit, it is shown that there exist cases in which the minimum delay is finite, but the path that achieves it is infinite.

Achieving network optima using Stackelberg routing strategies

In noncooperative networks users make control decisions that optimize their individual performance objectives. Nash equilibria characterize the operating points of such networks. Nash equilibria are generically inefficient and exhibit suboptimal network performance. Focusing on routing, a methodology is devised for overcoming this deficiency, through the intervention of the network manager. The manager controls part of the network flow, is aware of the noncooperative behavior of the users and performs its routing aiming at improving the overall system performance. The existence of maximally efficient strategies for the manager, i.e., strategies that drive the system into the global network optimum, is investigated. A maximally efficient strategy of the manager not only optimizes the overall performance of the network, but also induces an operating point that is efficient with respect to the performance of the individual users (Pareto efficiency). Necessary and sufficient conditions for the existence of a maximally efficient strategy are derived, and it is shown that they are met in many cases of practical interest. The maximally efficient strategy is shown to be unique and it is specified explicitly.

QoS routing in networks with uncertain parameters

We consider the problem of routing connections with quality of service (QoS) requirements across networks when the information available for making routing decisions is inaccurate. Such uncertainty about the actual state of a network component arises naturally in a number of different environments. The goal of the route selection process is then to identify a path that is most likely to satisfy the QoS requirements. For end-to-end delay guarantees, this problem is intractable. However, we show that by decomposing the end-to-end constraint into local delay constraints, efficient and tractable solutions can be established. Moreover, we argue that such decomposition better reflects the interoperability between the routing and reservation phases. We first consider the simpler problem of decomposing the end-to-end constraint into local constraints for a given path. We show that, for general distributions, this problem is also intractable. Nonetheless, by defining a certain class of probability distributions, which includes typical distributions, and restricting ourselves to that class, we are able to establish efficient and exact solutions. We then consider the general problem of combined path optimization and delay decomposition and present efficient solutions. Our findings are applicable also to a broader problem of finding a path that meets QoS requirements at minimal cost, where the cost of each link is some general increasing function of the QoS requirements from the link.

Networks with advance reservations: the routing perspective

This paper provides an initial look at how support for advance reservations affects the complexity of the path selection process in networks. Advance reservations are likely to become increasingly important as networks and distributed applications become functionally richer and there have been a number of previous works and investigations that explored various related aspects. However, the impact or advance reservations on path selection is a topic that has been left largely untouched. This paper investigates several service models for advance reservations, which range from the traditional basic model of reserving a given amount of bandwidth for some time in the future, to more sophisticated models aimed at increasing the flexibility of services available through advance reservations. The focus is primarily on the issue of computational complexity when supporting advance reservations, and in that context, we derive a number of algorithms and/or intractability results for the various models we consider.

QoS based routing in networks with inaccurate information: theory and algorithms

We investigate the problem of routing connections with QoS requirements across one or more networks, when the information available for making routing decisions is inaccurate and expressed in some probabilistic manner. This uncertainty about the actual state of a node or network arises naturally in a number of different environments, that are reviewed in the paper. The main focus is to determine the impact of such inaccuracies on the path selection process, whose goal is then to identify the path that is most likely to satisfy the QoS requirements.

Routing with end-to-end QoS guarantees in broadband networks

We consider routing schemes for connections with end-to-end delay requirements, and investigate several fundamental problems. First, we focus on networks which employ rate-based schedulers and, hence, map delay guarantees into nodal rate guarantees, as done with the guaranteed service class proposed for the Internet. We consider first the basic problem of identifying a feasible route for the connection, for which a straightforward yet computationally costly solution exists. Accordingly, we establish several approximation schemes that offer substantially lower computational complexity. We then consider the more general problem of optimizing the route choice in terms of balancing loads and accommodating multiple connections, for which we formulate and validate several optimal algorithms. We discuss the implementation of such schemes in the context of link-state and distance-vector protocols. Next, we consider the fundamental problem of constrained path optimization. This problem, typical of quality of service routing, is NP-hard. While standard approximation methods exist, their complexity may often be prohibitive in terms of scalability. Such approximations do not make use of the particular properties of large-scale networks, such as the face that the path selection process is typically presented with a hierarchical, aggregated topology. By exploiting the structure of such topologies, we obtain an /spl epsiv/-optimal algorithm for the constrained shortest-path problem, which offers a substantial improvement in terms of scalability.

Multipath routing algorithms for congestion minimization

Unlike traditional routing schemes that route all traffic along a single path, multipath routing strategies split the traffic among several paths in order to ease congestion. It has been widely recognized that multipath routing can be fundamentally more efficient than the traditional approach of routing along single paths. Yet, in contrast to the single-path routing approach, most studies in the context of multipath routing focused on heuristic methods. We demonstrate the significant advantage of optimal (or near optimal) solutions. Hence, we investigate multipath routing adopting a rigorous (theoretical) approach. We formalize problems that incorporate two major requirements of multipath routing. Then, we establish the intractability of these problems in terms of computational complexity. Finally, we establish efficient solutions with proven performance guarantees