Shortest expected delay routing for Erlang servers

The queueing problem with Poisson arrivals and two identical parallel Erlang servers is analyzed for the case of shortest expected delay routing. This problem may be represented as a random walk on the integer grid in the first quadrant of the plane. An important aspect of the random walk is that it is possible to make large jumps in the direction of the boundaries. This feature gives rise to complicated boundary behavior. Generating function approaches to analyze this type of random walk seem to be extremely complicated and have not been successful yet. The approach presented in this paper directly solves the equilibrium equations. It is shown that the equilibrium distribution of the random walk can be written as an infinite linear combination of products. This linear combination is constructed in a compensation procedure. The starting solutions for this procedure are found by solving the shortest expected delay problem with instantaneous jockeying. The results can be used for an efficient computation of performance criteria, such as the waiting time distribution and the moments of the waiting time and the queue lengths.     

Design of stochastic hitless‐prediction router by using the first exceed level theory

This paper deals with an enhanced hitless‐prediction router system that has the hitless‐restart capability with forecasting. Hitless‐restart means that the router can stay on the forwarding path and the network topology remains stable. But the major difficulty of the current hitless‐restart is that the router is always active to take the action, such as non‐stop forwarding (upgrade, maintenance and capacity expansion may be included as third party activities). Stochastic hitless‐prediction model gives the decision making factors that manage a router system more efficiently. An analogue of the first exceed level theory is applied for the restriction of the number of buffer size that is the router capacity. Analytically, tractable results are obtained by using a first exceed level process that enables us to determine the decision making factors such as recycle periods of the hitless‐prediction point to prevent a router shutdown. Copyright © 2005 John Wiley & Sons, Ltd.     

Cash flow optimization in delivery scheduling

The paper examines the inventory routing problem from the perspective of the present value of the cash flow associated with the distribution of a commodity such as propane. We analyze this problem for both deterministic and stochastic customer demands and validate our results on data from a real life distribution operation of propane. The analysis based on the present value of the cash flow indicates that optimization of propane deliveries based on efficiency/cost criteria alone will generate inferior solutions and it would be more advantageous for the company to set deliveries for a large percentage of the customers based on the present value of cash flow. In addition, in the case of stochastic demands, deliveries based on the cash flow consideration will tend to reduce the number of stockouts (i.e. improve both profit and service).     

Modeling a class of state-dependent routing in flexible manufacturing systems

We develop a closed queueing network model for flexible manufacturing systems (FMSs), where parts routing follows a probabilistic shortest-queue (PSQ) scheme, i.e. parts are routed to the shortest queue (or the most empty station) with the highest probability. We allow limited local buffer at each work station. We prove that with the PSQ routing, the Markovian queue-length process satisfies time reversibility and has a product-form equilibrium distribution. An algorithm is developed to compute the solutions to the model. The model can be used as a performance evaluation tool to study FMSs.     

Bit Constraints Analysis of Multihop All-Optical Networks with Deflection Routing

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无标度网络上队列资源分配研究

研究了节点队列资源有限的条件下,无标度网络上的信息流动力学过程,发现了网络由自由流通到拥塞的相变现象,提出了一种基于节点度的队列资源分配模型.模型的核心是使节点i的队列长度与kβi成正比(ki为节点i的度,β为分配参数).仿真结果表明,在网络使用最短路径算法进行信息包传送的条件下,β近似等于1.25时队列资源分配最合理,网络容量最大,且该最佳值与队列总资源多少以及网络的规模无关.     

Two phased hybrid local search for the periodic capacitated arc routing problem

The periodic capacitated arc routing problem (PCARP) is a challenging general model with important applications. The PCARP has two hierarchical optimization objectives: a primary objective of minimizing the number of vehicles (F_v) and a secondary objective of minimizing the total cost (F_c). In this paper, we propose an effective two phased hybrid local search (HLS) algorithm for the PCARP. The first phase makes a particular effort to optimize the primary objective while the second phase seeks to further optimize both objectives by using the resulting number of vehicles of the first phase as an upper bound to prune the search space. For both phases, combined local search heuristics are devised to ensure an effective exploration of the search space. Experimental results on 63 benchmark instances demonstrate that HLS performs remarkably well both in terms of computational efficiency and solution quality. In particular, HLS discovers 44 improved best known values (new upper bounds) for the total cost objective F_c while attaining all the known optimal values regarding the objective of the number of vehicles F_v. To our knowledge, this is the first PCARP algorithm reaching such a performance. Key components of HLS are analyzed to better understand their contributions to the overall performance.     

Robust and data-driven approaches to call centers

We propose both robust and data-driven approaches to a fluid model of call centers that incorporates random arrival rates with abandonment to determine staff levels and dynamic routing policies. We test the resulting models with real data obtained from the call center of a US bank. Computational results show that the robust fluid model is significantly more tractable as compared to the data-driven one and produces overall better solutions to call centers in most experiments.     

The school bus routing problem: A review

This paper aims to provide a comprehensive review of the school bus routing problem (SBRP). SBRP seeks to plan an efficient schedule for a fleet of school buses where each bus picks up students from various bus stops and delivers them to their designated schools while satisfying various constraints such as the maximum capacity of a bus, the maximum riding time of a student in a bus, and the time window of a school. This class of problem consists of different sub-problems involving data preparation, bus stop selection, bus route generation, school bell time adjustment, and bus scheduling. In this paper, the various assumptions, constraints, and solution methods used in the literature on SBRP are summarized. A list of issues requiring further research is also presented.     

An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles

The vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem. It arises when each vehicle performs several routes during the workday due to strict time limits on route duration (e.g., when perishable goods are transported). The routes are defined over customers with a revenue, a demand and a time window. Given a fixed-size fleet of vehicles, it might not be possible to serve all customers. Thus, the customers must be chosen based on their associated revenue minus the traveling cost to reach them. We introduce a branch-and-price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation, using column generation. The pricing subproblems are elementary shortest path problems with resource constraints. Computational results are reported on euclidean problems derived from well-known benchmark instances for the vehicle routing problem with time windows.