An origin-based model for unique shortest path routing

Link weights are the main parameters of shortest path routing protocols, the most commonly used protocols for IP networks. The problem of optimally setting link weights for unique shortest path routing is addressed. Due to the complexity of the constraints involved, there exist challenges to formulate the problem in such a way based on which a more efficient solution algorithm than the existing ones may be developed. In this paper, an exact formulation is first introduced and then mathematically proved correct. It is further illustrated that the formulation has advantages over a prior one in terms of both constraint structure and model size for a proposed decomposition method to solve the problem.     

一类网络速率控制和路由联合算法的稳定性

近年来,动态多路径路由下网络速率控制的研究受到广泛关注.本文提出了一个新的速率控制和多路径路由联合的算法,该算法的特点是具有唯一的平衡点.利用传统的Lyapunov方法,我们证明算法在没有传播时延情形下的全局稳定性.而且,更为重要的是,即使考虑传播时延,在一定的条件下,该算法是局部稳定的.在平衡点处,每条路由上的速率非零.这一事实不但去掉了Kelly F P,Voice T(2005)结果中内部平衡点的假设条件,而且也可以理解为一种探测机制.我们通过仿真证实了算法的正确性,同时仿真结果也表明局部稳定性的吸引域可以很大,甚至是全局稳定的.     

A branch-and-cut algorithm for the Steiner tree problem with delays

In this paper, we investigate the Steiner tree problem with delays, which is a generalized version of the Steiner tree problem applied to multicast routing. For this challenging combinatorial optimization problem, we present an enhanced directed cut-based MIP formulation and an exact solution method based on a branch-and-cut approach. Our computational study reveals that the proposed approach can optimally solve hard dense instances.     

Stability analysis for networked control systems with sampling,transmission protocols and input delays

In this paper, the stability problem is investigated for networked control systems. Input delays and multiple communication imperfections containing time-varying transmission intervals and transmission protocols are considered. A unified framework based on the hybrid systems with memory is proposed to model the whole networked control system. Hybrid systems with memory are used to model hybrid systems affected by delays and permit multiple jumps at a jumping instant. The stability analysis depends on the Lyapunov–Krasovskii functional approaches for hybrid systems with memory and the proposed stability theorem does not need strict decrease of the Lyapunov–Krasovskii functional during jumps. Based on the developed stability theorems, stability conditions for networked control systems are established. An explicit formula is given to compute the maximal allowable transmission interval. In the special case that the networked control system contains linear dynamics, an explicit Lyapunov functional is constructed and stability conditions in terms of linear matrix inequalities (LMI) are proposed. Finally, an example of a chemical batch reactor is given to illustrate the effectiveness of the proposed results.     

Deterministic Routing With Bounded Buffers: Turning Offline Into Online Protocols

In this paper we present a deterministic protocol for routing arbitrary permutations in arbitrary networks. The protocol is analyzed in terms of the size of the network and the routing number of the network. Given a network H of n nodes, the routing number of H is defined as the maximum over all permutations on {1, ..., n} of the minimal number of steps to route offline in H. We show that for any network H of size n with routing number R our protocol needs time to route any permutation in H using only constant size edge buffers. This significantly improves all previously known results on deterministic routing. In particular, our result yields optimal deterministic routing protocols for arbitrary networks with diameter or bisection width , constant. Furthermore we can extend our result to deterministic compact routing. This yields, e.g., a deterministic routing protocol with runtime O(R logn) for arbitrary bounded degree networks if only O(logn) bits are available at each node for storing routing information. Our protocol is a combination of a generalized ``routing via simulation' technique with an new deterministic protocol for routing h-relations in an extended version of a multibutterfly network. This protocol improves upon all previous routing protocols known for variants of the multibutterfly network. The ``routing via simulation' technique used here extends a method previously introduced by the authors for designing compact routing protocols. Received July 18, 1997     

A robust optimization approach to dispatching technicians under stochastic service times

We consider the problem of dispatching technicians to service/repair geographically distributed equipment. This problem can be cast as a vehicle routing problem with time windows, where customers expect fast response and small delays. Estimates of the service time, however, can be subject to a significant amount of uncertainty due to misdiagnosis of the reason for failure or surprises during repair. It is therefore crucial to develop routes for the technicians that would be less sensitive to substantial deviations from estimated service times. In this paper we propose a robust optimization model for the vehicle routing problem with soft time windows and service time uncertainty and solve real-world instances with a branch and price method. We evaluate the efficiency of the approach through computational experiments on real industry routing data.     

基于多目标规划的飞机路径恢复最优化算法研究

本文针对同一机场中同机型的多架飞机受到干扰后, 飞机路径恢复的多目标最优化问题进行研究。首先根据航空公司实际航班调整的常用原则和航班干扰管理的基本思想, 基于连接网络建立多目标规划模型, 其中两个目标按照优先级排列:第一个目标为最小化航班的最大延误时间, 第二个目标为最小化参与交换的飞机数量。然后根据该问题的航班波结构特点, 结合求解多目标规划的分层序列法, 分析优化问题的若干最优性质, 并基于快速排序算法和最小费用路算法设计出多项式算法。最后用算例验证了算法的有效性。该研究结果可以为航空公司减少航班延误提供理论和技术支持。     

Intra-domain traffic engineering with shortest path routing protocols

Throughout the last decade, extensive deployment of popular intra-domain routing protocols such as open shortest path first and intermediate system–intermediate system, has drawn an ever increasing attention to Internet traffic engineering. This paper reviews optimization techniques that have been deployed for managing intra-domain routing in networks operated with shortest path routing protocols, and the state-of-the-art research that has been carried out in this direction.     

Intra-domain traffic engineering with shortest path routing protocols

Throughout the last decade, extensive deployment of popular intra-domain routing protocols such as open shortest path first (OSPF) and intermediate system–intermediate system (IS-IS), has drawn an ever increasing attention to internet traffic engineering. This paper reviews optimization techniques that have been deployed for managing intra-domain routing in networks operated with shortest path routing protocols, and the state-of-the-art research that has been carried out in this direction.     

Routing optimization in packet switching communication networks

For routing assignments a special model and an optimization algorithm are proposed. The efficiency of the routing assignments is evaluated by the average value of the total cost of delays for all packets in the network. It is the objective function. The main idea is that traffic, which is transmitted from the source node to the destination node, can be split between two or more logical paths. The minimum of the objective function can be found by varying the traffic on every path and simultaneously from all the source nodes to the destination nodes. If this approach is applied, then the objective function is nonseparable and nonlinear. Because its shape is unknown in advance, an adaptive nonlinear optimization algorithm is proposed. For evaluating its efficiency a special set of test functions has been used.     

基于交通流的多模糊时间窗车辆路径优化

研究了基于交通流的多模糊时间窗车辆路径问题,考虑了实际中不断变化的交通流以及客户具有多个模糊时间窗的情况,以最小化配送总成本和最大化客户满意度为目标,构建基于交通流的多模糊时间窗车辆路径模型。根据伊藤算法的基本原理,设计了求解该模型的改进伊藤算法,结合仿真算例进行了模拟计算,并与蚁群算法的计算结果进行了对比分析,结果表明,利用改进伊藤算法求解基于交通流的多模糊时间窗车辆路径问题,迭代次数小,效率更高,能够在较短的时间内收敛到全局最优解,可以有效的求解多模糊时间窗车辆路径问题。     

Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks

In this study we deal with network routing decisions and approximate performance evaluation approaches for generalized open queuing networks (OQN), in which commodities enter the network, receive service at one or more arcs and then leave the network. Exact performance evaluation has been applied for the analysis of Jackson OQN, where the arrival and service processes of the commodities are assumed to be Poisson. However, the Poisson processes’ hypotheses are not a plausible or acceptable assumption for the analysis of generalized OQN, as their arrival and service processes can be much less variable than Poisson processes, resulting in overestimated system performance measures and inappropriate flow routing solutions. In this paper we merge network routing algorithms and network decomposition methods to solve multicommodity flow problems in generalized OQN. Our focus is on steady-state performance measures as average delays and waiting times in queue. The main contributions are twofold: (i) to highlight that solving the corresponding multicommodity flow problem by representing the generalized OQN as a Jackson OQN may be a poor approximation and may lead to inaccurate estimates of the system performance measures, and (ii) to present a multicommodity flow algorithm based on a routing step and on an approximate decomposition step, which leads to much more accurate solutions. Computational results are presented in order to show the effectiveness of the proposed approach.     

Optimal cost sharing for capacitated facility location games

We consider cost sharing for a class of facility location games, where the strategy space of each player consists of the bases of a player-specific matroid defined on the set of resources. We assume that resources have nondecreasing load-dependent costs and player-specific delays. Our model includes the important special case of capacitated facility location problems, where players have to jointly pay for opened facilities. The goal is to design cost sharing protocols so as to minimize the resulting price of anarchy and price of stability. We investigate two classes of protocols: basic protocols guarantee the existence of at least one pure Nash equilibrium and separable protocols additionally require that the resulting cost shares only depend on the set of players on a resource. We find optimal basic and separable protocols that guarantee the price of stability/price of anarchy to grow logarithmically/linearly in the number of players. These results extend our previous results (cf. von Falkenhausen & Harks, 2013), where optimal basic and separable protocols were given for the case of symmetric matroid games without delays.     

On the Hardness of Equal Shortest Path Routing

In telecommunication networks packets are carried from a source s to a destination t on a path that is determined by the underlying routing protocol. Most routing protocols belong to the class of shortest path routing protocols. In such protocols, the network operator assigns a length to each link. A packet going from s to t follows a shortest path according to these lengths. For better protection and efficiency, one wishes to use multiple (shortest) paths between two nodes. Therefore the routing protocol must determine how the traffic from s to t is distributed among the shortest paths. In the protocol called OSPF-ECMP (for Open Shortest Path First-Equal Cost Multiple Path) the traffic incoming at every node is uniformly balanced on all outgoing links that are on shortest paths. In that context, the operator task is to determine the “best” link lengths, toward a goal such as maximizing the network throughput for given link capacities.In this work, we show that the problem of maximizing even a single commodity flow for the OSPF-ECMP protocol cannot be approximated within any constant factor ratio. Besides this main theorem, we derive some positive results which include polynomial-time approximations and an exponential-time exact algorithm. We also prove that despite their weakness, our approximation and exact algorithms are, in a sense, the best possible.     

Fault tolerant routing algorithm based on the artificial potential field model in Network-on-Chip

Recent advances in semiconductor technology enable the VLSI chips to integrate hundreds of intellectual properties with complex functionality. However, as the chip scales, the probability of faults is increasing, making fault tolerance a key concern in designing the large scale chips. The fault tolerant routing algorithms can guarantee sustained communication even the faults exist. It is an efficient technique to achieve fault tolerance in Networks-on-Chip. In this paper, we propose a new model based on the theory of artificial potential field (APF) to design various fault tolerant routing algorithms. In our model, the faults are considered as the poles of the repulsive potential fields while the destinations as the poles of the attractive potential fields. Messages are attracted to destinations and repelled by faults in the combined artificial potential field. The parameters used in the proposed APF based model are optimized through theoretical analysis and simulation experiments. They can support flexible fault tolerant routing algorithms. Finally, we evaluate the performance of the proposed fault tolerant routing algorithm based on the APF model in 2D-mesh NoCs with random faults. The simulation results show that the proposed APF based model is feasible and the routing algorithm can maintain good network performance.     

LP-Based Heuristic Algorithms for Interconnecting Token Rings via Source Routing Bridges

We develop a method to determine the topology of a network that interconnects a number of token rings using source routing bridges. The purpose is to compute a topology that provides low response delays for network users at a minimal cost of bridge installations. We formulate this network design problem as a mixed binary integer linear program. We develop effective heuristic algorithms. The algorithms exploit the topology and routing solutions of the linear programming relaxation in a sophisticated manner which we believe is new in the literature. The model incorporates performance issues, such as network stability, bridge overflow, back pressure effect and broadcast storm, that are specific to the underlying communication technology. By formally incorporating these performance issues, we tighten the model formulation and improve the quality of the LP bound considerably. Computational results are reported for problems with up to 20 token rings and 190 potential bridge locations.     

Analytical Studies of Energy–Time Efficiency of Blocking Expanding Ring Search

This paper investigates the energy–time efficiency of the Blocking Expanding Ring Search algorithms (BERS) using an extended graph model. BERS is an energy efficient alternative that was developed recently based on the Expanding Ring Search (ERS). ERS is widely applied in reactive routing protocols for mobile ad hoc networks. Most studies in this area focus on minimising either energy consumption or search latency, but few look into the strong correlation between the energy saving and the increased latency incurred. We analyse, in this study, the concurrency mechanism of BERS and have developed BERS*, an enhanced scheme based on BERS. Our results show that, among the three schemes (BERS*, BERS and ERS), BERS* incurs the least latency when the hop number of the route nodes is greater than 3, and has achieved the best performance in terms of energy–time efficiency when the hop number of the route nodes is greater than 7. We have also discovered the conditions that allow collective optimisation of BERS* and ERS.     

Routing trains through a railway station based on a node packing model

In this paper, we describe the problem of routing trains through a railway station. This routing problem is a subproblem of the automatic generation of timetables for the Dutch railway system. The problem of routing trains through a railway station is the problem of assigning each of the involved trains to a route through the railway station, given the detailed layout of the railway network within the station and given the arrival and departure times of the trains. When solving this routing problem, several aspects such as capacity, safety, and customer service have to be taken into account. In this paper, we describe this routing problem in terms of a weighted node packing problem. Furthermore, we describe an algorithm for solving this routing problem to optimality. The algorithm is based on preprocessing, valid inequalities, and a branch-and-cut approach. The preprocessing techniques aim at identifying superfluous nodes which can be removed from the problem instance. The characteristics of the preprocessing techniques with respect to propagation are investigated. We also present the results of a computational study in which the model, the preprocessing techniques and the algorithm are tested based on data related to the railway stations Arnhem, Hoorn and Utrecht CS in the Netherlands.     

A comparison of routing sets for robust network design

Designing a network able to route a set of non-simultaneous demand vectors is an important problem arising in telecommunications. In this paper, we compare the optimal capacity allocation costs for six routing sets: affine routing, volume routing and its two simplifications, the routing based on an unrestricted 2-cover of the uncertainty set, and the routing based on a cover delimited by a hyperplane.