基于信源路由的时延受限点到点路由算法

本文研究了网络路由中的一个NPC问题:时延受限最小代价路由问题.文中提出了一个理论框架,并给出了多个简单有效的启发式算法,在满足给定时延约束条件可行路径存在时,算法总能找到满足约束条件的代价优化路径.文中提出的启发式算法复杂性为O(|V|²)且在线复杂性为O(|V|).仿真显示算法取得了良好的平均代价性能.最后将模型扩展到多QoS限制条件下的路由问题.     

A distributed algorithm for delay-constrained unicast routing

We study the NP-hard delay-constrained least cost (DCLC) path problem. A solution to this problem is needed to provide real-time communication service to connection-oriented applications, such as video and voice. We propose a simple, distributed heuristic solution, called the delay-constrained unicast routing (DCUR) algorithm, DCUR requires limited network state information to be kept at each node: a cost vector and a delay vector. We prove DCUR's correctness by showing that it is always capable of constructing a loop-free delay-constrained path within finite time, if such a path exists. The worst case message complexity of DCUR is O(|V|²) messages, where |V| is the number of nodes. However, simulation results show that, on the average, DCUR requires much fewer messages. Therefore, DCUR scales well to large networks. We also use simulation to compare DCUR to the optimal algorithm, and to the least delay path algorithm. Our results show that DCUR's path costs are within 10% of those of the optimal solution     

Finding a Path Subject to Many Additive QoS Constraints

A fundamental problem in quality-of-service (QoS) routing is to find a path between a source-destination node pair that satisfies two or more end-to-end QoS constraints. We model this problem using a graph with n vertices and m edges with K additive QoS parameters associated with each edge, for any constant Kges2. This problem is known to be NP-hard. Fully polynomial time approximation schemes (FPTAS) for the case of K=2 have been reported in the literature. We concentrate on the general case and make the following contributions. 1) We present a very simple (Km+nlogn) time K-approximation algorithm that can be used in hop-by-hop routing protocols. 2) We present an FPTAS for one optimization version of the QoS routing problem with a time complexity of O(m(n/epsi)^K-1). 3) We present an FPTAS for another optimization version of the QoS routing problem with a time complexity of O(nlogn+m(H/epsi)^K-1) when there exists an H-hop path satisfying all QoS constraints. When K is reduced to 2, our results compare favorably with existing algorithms. The results of this paper hold for both directed and undirected graphs. For ease of presentation, undirected graph is used     

An efficient QoS routing algorithm for solving MCP in ad hoc networks

Providing guaranteed quality of service (QoS) in wireless networks is a key issue for deploying multimedia applications. To support such a QoS, an arduous problem concerning how to find a feasible end to end path to satisfy multiple QoS constraints should be studied. In general, multi-constrained path selection, with or without optimization, is an NP-complete problem that cannot be exactly solved in polynomial time. Approximation algorithms and heuristics with polynomial and pseudo-polynomial time complexities are often used to deal with this problem. However, existing solutions suffer either from excessive computational complexities that cannot be used for multimedia applications in ad hoc networks characterized by mobility and performance constraints (e.g., limited energy, wireless medium, etc.). Recently a promising heuristic algorithm H_MCOP using a non linear Lagrange relaxation path functions has demonstrated an improvement in its success rate and in finding feasible paths. However, the H_MCOP is not suitable for ad hoc networks and has not exploited the full capability that a Lagrange relaxation could offer. In this paper, we propose an efficient multi-constrained path heuristic called E_MCP, which exploits efficiently the Lagrange relaxation and enhances the path search process to be adequate to mobile ad hoc networks. Using extensive simulations on random mobile network with correlated and uncorrelated link weights, we show that the same level of computational complexity, E_MCP can achieve a higher success ratio of finding feasible paths.     

Restorable dynamic quality of service routing

The focus of quality-of-service routing has been on the routing of a single path satisfying specified QoS constraints. Upon failure of a node or link on the path, a new path satisfying the constraints has to be established. However, resources needed to satisfy the QoS requirements are not guaranteed to be available at the rerouting instant, so QoS is not guaranteed upon failure. Restorable QoS routing, where active and backup paths must be simultaneously set up, has been previously studied. This is mostly motivated by the incorporation of mechanisms to establish QoS guaranteed paths with failure protection in multiprotocol label switching networks. This article describes some previously developed algorithms for dynamic routing of restorable QoS guaranteed paths     

Evaluation of multicast routing algorithms for real-timecommunication on high-speed networks

Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of real-time applications will be essential for future high-speed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric link loads. Each algorithm is judged based on the quality of the MC trees it generates and its efficiency in managing the network resources. Simulation results over random networks show that unconstrained algorithms are not capable of fulfilling the QoS requirements of real-time applications in wide-area networks. Simulations also reveal that one of the unconstrained algorithms, reverse path multicasting (RPM), is quite inefficient when applied to asymmetric networks. We study how combining routing with resource reservation and admission control improves the RPM's efficiency in managing the network resources. The performance of one semiconstrained heuristic, MSC, three constrained Steiner tree (CST) heuristics, Kompella, Pasquale, and Polyzos (1992), constrained adaptive ordering (CAO), and bounded shortest multicast algorithm (BSMA), and one constrained shortest path tree (CSPT) heuristic, the constrained Dijkstra heuristic (CDKS) are also studied. Simulations show that the semiconstrained and constrained heuristics are capable of successfully constructing MC trees which satisfy the QoS requirements of real-time traffic. However, the cost performance of the heuristics varies. The BSMA's MC trees are lower in cost than all other constrained heuristics. Finally, we compare the execution times of all algorithms, unconstrained, semiconstrained, and constrained     

Link‐disjoint paths for reliable QoS routing

The problem of finding link/node‐disjoint paths between a pair of nodes in a network has received much attention in the past. This problem is fairly well understood when the links in a network are only specified by a single link weight. However, in the context of quality of service routing, links are specified by multiple link weights and restricted by multiple constraints. Unfortunately, the problem of finding link/node disjoint paths in multiple dimensions faces different conceptual problems. This paper presents a first step to understanding these conceptual problems in link‐disjoint quality of service routing and proposes a heuristic link‐disjoint QoS algorithm that circumvents these problems. Copyright © 2003 John Wiley & Sons, Ltd.     

A new delay‐constrained algorithm for multicast routing tree construction

New multimedia applications provide guaranteed end‐to‐end quality of service (QoS) and have stringent constraints on delay, delay‐jitter, bandwidth, cost, etc. The main task of QoS routing is to find a route in the network, with sufficient resources to satisfy the constraints. Most multicast routing algorithms are not fast enough for large‐scale networks and where the source node uses global cost information to construct a multicast tree. We propose a fast and simple heuristic algorithm (EPDT) for delay‐constrained routing problem for multicast tree construction. This algorithm uses a greedy strategy based on shortest‐path and minimal spanning trees. It combines the minimum cost and the minimum radius objectives by combining respectively optimal Prim's and Dijkstra's algorithms. It biases routes through destinations. Besides, it uses cost information only from neighbouring nodes as it proceeds, which makes it more practical, from an implementation point of view. Copyright © 2004 John Wiley & Sons, Ltd.     

Algorithms for computing QoS paths with restoration

There is a growing interest among service providers to offer new services with Quality of Service (QoS) guarantees that are also resilient to failures. Supporting QoS connections requires the existence of a routing mechanism, that computes the QoS paths, i.e., paths that satisfy QoS constraints (e.g., delay or bandwidth). Resilience to failures, on the other hand, is achieved by providing, for each primary QoS path, a set of alternative QoS paths used upon a failure of either a link or a node. The above objectives, coupled with the need to minimize the global use of network resources, imply that the cost of both the primary path and the restoration topology should be a major consideration of the routing process. We undertake a comprehensive study of problems related to finding suitable restoration topologies for QoS paths. We consider both bottleneck QoS constraints, such as bandwidth, and additive QoS constraints, such as delay and jitter. This is the first study to provide a rigorous solution, with proven guarantees, to the combined problem of computing QoS paths with restoration. It turns out that the widely used approach of disjoint primary and restoration paths is not an optimal strategy. Hence, the proposed algorithms construct a restoration topology , i.e., a set of bridges, each bridge protecting a portion of the primary QoS path. This approach guarantees to find a restoration topology with low cost when one exists.     

Polynomial Time Approximation Algorithms for Multi-Constrained QoS Routing

We study the multi-constrained quality-of-service (QoS) routing problem where one seeks to find a path from a source to a destination in the presence of K ges 2 additive end-to-end QoS constraints. This problem is NP-hard and is commonly modeled using a graph with n vertices and m edges with K additive QoS parameters associated with each edge. For the case of K = 2, the problem has been well studied, with several provably good polynomial time-approximation algorithms reported in the literature, which enforce one constraint while approximating the other. We first focus on an optimization version of the problem where we enforce the first constraint and approximate the other K - 1 constraints. We present an O(mn log log log n + mn/epsi) time (1 + epsi)(K - 1)-approximation algorithm and an O(mn log log log n + m(n/epsi)^K-1) time (1 + epsi)-approximation algorithm, for any epsi > 0. When K is reduced to 2, both algorithms produce an (1 + epsi)-approximation with a time complexity better than that of the best-known algorithm designed for this special case. We then study the decision version of the problem and present an O(m(n/epsi)^K-1) time algorithm which either finds a feasible solution or confirms that there does not exist a source-destination path whose first weight is bounded by the first constraint and whose every other weight is bounded by (1 - epsi) times the corresponding constraint. If there exists an H-hop source-destination path whose first weight is bounded by the first constraint and whose every other weight is bounded by (1 - epsi) times the corresponding constraint, our algorithm finds a feasible path in O(m(H/epsi)^K-1) time. This algorithm improves previous best-known algorithms with O((m + n log n)n/epsi) time for K = 2 and 0(mn(n/epsi)^K-1) time for if ges 2.     

A dynamic multicast routing satisfying multiple QoS constraints

In this paper we propose a QoS‐based routing algorithm for dynamic multicasting. The complexity of the problem can be reduced to a simple shortest path problem by applying a Weighted Fair Queuing (WFQ) service discipline. Using a modified Bellman–Ford algorithm, the proposed routing builds a multicast tree, where a node is added to the existing multicast tree without re‐routing and satisfying QoS constraints. With user defined life‐time of connection this heuristic algorthm builds multicast tree which is near optimum over the whole duration of session. Simulation results show that tree costs are nearly as good as other dynamic multicast routings that does not consider QoS. Copyright © 2003 John Wiley & Sons, Ltd.     

Two Techniques for Fast Computation of Constrained Shortest Paths

Computing constrained shortest paths is fundamental to some important network functions such as QoS routing, MPLS path selection, ATM circuit routing, and traffic engineering. The problem is to find the cheapest path that satisfies certain constraints. In particular, finding the cheapest delay-constrained path is critical for real-time data flows such as voice/video calls. Because it is NP-complete, much research has been designing heuristic algorithms that solve the epsiv-approximation of the problem with an adjustable accuracy. A common approach is to discretize (i.e., scale and round) the link delay or link cost, which transforms the original problem to a simpler one solvable in polynomial time. The efficiency of the algorithms directly relates to the magnitude of the errors introduced during discretization. In this paper, we propose two techniques that reduce the discretization errors, which allows faster algorithms to be designed. Reducing the overhead of computing constrained shortest paths is practically important for the successful design of a high-throughput QoS router, which is limited at both processing power and memory space. Our simulations show that the new algorithms reduce the execution time by an order of magnitude on power-law topologies with 1000 nodes. The reduction in memory space is similar.     

面向绿色互联网的低功耗多播路由算法

基于路径节点驱动策略,提出了一种绿色互联网中的一对多组播路由算法,充分利用路径节点共享路径,生成低功耗最短路径树,提高用户QoS满意度。基于CERNET2拓扑仿真实现了该算法,通过与现有的能量感知启发式路由算法在网络功耗、路由成功率和运行时间等方面的性能对比,表明本文提出的算法具有更好的性能。     

Multipath routing for video delivery over bandwidth-limited networks

The delivery of quality video service often requires high bandwidth with low delay or cost in network transmission. Current routing protocols such as those used in the Internet are mainly based on the single-path approach (e.g., the shortest-path routing). This approach cannot meet the end-to-end bandwidth requirement when the video is streamed over bandwidth-limited networks. In order to overcome this limitation, we propose multipath routing, where the video takes multiple paths to reach its destination(s), thereby increasing the aggregate throughput. We consider both unicast (point-to-point) and multicast scenarios. For unicast, we present an efficient multipath heuristic (of complexity O(|V|/sup 3/)), which achieves high bandwidth with low delay. Given a set of path lengths, we then present and prove a simple data scheduling algorithm as implemented at the server, which achieves the theoretical minimum end-to-end delay. For a network with unit-capacity links, the algorithm, when combined with disjoint-path routing, offers an exact and efficient solution to meet a bandwidth requirement with minimum delay. For multicast, we study the construction of multiple trees for layered video to satisfy the user bandwidth requirements. We propose two efficient heuristics on how such trees can be constructed so as to minimize the cost of their aggregation subject to a delay constraint.     

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     

Quality-of-service routing for supporting multimedia applications

Several new architectures have been developed for supporting multimedia applications such as digital video and audio. However, quality-of-service (QoS) routing is an important element that is still missing from these architectures. In this paper, we consider a number of issues in QoS routing. We first examine the basic problem of QoS routing, namely, finding a path that satisfies multiple constraints, and its implications on routing metric selection, and then present three path computation algorithms for source routing and for hop-by-hop routing     

Conditions That Impact the Complexity of QoS Routing

Finding a path in a network based on multiple constraints (the MCP problem) is often considered an integral part of quality of service (QoS) routing. QoS routing with constraints on multiple additive measures has been proven to be NP-complete. This proof has dramatically influenced the research community, resulting into the common belief that exact QoS routing is intractable in practice. However, to our knowledge, no one has ever examined which “worst cases” lead to intractability. In fact, the MCP problem is not strong NP-complete, suggesting that in practice an exact QoS routing algorithm may work in polynomial time. The goal of this paper is to argue that in practice QoS routing may be tractable. We will provide properties, an approximate analysis, and simulation results to indicate that NP-completeness hinges on four conditions, namely: 1) the topology; 2) the granularity of link weights; 3) the correlation between link weights; and 4) the constraints. We expect that, in practice, these conditions are manageable and therefore believe that exact QoS routing is tractable in practice.     

QoS路由问题的反向优化算法

寻找满足两个加性QoS约束条件的路径是网络QoS路由研究的核心问题,线性搜索算法是重要近似算法之一。本文提出一种结合了反向优化策略的线性搜索算法。当线性搜索过程所得到的路径不满足QoS需求时,对搜索到的路径选取合适的节点进行反向优化。算法的时间复杂度为O(K(m+nlog2(n)))。仿真显示本文的搜索策略扩大了搜索空间,提高了寻找可行路径的成功率。     

Performance evaluation of constraint-based path selection algorithms

Constraint-based path selection is an invaluable part of a full-fledged quality of service (QoS) architecture. Internet service providers want to be able to select paths for QoS flows that optimize network utilization and satisfy user requirements and as such increase revenues. Unfortunately, finding a path subject to multiple constraints is known to be an NP-complete problem. Hence, accurate constraint-based path selection algorithms with a fast running time are scarce. Numerous heuristics and a few exact algorithms have been proposed. In this article we compare most of these algorithms. We focus on the restricted shortest path algorithms and multi-constrained path algorithms. The performance evaluation of these two classes of algorithms is presented based on complexity analysis and simulation results and may shed some light on the difficult task of selecting the proper algorithm for a QoS-capable network.     

A sustainable heuristic QoS routing algorithm for pervasive multi-layered satellite wireless networks

Due to the recent developments in wireless technology and electronics, it is feasible to develop pervasive algorithms for satellite environments. Multi-Layered Satellite Networks (MLSNs) that consist of low earth orbit and medium earth orbit satellites are becoming increasingly important since they have higher coverage and better service than single-layered satellite networks. One of the challenges in MLSNs is the development of specialized and efficient routing algorithms. In this paper, we improved the virtual topology strategy and import heuristic algorithm to satisfy the QoS requirements of the MLSN users. The QoS requirements include end to end delay; link utilization, bandwidth, and package loss rate are mainly focused in this paper. To satisfy the QoS requirements is a multi-parameter optimization problem, and it is convinced as a Non-deterministic Polynomial Complete problem already. As a solution, three typical heuristic algorithms—Ant Colony Algorithm, Taboo Search Algorithm and Genetic Algorithm are applied in the routing scheme in order to reduce package loss, link congestion and call blocking. Simulation results show that heuristic routing algorithm can provide more QoS guarantees than shortest path first algorithm on package loss rate, link congestion and call blocking.