Characteristic functions of directed graphs and applications to stochastic equilibrium problems

In this paper we introduce the notions of characteristic and potential functions of directed graphs and study their properties. The main motivation for our research is the stochastic equilibrium traffic assignment problem, in which the drivers choose their routes with some probabilities. Since the number of the strategies in this game is very big, we need to find an efficient way of computation of the expected arc flows in the network. We show that the characteristic functions of the graphs are very useful in this respect. Using this technique we can form and solve numerically the equilibrium traffic assignment problem in a reasonable computational time. As a byproduct of our results we show that the spectral radius of a matrix with non-negative elements admits a convex parameterization as a function of its entries.     

Enhancing transportation network capacity by congestion pricing with simultaneous toll location and toll level optimization

In previous studies of congestion pricing, the objective was to minimize total travel time or maximize total social welfare of all travellers in transportation networks. In this article, a new objective function of maximizing the reserve capacity of networks is proposed, and a new bi-level model is formulated for the implementation of congestion pricing, where either link tolls or path tolls are charged. Since the bi-level model is neither convex nor differentiable, the traditional gradient based methods cannot solve the problem for a global optimum. To circumvent the difficulty of computing, the congestion pricing problem of simultaneous toll link and toll level optimization is formulated as a single-level optimization program with equilibrium constraints. Then the equilibrium constraints, the travel time functions, and toll location constraints are all linearized by introducing mixed integer variables. As a result, the overall problem is formulated into a mixed-integer linear program, which can determine the global optimum. Numerical results show that this approach is effective and efficient.     

Weakly strict equilibria in finite normal form games

In this paper we introduce the weakly strict equilibrium for (mixed extensions of) finiten-person games. For those games we prove that our new concept is a strict refinement of the undominated Nash equilibrium concept. We show that their set of weakly strict equilibria is nonempty and coincides with their set of strict equilibria (when the latter is also non-empty) and we study the relation between our refinement and other noncooperative concepts.We thank Xunta de Galicia for financial support through project XUGA20702B93     

Robust bi-level optimization models in transportation science

Mathematical programmes with equilibrium constraints (MPECs) constitute important modelling tools for network flow problems, as they place 'what-if' analyses in a proper mathematical framework. We consider a class of stochastic MPEC traffic models that explicitly incorporate possible uncertainties in travel costs and demands. In stochastic programming terminology, we consider 'here-and-now' models where decisions must be made before observing the uncertain parameter values and the responses of the network users; the objective is to minimize the expectation of the upper-level objective function. Such a model could, for example, be used to derive a fixed toll pricing scheme that provides the best revenue for a given network over a time period, where variations in traffic conditions and demand elasticities are described by distributions of parameters in the travel time and demand functions.We present new results on the stability of globally optimal solutions to perturbations in the probability distribution, establishing the robustness of the model. We also discuss penalization and discretization algorithms, the latter enabling the use of standard MPEC algorithms, and provide many future research avenues.     

Dual command travel times and miniload system throughput with turnover-based storage

We analyze travel times for automated storage/retrieval systems. In particular, we apply our travel time model to turnover-based storage systems and determine the mean and variance of dual command travel times. We present detailed numerical results for selected rack shape factors and ABC inventory profiles. We then investigate the effect of alternative rack configurations on travel time performance measures. We also show how to determine the throughput of miniload systems with turnover-based storage and exponentially distributed pick times.     

有流量附加约束的动态交通网络平衡问题

在抽象空间上研究了有流量附加约束的动态交通网络的平衡问题,将这种附加约束等价的当作路径的新增阻抗,并给出了基于这个条件下的Wardrop用户平衡的变分不等式表达。这事实上是提供了计算这种平衡配流的另一种方法。此外,所研究的问题更接近现实的有路径流量限制的情形,还得出了相应的动态平衡性质。     

Optimal routing in an automated storage/retrieval system with dedicated storage

We address the sequencing of requests in an automated storage/retrieval system with dedicated storage. We consider the block sequencing approach, where a set of storage and retrieval requests is given beforehand and no new requests come in during operation. The objective for this static problem is to find a route of minimal total travel time in which all storage and retrieval requests may be performed. The problem of sequencing a list of retrievals is equivalent to the Traveling Salesman Problem (TSP), and thus NP-hard in general. We show that the special case of sequencing under the dedicated storage policy can be solved in polynomial time. The results apply to systems with arbitrary positions of the input and output stations. Tlus generalizes the models in the literature, where only combined input/output stations are considered. Furthermore we identify a single command area in the rack. At the end we evaluate the model against heuristic procedures.     

具有时滞和旅途过程中有传染的两斑块SIS模型的全局动力学

本文建立了一个具有时滞的SI S模型,研究了旅途过程中疾病的传染.得到了基本再生数.通过线性化方法和比较原理,证明了当基本再生数小于1时无病平衡点是全局渐近稳定的,疾病绝灭.当基本再生数大于1时,系统存在唯一的全局吸引的地方病平衡点,且疾病持续生存.数值模拟验证了扩散率对疾病传播的影响.分析了基本再生数对扩散率的依赖性.     

Modeling of the supersonic argon plasma jet at low gas pressure environment

Numerical simulation results are presented concerning the heat transfer and fluid flow within the supersonic argon plasma jet encountered in low pressure (or soft vacuum) plasma spraying (LPPS). The plasma parameters at the inlet section of the plasma jet are taken from our modeling results of the subsonic-to-supersonic d.c. arc plasma torch. The mach number, temperature and static pressure at the center of the plasma jet on the torch exit section are 2.8, 13 200 K and 6000 Pa, respectively, whereas the environment (i.e. vacuum chamber) pressure is 0.1 atm. Those parameters are typical for LPPS. The plasma jet is assumed to be axi-symmetrical and in local thermodynamic equilibrium state. The All-Speed SIMPLE algorithm is coupled with the FAST-2D program to simulate the whole plasma jet containing both the supersonic and subsonic flow regions. Modeling results clearly show that there exist several successive temperature, velocity and static wave crests and troughs. The fluctuation magnitudes of those parameters reduce rapidly in the flow direction, along with the flow transformation from the supersonic flow regime into the subsonic flow regime. The existence of a series of compression and expansion waves in the region near the torch nozzle exit shows clearly the over-expanded characteristics of the supersonic plasma flow.     

空间刚架动态失稳全过程分析

采用静动力非线性方法研究结构的后屈曲问题。基于连续介质力学对物质运动的描述方法,采用增量拉格朗日公式推导空间梁单元的切线刚度矩阵,包括节点大位移、大转角产生的几何非线性,及弹塑性本构关系。动力分析采用Newmark数值积分,结合Newton-Raphson平衡迭代。采用弧长法计算结构的屈曲前非线性反应,该方法不用卸荷跟踪荷载位移反应全过程,而在临界点继续缓慢加荷,用动力时程方法进行空间刚架结构的失稳破坏全过程仿真。