Critical Thresholds for Dynamic Routing in Queueing Networks

This paper studies dynamic routing in a parallel server queueing network with a single Poisson arrival process and two servers with exponential processing times of different rates. Each customer must be routed at the time of arrival to one of the two queues in the network. We establish that this system operating under a threshold policy can be well approximated by a one-dimensional reflected Brownian motion when the arrival rate to the network is close to the processing capacity of the two servers. As the heavy traffic limit is approached, thresholds which grow at a logarithmic rate are critical in determining the behavior of the limiting system. We provide necessary and sufficient conditions on the growth rate of the threshold for (i) approximation of the network by a reflected Brownian motion (ii) positive recurrence of the limiting Brownian diffusion and (iii) asymptotic optimality of the threshold policy.     

Analysis of a Rollout Approach to Sequencing Problems with Stochastic Routing Applications

The paper considers sequencing problems, the traveling salesman problem being their natural representative. It studies a rollout approach that employs a cyclic heuristic as its main base algorithm. The theoretical analysis establishes that it is guaranteed to improve (at least in a weak sense) the quality of any feasible solution to a given sequencing problem. Besides other applications, the paper shows that it is well suited for applications that are embedded in dynamic and stochastic environments. The computational performance of the approach is investigated with applications to two stochastic routing problems. The dynamic version of the heuristic appears to be the first algorithm available in the literature to approximately solve a variant of one of these problems.     

带特殊重试时间的M／M／1重试排队模型的另一个特征值

研究对应于带特殊重试时间的M／M／1重试排队模型主算子在左半复平面的谱,证明-（2λ＋α＋β＋√（α＋β）^2＋4λβ/4是该主算子的几何重数为1的特征值．     

Queueing models for police-fire merger analysis

Cities with under 100,000 in population expend a significant portion of their budgets on emergency services. One option that a number of these cities have considered for improving service and cutting costs is training personnel to handle both police and fire roles. In this paper we describe a hierarchy of models that we have used to assess the performance viability of a merger as well as to design specific deployment plans. The modeling environment is more complex than a traditional police or fire system. We need to model the response pattern of four or more patrol units along with the simultaneous dispatch of fire equipment from one or more fire stations. The major contribution of the paper is the manner in which a series of models is linked together to forecast a wide range of performance measures under differing dispatch assumptions. We use a queueing model of police patrol to calculate steady state probabilities and expected delays without preemption. We then model two types of preemptive dispatch strategies utilized in responding initially to a major fire by superimposing a binomial distribution on the basic queueing model. There is also a travel time simulation model to calculate conditional expected response time statistics. The queueing models and the travel time simulation are then combined to estimate unconditional expected values. Lastly, we describe a simulation model used to address transient performance issues that are of concern during a major fire.     

带有转换时间和阀值的非抢占优先权排队模型

在[3]中,我们研究了在抢占规则下带有转换时间和阈值的两类顾客优先权排队系统,本文就非抢占情形对这样的系统作进一步的研究,同样求出两类顾客队长的稳态联合概率母函数。籍助这些母函数可求出诸如平均队长这样一些重要的系统性能指标。     

时变路网条件下联合配送的开放式车辆路径问题

针对城市物流系统中的多物流中心联合配送问题,设计一种多物流中心处理方法共享物流资源;分析城市路网的时变特性,设计路段行驶时间计算方法;综合考虑客户需求、时间窗、车辆不同出发时间、油耗、碳排放与联合配送模式等因素,以总成本最小为目标构建联合配送的开放式时变车辆路径规划模型,设计改进蚁群算法求解;实验结果表明以上方法具有可行性与有效性。     

离散加工时间的可控排序问题

本文主要研究了离散加工时间的可控排序问题,目标函数是总压缩费用约束下极小化最大完工时间,对单机工件有不同到达时间以及同型机工件到达时间都相同这两个问题,我们设计了伪多项式时间的动态规划算法,并给出了相应的FPTAS算法．     

时变单车路径优化模型及动态规划算法

车辆路径问题由于其广泛的应用领域及经济价值而成为学术研究热点。然而,在已有的研究文献中,车辆的速度时变与服务多任务特性很少被关注。本文讨论了具有这两个特性的单车路径优化问题。建立了以送货完成时间最早为优化目标的时变单车送货路径优化模型。由于很难获得该模型的精确解,本文提出了一种贪婪补货策略压缩原问题解空间,设计动态规划算法给出了车辆行驶时间满足FIFO规则的送货顺序近似最优解。数值算例验证了该算法所得到的解仅是原问题的近似最优解这一结论。算例同时表明优化配送时间随着车辆装载能力的增大而缩短,并在车辆装载能力超过所有客户配送总需求时实现最短配送时间,即,使用较大装载能力车辆能节约更多配送时间。     

A network-consistent time-dependent travel time layer for routing optimization problems

In the vehicle routing literature, there is an increasing focus on time-dependent routing problems, where the time (or cost) to travel between any pair of nodes (customers, depots) depends on the departure time. The aim of such algorithms is to be able to take recurring congestion into account when planning logistics operations. To test algorithms for time-dependent routing problems, time-dependent problem data is necessary. This data usually comes in the form of three-dimensional travel time matrices that add the departure time as an extra dimension. However, most currently available time-dependent travel time matrices are not network-consistent, i.e., the travel times are not correlated both in time and in space. This stands in contrast to the behavior of real life congestion, which generally follows a specific pattern, appearing in specific areas and then affecting all travel times to and from those areas. As a result of the lack of available network-consistent travel time matrices, it is difficult to develop algorithms that are able to take this special structure of the travel time data into account.     

On the Modification of Rouche's Theorem for the Queueing Theory Problems

In analytic queueing theory, Rouche's theorem is frequently used to prove the existence of a certain number of zeros in the domain of regularity of a given function. If the theorem can be applied it leads in a simple way to results concerning the ergodicity condition and the construction of the solution of the functional equation for the generating function of the stationary distribution. Unfortunately, the verification of the conditions needed to apply Rouche's theorem is frequently quite difficult. We prove the theorem which allows to avoid some difficulties arising in applying classical Rouche's theorem to an analysis of queueing models.     

A Hybrid Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Time Windows

Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. The problem is solved by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize the objectives of traveling distance and number of vehicles. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW. The proposed HMOEA is featured with specialized genetic operators and variable-length chromosome representation to accommodate the sequence-oriented optimization in VRPTW. Unlike existing VRPTW approaches that often aggregate multiple criteria and constraints into a compromise function, the proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace. The HMOEA is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, which yields 20 routing solutions better than or competitive as compared to the best solutions published in literature.     

基于遗传算法的物流配送车辆调度问题研究

研究使用遗传算法求解物流配送组织过程中车辆调度问题 .通过把时间窗约束和车辆容量约束转嫁到最小费用目标函数中去 ,建立适合于遗传算法的车辆调度模型 .阐述放回式随机复制算子和适应度函数 ,设计描述行驶线路的染色体结构、初始群体生成方法、独特的交叉算子和交换变异算子 ,构造完整的遗传算法 .并给出算例 ,验证调度模型和遗传算法 .     

带时空相关性分析的行车时间估计模型

基于流体动力学方程的行车时间估计模型不能很好地反映真实的行车时间,需要对其进行一定的改进.在对交通流进行流体动力学建模的基础之上,引入对高速公路路网中不同路段之间的行车时间相关性和同一路段不同季节、不同时段的行车时间相关性分析,建立了带时空相关性分析的时间估计模型,使用统计学的方法消除动力学模型的误差.     

变邻域模拟退火算法求解速度时变的VRPTW问题

本文在经典的带时间窗的车辆路径问题(VRPTW)的基础上,考虑不同时间段车辆行驶速度不同的情况,研究速度时变的带时间窗车辆路径问题(TDVRPTW),使问题更具实际意义。本文用分段函数表示不同时间段下的车辆行驶速度,并解决了速度时变条件下行驶时间计算的问题。针对模拟退火算法(SA)在求解VRPTW问题时易陷入局部最优解,变邻域搜索算法(VNS)在求解VRPTW问题时收敛速度慢的问题,本文将模拟退火算法以一定概率接受非最优解的思想和变邻域搜索算法系统地改变当前解的邻域结构以拓展搜索范围的思想结合起来,提出了一种改进的算法——变邻域模拟退火算法(SAVN),使算法在退火过程中一陷入局部最优解就改变邻域结构,更换搜索范围,以此提升算法跳出局部最优解的能力,加快收敛速度。通过在仿真实验中将SAVN算法的求解结果与VNS算法、SA算法进行对比,验证了SAVN算法确实能显著提升算法跳出局部最优解的能力。     

车辆路径问题的混合优化算法

讨论了一类车辆路径调度问题(VRP)及其数学模型，并且分析了以遗传算法求解该类问题时的染色体表示和有关遗传操作，然后结合2-opt局部优化算法提出了GA with2-opt算法来求解VRP问题，试验结果说明了该算法的有效性和可行性。     

第二种服务可选的M/G/1排队模型的适定性

运用Hille-Yosida定理,Phillips定理与Fattorini定理证明第二种服务可选的M/G/1排队模型存在唯一的概率瞬态解.     

Stability of Fluid Networks with Proportional Routing

In this paper we investigate the stability of a class of two-station multiclass fluid networks with proportional routing. We obtain explicit necessary and sufficient conditions for the global stability of such networks. By virtue of a stability theorem of Dai [14], these results also give sufficient conditions for the stability of a class of related multiclass queueing networks. Our study extends the results of Dai and VandeVate [19], who provided a similar analysis for fluid models without proportional routing, which arise from queueing networks with deterministic routing. The models we investigate include fluid models which arise from a large class of two-station queueing networks with probabilistic routing. The stability conditions derived turn out to have an appealing intuitive interpretation in terms of virtual stations and push-starts which were introduced in earlier work on multiclass networks.     

Heuristics for Large Constrained Vehicle Routing Problems

This paper presents a heuristic for solving very large routing problems (thousands of customers and hundreds of vehicles) with side constraints such as time windows. When applied to traditional benchmarks (Solomon's), we obtain high quality results with short resolution time (a few seconds). We also introduce a LDS (Limited Discrepancy Search) variation that produces state-of-the-art results. The heart of this heuristic is a combination of a look-ahead insertion algorithm, an incremental local optimization scheme and a constraint solver for constrained traveling salesman problems. The incrementality means that instead of visiting some large neighborhood after an initial solution has been found, a limited number of moves is examined, after each insertion, on the partial solution. This incremental version is not only faster, it also yields better results than using local optimization once a full solution has been built. We also show how additional constraints can be used in order to guide the insertion process. Because of its use of separate CP (Constraint Programming) modules, this method is flexible and may be used to solve large dispatching problems that include many additional constraints such as setup times (asymmetrical distance) or skill matching.     

Network of Single-Server Queues with Dependent Service Times

A network of single-server nodes fed by customers of several classes is considered. Each customer is equipped with the random work to be done for completing service. The distribution of this work and the rate of its decreasing during the service depend on the node, the class of the customer, the queue contents and the residual work loads of the customers at the node. The service discipline is LCFS preemptive-resume. For both open and closed network, the stationary distribution is derived. In general, this distribution is not a product form. For the open network, sufficient conditions yielding the product form are given. For both open and closed network, sufficient invariance conditions are found.     

Explicit Solutions for Variational Problems in the Quadrant

We study a variational problem (VP) that is related to semimartingale reflecting Brownian motions (SRBMs). Specifically, this VP appears in the large deviations analysis of the stationary distribution of SRBMs in the d-dimensional orthant R ^d ₊. When d=2, we provide an explicit analytical solution to the VP. This solution gives an appealing characterization of the optimal path to a given point in the quadrant and also provides an explicit expression for the optimal value of the VP. For each boundary of the quadrant, we construct a cone of boundary influence, which determines the nature of optimal paths in different regions of the quadrant. In addition to providing a complete solution in the 2-dimensional case, our analysis provides several results which may be used in analyzing the VP in higher dimensions and more general state spaces.