Precomputation for intra-domain QoS routing

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.     

Search space reduction in QoS routing

To provide real-time service or engineer constrained-based paths, networks require the underlying routing algorithm to be able to find low-cost paths that satisfy given quality-of-service constraints. However, the problem of constrained shortest (least-cost) path routing is known to be NP-hard, and some heuristics have been proposed to find a near-optimal solution. However, these heuristics either impose relationships among the link metrics to reduce the complexity of the problem which may limit the general applicability of the heuristic, or are too costly in terms of execution time to be applicable to large networks. In this paper, we focus on solving the delay-constrained minimum-cost path problem, and present a fast algorithm to find a near-optimal solution. This algorithm, called delay-cost-constrained routing (DCCR), is a variant of the k-shortest-path algorithm. DCCR uses a new adaptive path weight function together with an additional constraint imposed on the path cost, to restrict the search space. Thus, DCCR can return a near-optimal solution in a very short time. Furthermore, we use a variant of the Lagrangian relaxation method proposed by Handler and Zang [Networks 10 (1980) 293] to further reduce the search space by using a tighter bound on path cost. This makes our algorithm more accurate and even faster. We call this improved algorithm search space reduction + DCCR (SSR + DCCR). Through extensive simulations, we confirm that SSR + DCCR performs very well compared to the optimal but very expensive solution.     

Time-Dependent SHARC-Routing

In recent years, many speed-up techniques for Dijkstra’s algorithm have been developed that make the computation of shortest paths in static road networks a matter of microseconds. However, only few of those techniques work in time-dependent networks which, unfortunately, appear quite frequently in reality: Roads are predictably congested by traffic jams, and efficient timetable information systems rely on time-dependent networks. Hence, a fast technique for routing in such networks is needed.     

多约束服务质量路由中的路径压缩算法

多约束服务质量路由是一种能够支持灵活的服务质量控制的有效方案.然而在多约束的环境下,从一个源节点到一个目的节点可能存在多条路径,因而必须相应地增大路由表容量.由于当前路由表的规模已相当庞大,尤其是在高速核心网中,因此,为了在QoS路由表中存储更少的路径信息,需要首先进行路径压缩.文章以解决最优路径压缩问题(OPR)为目标,力图在尽量减小路由表存储规模的同时使路由成功率最大化.为了实现这个目标,文中提出了两个基于贡献区域的算法:增量贡献算法和改进的增量贡献算法.这两个算法从一个大的多约束路径集合中依次计算出具有最大贡献区域的积的路径,最后得到一个小的结果路径集合.大量模拟实验表明,这两个算法能够以较低的运算复杂度获得令人满意的路由成功率.     

Applications of meta‐heuristics to traffic engineering in IP networks

Intra‐domain routing protocols are based on shortest path first (SPF) routing, where shortest paths are calculated between each pair of nodes (routers) using pre‐assigned link weights, also referred to as link metric. These link weights can be modified by network administrators in accordance with the routing policies of the network operator. The operator's objective is usually to minimize traffic congestion or minimize total routing cost subject to the traffic demands and the protocol constraints. However, determining a link weights combination that best suits the network operator's requirements is a difficult task. This paper provides a survey of meta‐heuristic approaches to traffic engineering, focusing on local search approaches and extensions to the basic problem taking into account changing demands and robustness issues with respect to network failures.     

Searching among intervals and compact routing tables

Shortest paths in weighted directed graphs are considered within the context of compact routing tables. Strategies are given for organizing compact routing tables so that extracting a requested shortest path will takeo(k logn) time, wherek is the number of edges in the path andn is the number of vertices in the graph. The first strategy takesO (k+logn) time to extract a requested shortest path. A second strategy takes (k) time on average, assuming alln(n–1) shortest paths are equally likely to be requested. Both strategies introduce techniques for storing collections of disjoint intervals over the integers from 1 ton, so that identifying the interval within which a given integer falls can be performed quickly.This research was supported in part by the National Science Foundation under Grants CCR-9001241 and CCR-9322501 and by the Office of Naval Research under Contract N00014-86-K-0689.     

Fault-tolerant routing over shortest node-disjoint paths in hypercubes

This paper presented a routing algorithm that finds n disjoint shortest paths from the source node s to target node d in the n-dimensional hypercube. Fault-tolerant routing over all shortest node-disjoint paths has been investigated to overcome the failure encountered during routing in hypercube networks. In this paper, we proposed an efficient approach to provide fault-tolerant routing which has been investigated on hypercube networks. The proposed approach is based on all shortest node-disjoint paths concept in order to find a fault-free shortest path among several paths provided. The proposed algorithm is a simple uniform distributed algorithm that can tolerate a large number of process failures, while delivering all n messages over optimal-length disjoint paths. However, no distributed algorithm uses acknowledgement messages (acks) for fault tolerance. So, for dealing the faults, acknowledgement messages (acks) are included in the proposed algorithm for routing messages over node-disjoint paths in a hypercube network.     

Minimal Adaptive Routing on the Mesh with Bounded Queue Size

An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around “hot spots.” Minimal adaptive routing algorithms have the additional advantage that the path each packet takes is a shortest one. For a large class of minimal adaptive routing algorithms, we present an Ω(n²/k²) bound on the worst case time to route a static permutation of packets on ann×nmesh or torus with nodes that can hold up tok≥ 1 packets each. This is the first nontrivial lower bound on adaptive routing algorithms. The argument extends to more general routing problems, such as theh–hrouting problem. It also extends to a large class of dimension order routing algorithms, yielding an Ω(n²/k) time bound. To complement these lower bounds, we present two upper bounds. One is anO(n²/k+n) time dimension order routing algorithm that matches the lower bound. The other is the first instance of a minimal adaptive routing algorithm that achievesO(n) time with constant sized queues per node. We point out why the latter algorithm is outside the model of our lower bounds.     

Complexity results on labeled shortest path problems from wireless routing metrics

Metrics to assess the cost of paths through networks are critical to ensuring the efficiency of network routing. This is particularly true in multi-radio multi-hop wireless networks. Effective metrics for these networks must measure the cost of a wireless path based not only on traditional measures such as throughput, but also on the distribution of wireless channels used. In this paper, we argue that routing metrics over such networks may be viewed as a class of existing shortest path problems, the formal language constrained path problems.On this basis, we describe labeled path problems corresponding to two multi-radio wireless routing metrics: Weighted Cumulative Expected Transmission Time (WCETT), developed by Draves et al., and Metric for Interference and Channel-switch (MIC), developed by Yang et al. For the first, we give a concise proof that calculating shortest WCETT paths is strongly NP-Complete for a variety of graph classes. We also show that the existing heuristic given by Draves et al. is an approximator. For the second, we show that calculating loop-free (simple) shortest MIC paths is NP-Complete, and additionally show that the optimization version of the problem is NPO PB-Complete. This result implies that shortest simple MIC paths are only poorly approximable in the worst case.Furthermore, we demonstrate how the polynomial-time algorithm for shortest MIC paths is derivable from an existing language constrained shortest path algorithm. We use this as a basis to exhibit the general utility of viewing multi-channel wireless routing metrics as labeled graph problems, and discuss how a class of related polynomial-time computable metrics are derivable from this algorithm.     

LABILE: link quAlity-based lexIcaL routing mEtric for reactive routing protocols in IEEE 802.15.4 networks

In this paper, we propose a lexical routing metric to enable path-wise link quality-aware routing in Wireless Sensor Networks (WSNs). The realization of this routing metric is achieved by applying the indexing techniques of formal language processing in multi-metric route classification and cost evaluation for WSNs. In particular, the metric is motivated from the fact that IEEE 802.15.4 networks are formed on links with highly variable quality, and selection of poor quality links degrades the data delivery considerably. Although IEEE 802.15.4 supports link-level awareness through LQI, (a)?it remains unbeknownst at the path level, and therefore, (b)?its processing is link-local in scope. We propose LABILE, a composite routing metric, that is implemented through modifying RREQ and RREP structures of AODV to capture and convey two-state link information to destination which in turn is processed through an easy to compute routing lexicon and a corresponding lexical algorithm for path selection in case of availability of multiple paths. Multiple paths are represented in a path space through a proposed cost model that encompasses hop-count, weak links and a quantity weakness factor of each link, depending upon a thresholding mechanism which in turn declares a link to be either healthy (aka usable) or weak (aka unusable). Using the weakness factor, the success probability of data delivery over weak link turns out to be a fraction of success probability at healthy link. The mathematical model along with the experiments done for LABILE show that proposed composite metric and its parsing scheme together achieve link robustness consistently by evading the link failures, as the number of weak links is fairly reduced in lexical path as compared to the hop-count-based metric. Increased data delivery is obtained through preventing retransmissions as on failure-prone links.     

一种支持多维资源描述的高效P2P路由算法

在分析现有P2P(peer to peer)路由算法的基础上,提出了一种基于二阶矩定位、支持多维资源数据描述的高效资源路由算法--FAN(flabellate addressable network)路由算法.FAN算法将节点映射到统一的多维笛卡尔空间,并以节点相对空间原点的二阶矩作为子空间管理和资源搜索的依据.FAN路由算法具有O(log(N/k))的高路由效率,在节点加入和退出FAN网络时,更新路由信息的代价为O(klog(N/k)).实验结果表明,FAN路由算法具有路由效率高、维护代价小的优点,是一种P2P环境中支持多维资源数据描述的高效结构化资源路由算法.而且,目前部分基于CAN(content-addressable network)网络的改进算法也可以在FAN网络中适用,并获得更好的路由效率和更低的维护代价.     

基于矢量测量的多约束路径选择

多约束路径(multi-constrained path,简称MCP)选择问题是QoS路由问题面临的重要挑战之一.现有的MCP算法不能兼顾降低计算复杂性、提高响应速度和防止可行解丢失等方面的缺点.另外,单纯依靠线性路径长度方程(LPLF)或非线性路径长度方程(NLPLF)都不能有效解决QoS路由问题.定义了崭新的法线测量路径长度方程,并基于该方程提出了解决m约束MCP问题的NMMCP(normal measure based MCP)算法.NMMCP不仅是在线计算与预计算,同时也是LPLF与NLPLF的良     

Optimal paths in probabilistic networks: A case with temporary preferences

The classical shortest route problem in networks assumes deterministic arc weights and a utility (or cost) function that is linear over path weights for route evaluation. When the environment is stochastic and the “traveler's” utility function for travel attributes is nonlinear, we define “optimal paths” that maximize the expected utility.We review the concepts of temporary and permanent preferences for comparing a traveler's preference for available subpaths. It has been shown before that when the utility function is linear or exponential, permanent preferences prevail and an efficient Dijkstra-type algorithm [3] is available that determines the optimal path.In this paper an exact procedure is developed for determining an optimal path when the utility function is quadratic—a case where permanent preferences do not always prevail. The algorithm uses subpath comparison rules to establish permanent preferences, when possible, among subpaths of the given network. Although in the worst case the algorithm implicitly enumerates all paths (the number of operations increasing exponentially with the size of the network), we find, from the computational experience reported, that the number of potentially optimal paths to evaluate is generally manageable.     

Dynamic routing with inaccurate link state information in integrated IP-over-WDM networks

In this paper, we investigate the problem of dynamically routing bandwidth-guaranteed label switched paths (LSPs) in integrated IP-over-wavelength division multiplexed (WDM) networks with inaccurate link state information. To select a good path, a routing algorithm needs up-to-date link state information. This leads to excessive update overhead and scalability problems. In real networks, from the practical point of view, in order to avoid extensive overhead of advertising and processing link state information, updates need to be made periodically or based on a threshold trigger. This leads to inaccuracies in the link state information. Our contribution is that we consider the routing problem taking into consideration the uncertainty of link state parameters due to wavelength inaccuracy in addition to bandwidth inaccuracy. Based on the threshold-triggered update scheme, we present a probabilistic method to model the uncertainty of link state parameters. We then define a cost function reflecting the uncertainty. Depending on different cost metrics chosen to be optimized, we propose two routing algorithms considering the uncertainty of link state parameters. The objective is to minimize the impact of inaccurate information so that the blocking probability as well as setup failures are reduced. We use various performance metrics such as total blocking probability, blocking probability due to setup failures, blocking probability due to routing failures, bandwidth update frequency, and wavelength update frequency to evaluate the effectiveness of the proposed algorithms. Through extensive simulation experiments, we show that our algorithms can significantly reduce the impact of inaccurate link state information and perform very well.     

Packet Routing in Networks with Long Wires

In this paper, we examine the packet routing problem for networks with wires of differing length. We consider this problem in a network independent context, in which routing time is expressed in terms of "congestion" and "dilation" measures for a set of packet paths. We give, for any constant ε > 0, a randomized on-line algorithm for routing any set of N packets in O((C lg^ε(Nd) + D lg(Nd))/lg lg(Nd)) time, where C is the maximum congestion and D is the length of the longest path, both taking wire delays into account, and d is the longest path in terms of number of wires. We also show that for edge-simple paths, there exists a schedule (which could be found off-line) of length O((cd_max + D) (lg(d_max)/lg lg (d_max))), where d_max is the maximum wire delay in the network. These results improve upon previous routing results which assume that unit time suffices to traverse a wire of any length. They also yield improved results for job-shop scheduling as long as we incorporate a technical restriction on the job-shop problem.     

A parallel routing algorithm on recursive cube of rings networks employing Hamiltonian circuit Latin square

Recursive cube of rings (RCR) networks [Y. Sun, P. Cheung, X. Lin, Recursive cube of rings: a new topology for interconnection networks, IEEE Trans. Parallel Dist. Syst. 11 (3) (2000) 275-286] can be widely used in the design and implementation of parallel processing architectures. In this paper, we investigate the routing of a message on RCR networks, that is a key to the performance of this network. We would like to transmit k+1 packets from a source node to a destination node simultaneously along paths on RCR networks, the ith packet will traverse along the ith path (1?i?k+1). In order for all packets to arrive at a destination node quickly and securely, the ith path must be node-disjoint from all other paths. For construction of these paths, employing Hamiltonian circuit Latin square (HCLS), we present O(n²) parallel routing algorithm on RCR networks.     

Araneola: A scalable reliable multicast system for dynamic environments

This paper presents Araneola (Araneola means “little spider” in Latin.), a scalable reliable application-level multicast system for highly dynamic wide-area environments. Araneola supports multi-point to multi-point reliable communication in a fully distributed manner, while incurring constant load (in terms of message and space complexity) on each node. For a tunable parameter k≥3, Araneola constructs and dynamically maintains a basic overlay structure in which each node’s degree is either k or k+1, and roughly 90% of the nodes have degree k. Empirical evaluation shows that Araneola’s basic overlay achieves three important mathematical properties of k-regular random graphs (i.e., random graphs in which each node has exactly k neighbors) with N nodes: (i) its diameter grows logarithmically with N; (ii) it is generally k-connected; and (iii) it remains highly connected following random removal of linear-size subsets of edges or nodes. The overlay is constructed and maintained at a low cost: each join, leave, or failure is handled locally, and entails the sending of only about 3k messages in total, independent of N. Moreover, this cost decreases as the churn rate increases.The low degree of Araneola’s basic overlay structure allows for allocating plenty of additional bandwidth for specific application needs. In this paper, we give an example for such a need — communicating with nearby nodes; we enhance the basic overlay with additional links chosen according to geographic proximity and available bandwidth. We show that this approach, i.e., a combination of random and nearby links, reduces the number of physical hops messages traverse without hurting the overlay’s robustness, as compared with completely random Araneola overlays (in which all the links are random) with the same average node degree.Given Araneola’s overlay, we sketch out several message dissemination techniques that can be implemented on top of this overlay. We present a full implementation and evaluation of a gossip-based multicast scheme, with up to 10,000 nodes. We show that compared with a (non-overlay-based) gossip-based multicast protocol, gossiping over Araneola achieves substantial improvements in load, reliability, and latency.     

Dynamic load balancing in IP-over-WDM optical burst switching networks

In this paper, we consider the problem of dynamic load balancing in wavelength division multiplexing (WDM)-based optical burst switching (OBS) networks. We propose a load balancing scheme based on adaptive alternate routing aimed at reducing burst loss. The key idea of adaptive alternate routing is to reduce network congestion by adaptively distributing the load between two pre-determined link-disjoint alternative paths based on the measurement of the impact of traffic load on each of them. We develop two alternative-path selection schemes to select link-disjoint alternative paths to be used by adaptive alternate routing. The path selection schemes differ in the way the cost of a path is defined and in the assumption made about the knowledge of the traffic demands. Through extensive simulation experiments for different traffic scenarios, we show that the proposed dynamic load balancing algorithm outperforms the shortest path routing and static alternate routing algorithms.     

一种SRIO网络负载均衡最短路径路由算法

在串行RapidIO传输过程中,路由选路算法是影响传输性能的重要因素之一。针对串行高速输入-输出(SRIO)网络深度优先搜索分配路径非最优问题,提出一种负载均衡最短路径路由算法。通过广度优先搜索对SRIO网络中的节点进行枚举并建立网络拓扑信息,以路由跳数定义路由的成本,根据改进Floyd-WarShall算法计算并保存交换节点间的K最短路径。给出预期负载的概念和链路上的路由路径数量来定义链路的负载,采用负载均衡算法从K最短路径中进行选路,建立SRIO网络最短路径约束的负载均衡路由。实验结果表明,与深度遍历路由算法、最小跳数算法相比,该算法在网络传输平均跳数、链路平均负载和链路负载均衡方面有更好的表现,能够有效提升SRIO路由网络的稳定性。     

Stability routing with constrained path length for improved routability in dynamic MANETs

Quality of service (QoS) routing is known to be an NP-hard problem in case of two or more additive constraints, and several exact algorithms and heuristics have been proposed to address this issue. In this paper, we consider a particular two-constrained quality of service routing problem maximizing path stability with a limited path length in the quest of improving routability in dynamic multi-hop mobile wireless ad hoc networks. First, we propose a novel exact algorithm to solve the optimal weight-constrained path problem. We instantiate our algorithm to solve the most stable path not exceeding a certain number of hops, in polynomial time. This algorithm is then applied to the practical case of proactive routing in dynamic multi-hop wireless ad hoc networks. In these networks, an adequate compromise between route stability and its length in hops is essential for appropriately mitigating the impact of the network dynamics on the validity of established routes. Secondly, we set up a common framework for the comparison between three families of proactive routing: the shortest path-based routing, the most stable path-based routing and our proposed most stable constrained path routing. We show then through extensive simulations that routing based on our proposed algorithm selects appropriate stable paths yielding a very high routability with an average path length just above that of the shortest paths.