Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

Lying Your Way to Better Traffic Engineering

To optimize the flow of traffic in IP networks, operators do traffic engineering (TE), i.e., tune routing-protocol parameters in response to traffic demands. TE in IP networks typically involves configuring static link weights and splitting traffic between the resulting shortest-paths via the Equal-Cost-MultiPath (ECMP) mechanism. Unfortunately, ECMP is a notoriously cumbersome and indirect means for optimizing traffic flow, often leading to poor network performance. Also, obtaining accurate knowledge of traffic demands as the input to TE is elusive, and traffic conditions can be highly variable, further complicating TE. We leverage recently proposed schemes for increasing ECMP's expressiveness via carefully disseminated bogus information ("lies") to design COYOTE, a readily deployable TE scheme for robust and efficient network utilization. COYOTE leverages new algorithmic ideas to configure (static) traffic splitting ratios that are optimized with respect to all (even adversarially chosen) traffic scenarios within the operator's "uncertainty bounds". Our experimental analyses show that COYOTE significantly outperforms today's prevalent TE schemes in a manner that is robust to traffic uncertainty and variation. We discuss experiments with a prototype implementation of COYOTE

Optimizing IGP Link Costs for Improving IP-level Resilience

Recently, major vendors have introduced new router platforms to the market that support fast IP-level failure pro- tection out of the box. The implementations are based on the IP Fast ReRoute–Loop Free Alternates (LFA) standard. LFA is simple, unobtrusive, and easily deployable. This simplicity, however, comes at a severe price, in that LFA usually cannot protect all possible failure scenarios. In this paper, we give new graph theoretical tools for analyzing LFA failure case coverage and we seek ways for improvement. In particular, we investigate how to optimize IGP link costs to maximize the number of protected failure scenarios, we show that this problem is NP- complete even in a very restricted formulation, and we give exact and approximate algorithms to solve it. Our simulation studies show that a deliberate selection of IGP costs can bring many networks close to complete LFA-based protection

Combined Intra- and Inter-domain Traffic Engineering using Hot-Potato Aware Link Weights Optimization

A well-known approach to intradomain traffic engineering consists in finding the set of link weights that minimizes a network-wide objective function for a given intradomain traffic matrix. This approach is inadequate because it ignores a potential impact on interdomain routing. Indeed, the resulting set of link weights may trigger BGP to change the BGP next hop for some destination prefixes, to enforce hot-potato routing policies. In turn, this results in changes in the intradomain traffic matrix that have not been anticipated by the link weights optimizer, possibly leading to degraded network performance. We propose a BGP-aware link weights optimization method that takes these effects into account, and even turns them into an advantage. This method uses the interdomain traffic matrix and other available BGP data, to extend the intradomain topology with external virtual nodes and links, on which all the well-tuned heuristics of a classical link weights optimizer can be applied. A key innovative asset of our method is its ability to also optimize the traffic on the interdomain peering links. We show, using an operational network as a case study, that our approach does so efficiently at almost no extra computational cost.Comment: 12 pages, Short version to be published in ACM SIGMETRICS 2008, International Conference on Measurement and Modeling of Computer Systems, June 2-6, 2008, Annapolis, Maryland, US

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

Aspects of proactive traffic engineering in IP networks

To deliver a reliable communication service over the Internet it is essential for the network operator to manage the traffic situation in the network. The traffic situation is controlled by the routing function which determines what path traffic follows from source to destination. Current practices for setting routing parameters in IP networks are designed to be simple to manage. This can lead to congestion in parts of the network while other parts of the network are far from fully utilized. In this thesis we explore issues related to optimization of the routing function to balance load in the network and efficiently deliver a reliable communication service to the users. The optimization takes into account not only the traffic situation under normal operational conditions, but also traffic situations that appear under a wide variety of circumstances deviating from the nominal case. In order to balance load in the network knowledge of the traffic situations is needed. Consequently, in this thesis we investigate methods for efficient derivation of the traffic situation. The derivation is based on estimation of traffic demands from link load measurements. The advantage of using link load measurements is that they are easily obtained and consist of a limited amount of data that need to be processed. We evaluate and demonstrate how estimation based on link counts gives the operator a fast and accurate description of the traffic demands. For the evaluation we have access to a unique data set of complete traffic demands from an operational IP backbone. However, to honor service level agreements at all times the variability of the traffic needs to be accounted for in the load balancing. In addition, optimization techniques are often sensitive to errors and variations in input data. Hence, when an optimized routing setting is subjected to real traffic demands in the network, performance often deviate from what can be anticipated from the optimization. Thus, we identify and model different traffic uncertainties and describe how the routing setting can be optimized, not only for a nominal case, but for a wide range of different traffic situations that might appear in the network. Our results can be applied in MPLS enabled networks as well as in networks using link state routing protocols such as the widely used OSPF and IS-IS protocols. Only minor changes may be needed in current networks to implement our algorithms. The contributions of this thesis is that we: demonstrate that it is possible to estimate the traffic matrix with acceptable precision, and we develop methods and models for common traffic uncertainties to account for these uncertainties in the optimization of the routing configuration. In addition, we identify important properties in the structure of the traffic to successfully balance uncertain and varying traffic demands