Efficient techniques and tools for intra‐domain traffic engineering

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 costs subject to the traffic demands and the protocol constraints. However, determining a link weight combination that meets a network operator's objectives is a difficult task. In this paper, we study the link weight optimization problem in intra‐domain networks. This problem is proved to be NP‐hard with hard protocol constraints, e.g., a flow is evenly distributed along the shortest paths between its origin and destination nodes. We present two fast heuristic approaches to generate efficient link metrics for intra‐domain routing. Some promising experimental results are reported.     

Caching and optimized request routing in cloud-based content delivery systems

Geographically distributed cloud platforms enable an attractive approach to large-scale content delivery. Storage at various sites can be dynamically acquired from (and released back to) the cloud provider so as to support content caching, according to the current demands for the content from the different geographic regions. When storage is sufficiently expensive that not all content should be cached at all sites, two issues must be addressed: how should requests for content be routed to the cloud provider sites, and what policy should be used for caching content using the elastic storage resources obtained from the cloud provider. Existing approaches are typically designed for non-elastic storage and little is known about the optimal policies when minimizing the delivery costs for distributed elastic storage.In this paper, we propose an approach in which elastic storage resources are exploited using a simple dynamic caching policy, while request routing is updated periodically according to the solution of an optimization model. Use of pull-based dynamic caching, rather than push-based placement, provides robustness to unpredicted changes in request rates. We show that this robustness is provided at low cost. Even with fixed request rates, use of the dynamic caching policy typically yields content delivery cost within 10% of that with the optimal static placement. We compare request routing according to our optimization model to simpler baseline routing policies, and find that the baseline policies can yield greatly increased delivery cost relative to optimized routing. Finally, we present a lower-cost approximate solution algorithm for our routing optimization problem that yields content delivery cost within 2.5% of the optimal solution.     

DHT协议设计选项与抖动问题关联分析

因节点加入和离开引起的抖动是增加结构化P2P网络路由表更新代价的主要原因。为了找出影响网络抖动的关键因素,分析了影响抖动的路由方式、邻居选择、节点加入和节点离开以及并行查找等策略因素,发现任意两种DHT网络分别采用的五种策略都至少有两种不同,对两种DHT网络直接进行比较就很难确定哪些策略能更有效地降低抖动。因此,提出在同一网络内用不同的单个策略对网络抖动进行比较和分析的方法,称之为CSP。通过对现有DHT算法进行改进,使用CSP方法对不同的单个策略进行比较,得出以下结论:迭代路由、快速加入和周期性恢复策略和有效的邻居选择算法能更有效地降低网络的抖动。     

Management of Railroad Impedances for Shortest Path-based Routing

The routing of traffic is a major logistical concern for transportation services. For railroads, routing has historically been handled by large, hard-coded tables. Norfolk Southern Railways developed a more sophisticated routing system that takes advantage of network flow theory. Their Algorithmic Blocking and Classification (ABC) system routes traffic commodities (waybills) according to shortest paths. The routing of multiple waybills is a form of the Multicommodity Flow Problem (MCFP).Since routes for commodities are often predetermined, the success of ABC relies on finding costs that make the desired routes shortest paths. The problem of finding costs to make a solution optimal is called inverse optimization. The procedure of finding an adequate set of costs for the ABC system is known as calibration and is a form of the Inverse Multicommodity Flow Problem (IMCFP).Calibration seeks a solution that makes all predetermined paths uniquely optimal with respect to the costs. The calibration problem (IMCFP) can be solved optimally using the simplex method. However, direct application of the simplex algorithm is not always advantageous, especially for large problems. We present formulations, a primal-dual solution algorithm, and a hot start basis-finding algorithm for deriving optimal solutions. In addition, we can use Lagrangian relaxation to find good heuristic solutions.     

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.     

A tabu search procedure for coordinating production,inventory and distribution routing problems

This paper addresses the problem of optimally coordinating a production‐distribution system over a multi‐period finite horizon, where a facility production produces several items that are distributed to a set of customers by a fleet of homogeneous vehicles. The demand for each item at each customer is known over the horizon. The production planning determines how much to produce of each item in every period, while the distribution planning defines when customers should be visited, the amount of each item that should be delivered to customers and the vehicle routes. The objective is to minimize the sum of production and inventory costs at the facility, inventory costs at the customers and distribution costs. We also consider a related problem of inventory routing, where a supplier receives or produces known quantities of items in each period and has to solve the distribution problem. We propose a tabu search procedure for solving such problems, and this approach is compared with vendor managed policies proposed in the literature, in which the facility knows the inventory levels of the customers and determines the replenishment policies.     

Solving capacitated part‐routing problems with setup times and costs: a Dantzig–Wolfe decomposition‐based solution approach

We develop a Dantzig–Wolfe decomposition‐based approach for solving the capacitated part‐routing problem with routing flexibilities, setup times, and setup costs. Large instances of the problem are solved to near‐optimality using the proposed approach. The computational performance of the approach is compared with that of the existing Lagrangean relaxation‐based approach in terms of solution quality and computational times.     

Dynamic shortest path problems: Hybrid routing policies considering network disruptions

Traffic network disruptions lead to significant increases in transportation costs. We consider networks in which a number of links are vulnerable to these disruptions leading to a significantly higher travel time on these links. For these vulnerable links, we consider known link disruption probabilities and knowledge of transition probabilities for recovering from or getting into a disruption. We develop a framework based on dynamic programming in which we formulate and evaluate different known online and offline routing policies. Next to this, we develop computation-time-efficient hybrid routing policies. To test the efficiency of the different routing policies, we develop a test bed of networks based on a number of characteristics and analyze the results in terms of routes, cost performance and calculation times. Our results show that a significant part of the cost reduction can be obtained by considering only a limited part of the network in detail. The performance of our proposed hybrid policy is only slightly worse than the optimal policy.     

A variable neighborhood search simheuristic for the multiperiod inventory routing problem with stochastic demands

The inventory routing problem (IRP) combines inventory management and delivery route‐planning decisions. This work presents a simheuristic approach that integrates Monte Carlo simulation within a variable neighborhood search (VNS) framework to solve the multiperiod IRP with stochastic customer demands. In this realistic variant of the problem, our goal is to establish the optimal refill policies for each customer–period combination, that is, those individual refill policies that minimize the total expected cost over the periods. This cost is the aggregation of both expected inventory and routing costs. Our simheuristic algorithm allows to consider the inventory changes between periods generated by the realization of the random demands in each period, which have an impact on the quantities to be delivered in the next period and, therefore, on the associated routing plans. A range of computational experiments are carried out in order to illustrate the potential of our simulation–optimization approach.     

Analysis of the maximum level policy in a production-distribution system

We consider a production-distribution system, where a facility produces one commodity which is distributed to a set of retailers by a fleet of vehicles. Each retailer defines a maximum level of the inventory. The production policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The overall cost is composed by fixed and variable production costs at the facility, inventory costs at both facility and retailers and routing costs. We study two different types of replenishment policies. The well-known order-up to level (OU) policy, where the quantity shipped to each retailer is such that the level of its inventory reaches the maximum level, and the maximum level (ML) policy, where the quantity shipped to each retailer is such that the inventory is not greater than the maximum level. We first show that when the transportation is outsourced, the problem with OU policy is NP-hard, whereas there exists a class of instances where the problem with ML policy can be solved in polynomial time. We also show the worst-case performance of the OU policy with respect to the more flexible ML policy. Then, we focus on the ML policy and the design of a hybrid heuristic. We also present an exact algorithm for the solution of the problem with one vehicle. Results of computational experiments carried out on small size instances show that the heuristic can produce high quality solutions in a very short amount of time. Results obtained on a large set of randomly generated problem instances are also shown, aimed at comparing the two policies.     

ON MULTI‐CLASS COST‐SENSITIVE LEARNING

Rescaling is possibly the most popular approach to cost‐sensitive learning. This approach works by rebalancing the classes according to their costs, and it can be realized in different ways, for example, re‐weighting or resampling the training examples in proportion to their costs, moving the decision boundaries of classifiers faraway from high‐cost classes in proportion to costs, etc. This approach is very effective in dealing with two‐class problems, yet some studies showed that it is often not so helpful on multi‐class problems. In this article, we try to explore why the rescaling approach is often helpless on multi‐class problems. Our analysis discloses that the rescaling approach works well when the costs are consistent, while directly applying it to multi‐class problems with inconsistent costs may not be a good choice. Based on this recognition, we advocate that before applying the rescaling approach, the consistency of the costs must be examined at first. If the costs are consistent, the rescaling approach can be conducted directly; otherwise it is better to apply rescaling after decomposing the multi‐class problem into a series of two‐class problems. An empirical study involving 20 multi‐class data sets and seven types of cost‐sensitive learners validates our proposal. Moreover, we show that the proposal is also helpful for class‐imbalance learning.     

A column‐generation‐based approach to fleet design problems mixing owned and hired vehicles

We look at the problem of choosing a fleet of vehicles to carry out delivery tasks across a long time horizon. The delivery quantities may vary significantly from day to day, and from season to season, and the underlying routing problem may have rich constraints, for example, time windows, multiple compartments, multiple commodities, and compatibility constraints. We consider the option of hiring extra vehicles from external carriers in order to efficiently carry out the day‐to‐day operations while containing the costs of owning the fleet. The goal is to design a fleet so as to minimize the sum of costs of routing the fleet every day of the horizon, the acquisition costs, the maintenance costs, and the costs of hiring external vehicles. In the literature, there is no previous work on fleet design for a long time horizon, which also considers the hiring options. We propose to tackle the problem using column generation and develop three different heuristics. The methods proposed are tested and compared on a set of real‐world problems. It is also shown how introducing the possibility of hiring helps reducing the overall cost and the number of idle vehicles over the planning horizon.     

Dynamic vs. Oblivious Routing in Network Design

Consider the robust network design problem of finding a minimum cost network with enough capacity to route all traffic demand matrices in a given polytope. We investigate the impact of different routing models in this robust setting: in particular, we compare oblivious routing, where the routing between each terminal pair must be fixed in advance, to dynamic routing, where routings may depend arbitrarily on the current demand. Our main result is a construction that shows that the optimal cost of such a network based on oblivious routing (fractional or integral) may be a factor of Ω(log n) more than the cost required when using dynamic routing. This is true even in the important special case of the asymmetric hose model. This answers a question in (Chekuri, SIGACT News 38(3):106–128, 2007), and is tight up to constant factors. Our proof technique builds on a connection between expander graphs and robust design for single-sink traffic patterns (Chekuri et al., Networks 50(1):50–54, 2007).     

Information sharing under different warranty policies with cost sharing in supply chains

In practice, it is found that a product warranty can be provided by either the supplier or the manufacturer. As supply chains are increasingly integrated today, warranty costs are usually shared between the supplier and the manufacturer. In this paper, we model two different warranty policies based on which party provides the warranty: manufacturer warranty and supplier warranty. Considering the demand uncertainty and demand forecast, we analyze the information sharing strategy under these two warranty policies. Our results show that the manufacturer has an incentive to share the demand forecast information under both warranty policies when the cost efficiency in providing a warranty is high, which is different from the existing literature on the incentive for demand information sharing in the supply chain. Moreover, we find that it will hurt the party who determines the warranty period but benefit the other party.     

Coordination of split deliveries in one-warehouse multi-retailer distribution systems

In this paper, we consider a distribution system where a warehouse is responsible for replenishing the inventories at multiple retailers by a fleet of vehicles of limited capacity. If a distribution policy of the system involves split deliveries, that is, the inventory of at least one retailer is replenished by using multiple vehicle routes, the coordination of the deliveries can further reduce the inventory cost of the retailer. We consider the coordination where two split deliveries are realized by direct shipping and multiple-stop shipping, respectively. To the best of our knowledge, this kind of coordination was never studied in the literature but can find its application in inventory routing problems. This paper proposes and analyses a class of coordination policies for the split deliveries which can reduce the inventory costs of the retailers without increasing transportation costs. A non-linear programming model is established for formulating the class of polices. Because the optimal coordination policy corresponding to an optimal solution of the model may be hard to find and/or implement, two simple but effective coordination policies are proposed. The inventory cost savings realized by the two policies are evaluated analytically and algorithmically. Our theoretical analysis and computational experiments show that both policies are effective. Under certain conditions, they can save 50% of the inventory costs at the retailers without increasing transportation costs.     

Subjective-cost policy routing

We study a model of path-vector routing in which nodes’ routing policies are based on subjective cost assessments of alternative routes. The routes are constrained by the requirement that all routes to a given destination must be confluent. We show that it is NP-hard to determine whether there is a set of stable routes. We also show that it is NP-hard to find a set of confluent routes that minimizes the total subjective cost; it is hard even to approximate the minimum cost closely. These hardness results hold even for very restricted classes of subjective costs.     

Routing fleets with multiple driving ranges: Is it possible to use greener fleet configurations?

This paper discusses the vehicle routing problem with multiple driving ranges (VRPMDR), an extension of the classical routing problem where the total distance each vehicle can travel is limited and is not necessarily the same for all vehicles – heterogeneous fleet with respect to maximum route lengths. The VRPMDR finds applications in routing electric and hybrid-electric vehicles, which can only cover limited distances depending on the running time of their batteries. Also, these vehicles require from long charging times, which in practice makes it difficult to consider en route recharging. The paper formally introduces the problem, describes an integer programming formulation and a multi-round heuristic algorithm that iteratively constructs a solution for the problem. Using a set of benchmarks adapted from the literature, the algorithm is then employed to analyze how distance-based costs are increased when considering ‘greener’ fleet configurations – i.e., when using electric vehicles with different degrees of autonomy.     

Sensor-centric energy-constrained reliable query routing for wireless sensor networks

Standard wireless sensor network models emphasize energy efficiency and distributed decision-making by considering untethered and unattended sensors. To this we add two constraints—the possibility of sensor failure and the fact that each sensor must tradeoff its own resource consumption with overall network objectives. In this paper, we develop an analytical model of energy-constrained, reliable, data-centric information routing in sensor networks under all the above constraints. Unlike existing techniques, we use game theory to model intelligent sensors thereby making our approach sensor-centric. Sensors behave as rational players in an N-player routing game, where they tradeoff individual communication and other costs with network wide benefits. The outcome of the sensor behavior is a sequence of communication link establishments, resulting in routing paths from reporting to querying sensors. We show that the optimal routing architecture is the Nash equilibrium of the N-player routing game and that computing the optimal paths (which maximizes payoffs of the individual sensors) is NP-Hard with and without data-aggregation. We develop a game-theoretic metric called path weakness to measure the qualitative performance of different routing mechanisms. This sensor-centric concept which is based on the contribution of individual sensors to the overall routing objective is used to define the quality of routing (QoR) paths. Analytical results on computing paths of bounded weakness are derived and game-theoretic heuristics for finding approximately optimal paths are presented. Simulation results are used to compare the QoR of different routing paths derived using various energy-constrained routing algorithms.     

Robust routing and optimal partitioning of a traffic demand polytope

In this paper we consider the problem of optimal partitioning of a traffic demand polytope using a hyperplane. In our model all possible demand matrices belong to a polytope. The polytope can be divided into parts, and different routing schemes can be applied while dealing with traffic matrices from different parts of the polytope. We consider three basic models: Robust‐Routing, No‐Sharing and Dynamic‐Routing. We apply two different partitioning strategies depending on whether the reservation vectors on opposite sides of the hyperplane are required to be identical, or allowed to differ. We provide efficient algorithms that solve these problems. Moreover, we prove polynomiality of some of the considered cases. Finally, we present numerical results proving the applicability of the introduced algorithms and showing differences between the routing strategies.     

Proof Pearl: A Formal Proof of Dally and Seitz’ Necessary and Sufficient Condition for Deadlock-Free Routing in Interconnection Networks

Avoiding deadlock is crucial to interconnection networks. In ’87, Dally and Seitz proposed a necessary and sufficient condition for deadlock-free routing. This condition states that a routing function is deadlock-free if and only if its channel dependency graph is acyclic. We formally define and prove a slightly different condition from which the original condition of Dally and Seitz can be derived. Dally and Seitz prove that a deadlock situation induces cyclic dependencies by reductio ad absurdum. In contrast we introduce the notion of a waiting graph from which we explicitly construct a cyclic dependency from a deadlock situation. Moreover, our proof is structured in such a way that it only depends on a small set of proof obligations associated to arbitrary routing functions and switching policies. Discharging these proof obligations is sufficient to instantiate our condition for deadlock-free routing on particular networks. Our condition and its proof have been formalized using the ACL2 theorem proving system.