Elsevier

Computer Networks

Volume 47, Issue 6, 22 April 2005, Pages 923-937
Computer Networks

Precomputation for intra-domain QoS routing

https://doi.org/10.1016/j.comnet.2004.11.002Get rights and content

Abstract

Quality-of-service routing (QoSR), seeking to find a feasible path with multiple constraints, is an NP-complete problem. We propose a novel precomputation approach to multi-constrained intra-domain QoS routing (PMCP). It is assumed that a router maintains the link state information of the entire domain. PMCP cares each QoS weight to several degrees, and computes a number of QoS coefficients uniformly distributed in the multi-dimensional QoS metric space. Based on each coefficient, a linear QoS function is constructed to convert the multiple QoS metrics to a single QoS value. We then create a shortest path tree with respect to the QoS value by Dijkstra’s algorithm. Finally, according to the multiple coefficients, different shortest path trees are calculated to compose the QoS routing table. We analyze linear QoS functions in the QoS metric space, and give a mathematical model to determine the feasibility of a QoS request in the space. After PMCP is introduced, we analyze its computational complexity and present a method of QoS routing table lookup. Extensive simulations evaluate the performance of the proposed algorithm and present a comparative study.

Introduction

Internet multimedia applications emerge continuously in recent years. With the increase of multimedia information and application classes, Internet turns to be an integrated multimedia-transmission network from the traditional simple data-transmission network. However, the network layer of Internet cannot distinguish the classes or requests of applications, and only fairly provide network resources to all kinds of applications (e.g. bandwidth, buffer and CPU resources on routers). Consequently, Internet takes best-effort forwarding as the only one object. Therefore, such a service of best-effort forwarding cannot satisfy different users and multimedia applications with the evolution of Internet.

It becomes a challenging issue to provide different quality-of-services (QoS) for different applications in the Internet [1]. QoS routing (QoSR) seeks to find a feasible path that satisfies multiple QoS constraints requested by an application. Since there are usually a lot of paths with different characteristics from a given node to another in the network, QoSR is a potential solution to this problem [2]. QoS constraints can be divided into link constraints and path constraints. A link constraint of a path is the constraint of the bottleneck link in the path, such as the bandwidth constraint. It can be easily dealt with in a preprocessing step by pruning all links that do not satisfy the constraint and computing a path from the rest sub-graph. The path constraint is the restriction of each link along the path, such as delay. Since finding a feasible path with multiple path constraints has the NP-complete computational complexity [3], [4], we will focus on path constraints in the paper.

Many heuristics have been proposed for the problem. However, these algorithms have some or all of the following limitations [2]: (1) high-computational complexity prevents their practical applications; (2) low routing performance causes that a feasible path sometimes cannot be found even when it does exist; (3) some algorithms only work for an environment with a specific network.

Furthermore, most of them use an on-line computation scheme, which calculates the feasible path when a QoS request arrives. Even if we do not consider the long delay of a request induced by the on-line calculation, the computation for each flow may cause an insufferable computational overload in the high-speed next-generation networks. Contrarily, the scheme of routing precomputation uses an off-line procedure to calculate the routing table, and when a request arrives at a router, the router looks up a feasible path in the table and then forwards the request. In most cases, a considerable reduction in the overall computational load could be achieved by precomputation, especially when the rate of QoS request arrivals is much higher than that of significant changes in the network state [5]. Moreover, precomputation provides the possibility of packet-based hop-by-hop distributed routing.

This paper proposes a novel approach, precomputation for multi-constrained path (PMCP). We assume that each intra-domain router s maintains a consistent copy of link states in the entire domain with k different QoS metrics. The algorithm cares each QoS weight to b degrees. It then computes B (B=Cb+k-2k-1) coefficients that are distributed uniformly in the k-dimensional QoS weight space. A linear QoS function (LQF) is constructed for each coefficient to convert multiple QoS metrics to a single QoS value. Node s then uses Dijkstra’s algorithm to calculate a shortest path tree rooted by s with respect to each LQF, and a part of QoS routing table is created based on the shortest path tree. At last, s combines the B parts of the routing table to form an entire intra-domain QoS routing table it maintains. For distributed routing, the QoS routing table only needs to save the next hop of each path in addition to the destination and the weights of each path. For source routing, the end-to-end path along the least QoS-value tree should be saved in the routing table. Therefore, when a QoS connection request arrives, it can be routed by looking up a feasible path in the routing table that satisfies the QoS constraints.

Experimental results show that PMCP can be easily implemented with high performance and high scalability. There are two major contributions in this paper. (1) We present a mathematical model to partition the k-dimensional QoS constraint space, so that the feasibility of a QoS request can (cannot) be determined by the continuous change of k-dimensional LQF. (2) PMCP is proposed to precompute the QoS routing table for the multi-constrained QoSR problem.

The rest of the paper is organized as follows. Related work is discussed in Section 2. An overview of the proposed PMCP is given in Section 3. We analyze LQF to give the theoretical basis in Section 4 and PMCP is described in Section 5. Section 6 shows the performance evaluation and Section 7 presents a comparative study. Finally conclusions appear in Section 8.

Section snippets

Related work

Finding a feasible path that satisfies multiple constraints is a NP-complete problem, for which many heuristic algorithms have been proposed. An extensive survey on QoSR can be found in [2], [6]. If some scheduling schemes [7], [8] (e.g. weighted fair queuing) are used, the queuing delay, jitter, and loss can be formulated as a function of bandwidth. The original NP-complete QoSR problem is then reduced to the standard shortest path problem based on the dependencies among QoS parameters [9],

Problem formulation

A directed graph G(V, E) presents a network. V is the node set and the element v  V is called a node representing a router in the network. E is the set of edges representing links that connect the routers. The element eij  E represents the edge e = vi   vj in G. In QoSR, each link has a group of independent metrics (w0(e),w1(e),  ,wk−1(e)), which is also called QoS metric w(e).

Definition 1 Multi-constrained path

For a given graph G(V, E), source node s, destination node t, k  2 and a constraint vector c = (c0,c1,  ,ck− 1), the path p from s

Linear QoS function analysis

If we take the QoS coefficient a as an independent variable, the question is changed: For a given G and source-destination pair (s, t), when QoS coefficient a reaches to all of the feasible values, what characteristics does the set {pa∣∀a} have? For example, how many elements does it have and how do they distribute? For convenience, we will first define the QoS metric space and then present theoretical basis of the proposed algorithm.

The idea of PMCP

For a given QoS request with constraint c, there are three possibilities for the feasibility of the request according to the position of c in the space Wk. (1) For c  MFEASIBLE, we know the feasibility and can find an element in the {pa} as the feasible path. (2) For c  MNOT, we know that there is NO feasible path, so we refuse the request or start QoS negotiation. (3) For c  MUNKNOWN, we do not know whether a feasible path exists. In the following performance evaluation section, simulations will

Performance evaluation

The routing performance of QoSR algorithms is often evaluated by two methods. (1) Competitive ratio, which indicates how well a heuristic algorithm performs, is defined as the ratio of the number of requests satisfied by using a heuristic algorithm and the number of requests satisfied by using an exhaustive algorithm. (2) Success ratio (SR) is defined as the ratio of the number of requests satisfied by using a heuristic algorithm and the total number of requests generated.

The difference between

Comparative study

Having showed the performance evaluation of PMCP, we then give a comparative study in this section. From the related work in Section 2, it is seen that there are only a few precomputation algorithms for QoSR at present. Some of them tend to have the prohibitive computational complexity or low performance, and some are based on distance vectors, so they are not fit for large-scale networks. In order to show the performance of PMCP, we compare PMCP with H_MCOP [18], which is also based on

Conclusion

The multi-constrained routing problem has an NP-complete complexity. We propose a novel intra-domain precomputation algorithm PMCP based on linear QoS functions. With this algorithm, a router constructs a number (B) of uniform coefficients to construct B linear QoS functions. It then calculates B least QoS-value trees to compose the QoS routing table with computational complexity O(B(m + n log n + n)). The size of the QoS routing table is less than or equal to B times that of the current routing

Acknowledgement

The authors would like to thank the editor of Computer Networks and the anonymous reviewers for their valuable comments.

Yong Cui, male, born in 1976, received the B.S., M.S. and Ph.D. degrees in computer science from Tsinghua University, P. R. China, in 1999, 2001 and 2004 respectively. He is now an assistant professor in the Department of Computer Science of Tsinghua University. During his Ph.D. study, he published 20 technical papers in journals and international conferences. He has also applied for several patents in China. His major research interests include computer network architecture, distributed

References (31)

  • P. Van Mieghem et al.

    Hop-by-hop quality of service routing

    Computer Netwroks

    (2001)
  • X. Xiao et al.

    Internet QoS: a big picture

    IEEE Network

    (1999)
  • Y. Cui et al.

    Research on internetwork QoS routing algorithms: a survey

    Chinese Journal of Software

    (2002)
  • M.S. Garey et al.

    Computers and Intractability: A Guide to the Theory of NP-completeness

    (1979)
  • Z. Wang et al.

    Quality-of-service routing for supporting multimedia applications

    IEEE Journal on Selected Areas in Communications

    (1996)
  • A. Orda, A. Sprintson, QoS routing: the precomputation perspective, IEEE INFOCOM’00, vol. 1, 2000, pp....
  • S. Chen et al.

    An overview of quality-of-service routing for next-generation high-speed networks: problems and solutions

    IEEE Network

    (1998)
  • J. Bennett, H. Zhang, Hierarchical packet fair queueing algorithms, ACM SIGCOMM’96, August...
  • L. Zhang, Virtual clock: A new traffic control algorithm for packet switching networks, ACM SIGCOMM’90, September 1990,...
  • Q. Ma, P. Steenkiste, Quality-of-service routing with performance guarantees. 4th International IFIP Workshop on...
  • C. Pornavalai, G. Chakraborty, N. Shiratori, QoS based routing algorithm in integrated services packet networks, IEEE...
  • A. Orda

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

    IEEE/ACM Transactions on Networking

    (1999)
  • H.F. Salama, D.S. Reeves, Y. Viniotis, A distributed algorithm for delay-constrained unicast routing, IEEE INFOCOM’97,...
  • J.M. Jaffe

    Algorithms for finding paths with multiple constraints

    IEEE Networks

    (1984)
  • D. Raz, Y. Shavitt, Optimal partition of QoS requirements with discrete cost functions, IEEE INFOCOM’00, vol. 2, 2000,...
  • Cited by (0)

    Yong Cui, male, born in 1976, received the B.S., M.S. and Ph.D. degrees in computer science from Tsinghua University, P. R. China, in 1999, 2001 and 2004 respectively. He is now an assistant professor in the Department of Computer Science of Tsinghua University. During his Ph.D. study, he published 20 technical papers in journals and international conferences. He has also applied for several patents in China. His major research interests include computer network architecture, distributed routing protocols, QoS routing and core routers. He is an IEEE member.

    Jianping Wu, male, born in 1953. He received master and doctor degrees in computer science from Tsinghua University. He is a full professor in the Department of Computer Science, Tsinghua University. In the research areas of the network architecture, high performance routing and switching, protocol testing and formal methods, he has published more than 200 technical papers in the academic journals and proceedings of international conferences.

    Ke Xu, male, born in Jiangsu, P.R.China, in 1974. He received the B.S., M.S. and Ph.D. degrees in computer science from Tsinghua University, China in 1996, 1998 and 2001 respectively. Currently he is an Assistant Professor in the department of computer science of Tsinghua University. His researching interests include high-speed networks, switch and router architecture, QoS routing and congestion control. He is a member of IEEE and IEEE Communication Society.

    Supported by: (1) the National Natural Science Foundation of China (No. 60403035); (2) the National Major Basic Research Program of China (No. 2003CB314801).

    View full text