Predicting the elastoplastic response of fiber-reinforced metal matrix composites

This paper aims to investigate the effect of microstructure parameters (such as the cross-sectional shape of fibers and fiber volume fraction) on the stress–strain behavior of unidirectional composites subjected to off-axis loadings. A micromechanical model with a periodic microstructure is used to analyze a representative volume element. The fiber is linearly elastic, but the matrix is nonlinear. The Bodner–Partom model is used to characterize the nonlinear response of the fiber-reinforced composites. The analytical results obtained show that the flow stress of composites with square fibers is higher than with circular or elliptic ones. The difference in the elastoplastic response, which is affected by the fiber shape, can be disregarded if the fiber volume fraction is smaller than 0.15. Furthermore, the effect of fiber shape on the stress–strain behavior of the composite can be ignored if the off-axis loading angle is smaller than 30°.     

Modeling traffic flow interrupted by incidents

A steady-state M/M/c queueing system under batch service interruptions is introduced to model the traffic flow on a roadway link subject to incidents. When a traffic incident happens, either all lanes or part of a lane is closed to the traffic. As such, we model these interruptions either as complete service disruptions where none of the servers work or partial failures where servers work at a reduced service rate. We analyze this system in steady-state and present a scheme to obtain the stationary number of vehicles on a link. For those links with large c values, the closed-form solution of M/M/∞ queues under batch service interruptions can be used as an approximation. We present simulation results that show the validity of the queueing models in the computation of average travel times.     

Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem

The purpose of the traffic assignment problem is to obtain a traffic flow pattern given a set of origin-destination travel demands and flow dependent link performance functions of a road network. In the general case, the traffic assignment problem can be formulated as a variational inequality, and several algorithms have been devised for its efficient solution. In this work we propose a new approach that combines two existing procedures: the master problem of a simplicial decomposition algorithm is solved through the analytic center cutting plane method. Four variants are considered for solving the master problem. The third and fourth ones, which heuristically compute an appropriate initial point, provided the best results. The computational experience reported in the solution of real large-scale diagonal and difficult asymmetric problems—including a subset of the transportation networks of Madrid and Barcelona—show the effectiveness of the approach.     

基于Stackelberg博弈的时变双层交通分配模型

提出一个时变双层交通分配模型,其中上层网络管理者设立了一个路段的最大排队长度,其目标是使由网络流和排队长度定义的总出行时间最小.目标函数在离散时段内以路段流量和排队长度作为决策变量,同时考虑不同类型的信号交叉口延误的影响.下层网络用户的反应依赖于上层管理者的决策,其选择是使自身感知阻抗最小的路径,服从一个基于成对组合Logit的路径选择模型,构成一个成对组合Logit的均衡分配问题.结合了交通分配和流传播方法,将其表示为一个均衡约束下的双层数学规划问题,形成了一个Stackelberg非合作博弈.使用遗传算法求解该双层规划问题,并采用实证分析来表现模型的特征和算法的计算表现.结果表明路径重叠、路段流量、路段排队长度等因素对网络均衡流分布均有显著影响.     

Planning computations in a multiprocessor system with unfixed parameters

The problem of constructing a feasible preemptive multiprocessor schedule is considered for a case where directive intervals are assigned, processors can have arbitrary performance, and the amount of tasks depends linearly on the volume of additional resources allocated for them. In cases where a feasible schedule is not found with an allocated volume of additional resources, the problem of optimally correcting the directive intervals is considered. The solution is based on an analysis of the necessary and sufficient conditions of a feasible schedule’s existence.     

Reliability-based user equilibrium in a transport network under the effects of speed limits and supply uncertainty

This study investigates the system-wide traffic flow re-allocation effect of speed limits in uncertain environments. Previous studies have only considered link capacity degradation, which is only one of the factors that lead to supply uncertainty. This study examines how imposing speed limits reallocates the traffic flows in a situation of general supply uncertainty with risk-averse travelers. The effects of imposing a link-specific speed limit on link driving speed and travel time are analyzed, given the link travel time distribution before imposing the speed limit. The expected travel time and travel time standard deviation of a link with a speed limit are derived from the link travel time distribution and are both continuous, monotone, and convex functions in terms of link flow. A distribution-free, reliability-based user equilibrium with speed limits is established, in which travelers are assumed to choose routes that minimize their own travel time budget. A variational inequality formulation for the equilibrium problem is proposed and the solution properties are provided. In this study, the inefficiency of a reliability-based user equilibrium flow pattern with speed limits is defined and found to be bounded above when supply uncertainty refers to capacity degradation. The upper bound depends on the level of risk aversion of travelers, a ratio related to the design and worst-case link capacities, and the highest power of all link performance functions.     

A novel algorithm for area traffic capacity control with elastic travel demands

A non-linear area traffic control system with limited capacity is considered in this paper. Optimal signal settings and link capacity expansions can be determined while trip distribution and network flow are in equilibrium. This problem can be formulated as a non-linear mathematical program with equilibrium constraints. For the objective function a non-linear constrained optimization program for signal settings and link capacity expansion is determined. For the constraint set the elastic user equilibrium traffic assignment obeying Wardrop’s first principle can be formulated as a variational inequality. Since the constrained optimization problem is non-convex, only local optima can be obtained. In this paper, a novel algorithm using a non-smooth trust region approach is proposed. Numerical tests are performed using a real data city network and various example test networks in which the effectiveness and robustness of the proposed method are confirmed as compared to other well-known solution methods.     

主路多车道无信号交叉口混合交通流的通行能力

Highway capacity is defined as maximum volume of traffic flow through the particular highway section under given traffic conditions,road conditions and so on.Highway construction and management is judged by capacity standard.The reasonable scale and time of highway construction,rational network structure and optimal management mode of highway network can be determined by analyzing the fitness between capacity and traffic volume.All over the world,highway capacity is studied to different extent in different country. Based on the gap acceptance theory,the mixed traffic flow composed of two representative vehicle types heavy and light vehicles is analyzed with probability theory.Capacity model of the minor mixed traffic flows crossing m major lanes,on which the traffic flows fix in with M3 distributed headway,on the unsignalized intersection is set up,and it is an extension of minor lane capacity theory for one vehicle-type and one major-lane traffic flow.     

Bounds for the tail distribution in a queue with a superposition of general periodic Markov sources: theory and application

An efficient yet accurate estimation of the tail distribution of the queue length has been considered as one of the most important issues in call admission and congestion controls in ATM networks. The arrival process in ATM networks is essentially a superposition of sources which are typically bursty and periodic either due to their origin or their periodic slot occupation after traffic shaping. In this paper, we consider a discrete-time queue where the arrival process is a superposition of general periodic Markov sources. The general periodic Markov source is rather general since it is assumed only to be irreducible, stationary and periodic. Note also that the source model can represent multiple time-scale correlations in arrivals. For this queue, we obtain upper and lower bounds for the asymptotic tail distribution of the queue length by bounding the asymptotic decay constant. The formulas can be applied to a queue having a huge number of states describing the arrival process. To show this, we consider an MPEG-like source which is a special case of general periodic Markov sources. The MPEG-like source has three time-scale correlations: peak rate, frame length and a group of pictures. We then apply our bound formulas to a queue with a superposition of MPEG-like sources, and provide some numerical examples to show the numerical feasibility of our bounds. Note that the number of states in a Markov chain describing the superposed arrival process is more than 1.4 × 10⁸⁸. Even for such a queue, the numerical examples show that the order of the magnitude of the tail distribution can be readily obtained.     

Simultaneously optimizing link tolls and signal settings in a road network

The problem of determining link tolls to reduce traffic congestion is often referred as a toll design problem. In this paper, optimal tolls are determined for signal-controlled junctions in urban traffic road networks where the rerouting traffic is properly taken into account. This problem can be formulated as a mathematical program with equilibrium constraints (MPEC) where the user equilibrium is expressed as a variational inequality problem. Due to the non-differentiability of the equilibrium problem, an efficient convergent solution scheme is established. Numerical calculations are conducted on a variety of example road networks and comparisons are made with earlier methods.     

Calculation of traffic flow breakdown probability to optimize link throughput

Traffic breakdown phenomenon is prevalent in empirical traffic system observations. Traffic flow breakdown is usually defined as an amount of sudden drop in traffic flow speed when traffic demand exceeds capacity. Modeling and calculating traffic flow breakdown probability remains an important issue when analyzing the stability and reliability of transportation system. The breakdown mechanism is still mysterious to practitioners and researchers in varying manner. Treating breakdown as a random event, this paper use discrete time Markov chain (DTMC) to model traffic state transition path, as a result, a transition probability matrix can be generated from empirical observations. From empirical analysis of breakdown, we found this formulation of breakdown probability follows the Zipf distribution. Therefore, a connection from traffic flow breakdown probability to how many vehicles are occupying a certain freeway segment (e.g. a link) will be established. Following from the results, a quantitative measure of breakdown probability can be obtained to optimize ramp metering rates to achieve optimum system performance measures.     

Diffusion approximation for a heavily loaded multi-user wireless communication system with cooperation

A cellular wireless communication system in which data is transmitted to multiple users over a common channel is considered. When the base stations in this system can cooperate with each other, the link from the base stations to the users can be considered a multi-user multiple-input multiple-output (MIMO) downlink system. For such a system, it is known from information theory that the total rate of transmission can be enhanced by cooperation. The channel is assumed to be fixed for all transmissions over the period of interest and the ratio of anticipated average arrival rates for the users, also known as the relative traffic rate, is fixed. A packet-based model is considered where data for each user is queued at the transmit end. We consider a simple policy which, under Markovian assumptions, is known to be throughput-optimal for this coupled queueing system. Since an exact expression for the performance of this policy is not available, as a measure of performance, we establish a heavy traffic diffusion approximation. To arrive at this diffusion approximation, we use two key properties of the policy; we posit the first property as a reasonable manifestation of cooperation, and the second property follows from coordinate convexity of the capacity region. The diffusion process is a semimartingale reflecting Brownian motion (SRBM) living in the positive orthant of N-dimensional space (where N is the number of users). This SRBM has one direction of reflection associated with each of the 2 ^N −1 boundary faces, but show that, in fact, only those directions associated with the (N−1)-dimensional boundary faces matter for the heavy traffic limit. The latter is likely of independent theoretical interest.     

A Reduced-Load Equivalence for Generalised Processor Sharing Networks with Long-Tailed Input Flows

We consider networks where traffic is served according to the Generalised Processor Sharing (GPS) principle. GPS-based scheduling algorithms are considered important for providing differentiated quality of service in integrated-services networks. We are interested in the workload of a particular flow i at the bottleneck node on its path. Flow i is assumed to have long-tailed traffic characteristics. We distinguish between two traffic scenarios, (i) flow i generates instantaneous traffic bursts and (ii) flow i generates traffic according to an on/off process. In addition, we consider two configurations of feed-forward networks. First we focus on the situation where other flows join the path of flow i. Then we extend the model by adding flows which can branch off at any node, with cross traffic as a special case. We prove that under certain conditions the tail behaviour of the workload distribution of flow i is equivalent to that in a two-node tandem network where flow i is served in isolation at constant rates. These rates only depend on the traffic characteristics of the other flows through their average rates. This means that the results do not rely on any specific assumptions regarding the traffic processes of the other flows. In particular, flow i is not affected by excessive activity of flows with heavier-tailed traffic characteristics. This confirms that GPS has the potential to protect individual flows against extreme behaviour of other flows, while obtaining substantial multiplexing gains.     

Reconstructing freeway travel times with a simplified network flow model alternating the adopted fundamental diagram

The present study summarises the travel time reconstruction performance of a network flow model by explicitly analysing the adopted fundamental diagram relation under congested and un-congested traffic patterns. The incorporated network flow model uses a discrete meso-simulation approach in which the anisotropic property of traffic flow and the uniform acceleration of vehicle packets are explicitly considered. The flow performances on link-route dynamics have been derived by reasonably alternating the adopted two-phase, i.e., congested and un-congested, fundamental relation of traffic flow. The linear speed–density relation with the creeping speed assumption is substituted with the triangular flow–density relation in order to investigate the performance of the network flow model in varying flow patterns. Applying the anisotropic mesoscopic model, the measure of travel time is obtained as a link performance from a simplified dynamic network loading process. Travel time reconstruction performance of the network flow model is sought considering the actual measures that are obtained by a probe vehicle, in addition to reconstructions by a macroscopic network flow model. The main improvements on travel time reconstruction process are encountered in terms of the computation load within the explicit analyses by the alternation of adopted two-phase fundamental diagram. Although the accuracies of the flow model with the adoption of two different fundamental diagrams are hard to differentiate, the computational burden of the simulation process by the triangular fundamental diagram is found to be considerably different.     

由路段交通量推算OD矩阵的一种有效方法及其应用

针对现有OD矩阵估计方法的不足，本讨论了一种新的有效的估计方法，它包括一个路段流量的预处理过程，以消除路段观测流量的不相容，然后经过流量加载和卸载两个逆过程，进行反复迭代，最终得到再现路段交通量的OD矩阵，中例证了该方法的有效性。     

A Combinatorial user optimal dynamic traffic assignment algorithm

This paper introduces a polynomial combinatorial optimization algorithm for the dynamic user optimal problem. The approach can efficiently solve single destination networks and can be potentially extended to heuristically solve multidestinational networks. In the model, traffic is propagated according to sound traffic flow theoretical models rather than link exit functions; thereby allowing link queue evolution to be modeled more precisely. The algorithm is designed, proven, implemented and computationally tested.     

Dynamic behaviors of the periodic predator–prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect

In this paper, a predator–prey system which based on a modified version of the Leslie–Gower scheme and Holling-type II scheme with impulsive effect are investigated, where all the parameters of the system are time-dependent periodic functions. By using Floquet theory of linear periodic impulsive equation, some conditions for the linear stability of trivial periodic solution and semi-trivial periodic solutions are obtained. It is proved that the system can be permanent if all the trivial and semi-trivial periodic solutions are linearly unstable. We use standard bifurcation theory to show the existence of nontrivial periodic solutions which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.     

Incompressible flows in elastic domains: an immersed boundary method approach

This study illustrates how the immersed boundary method may be applied to perform the numerical simulation of incompressible flows in two-dimensional domains bounded by elastic boundaries. It presents the basic intermediate steps involved in the derivation of a solution methodology, from a scientific motivation to the numerical results, which can be applied for both steady and transient problems, even when the boundaries have an arbitrary shape. Its motivation, briefly presented, was borne in a bioengineering problem: the numerical simulation of the performance of ventricular assist devices. The mathematical model is composed by the Navier–Stokes equations, where the forcing term contains singular forces which arise from the elastic stresses acting on the boundaries. The incompressibility constraint is modified to introduce the inflow and outflow conditions into the problem through the use of sources and sinks. The methodology is applied to simulate two problems: the steady flow between two parallel plates, for which the exact solution is known and can be used to validate the approach, and the periodic flow in a winding channel, a transient problem in a non-trivial domain.     

Thermally Enhanced Motions of Variable-Inflow Surface Gravity-Driven Flows

In this paper, we report on theoretical and numerical studies of models for suddenly initiated variable-inflow surface gravity currents having temperature-dependent density functions when these currents are subjected to incoming radiation. This radiation leads to a heat source term that, owing to the spatial and temporal variation in surface layer thickness, is itself a function of space and time. This heat source term, in turn, produces a temperature field in the surface layer having nonzero horizontal spatial gradients. These gradients induce shear in the surface layer so that a depth-independent velocity field can no longer be assumed and the standard shallow-water theory must be extended to describe these flow scenarios. These variable-inflow currents are assumed to enter the flow regime from behind a partially opened lock gate with the lock containing a large volume of fluid whose surface is subjected to a variable pressure. Flow filament theory is used to arrive at expressions for the variable inflow velocity under the assumptions of an inviscid and incompressible fluid moving through a small opening under a lock gate at one end of a large rectangular tank containing the deep slightly more dense ambient fluid. Finding this time-dependent inflow velocity, which will then serve as a boundary condition for the solution of our two-layer system, involves solving a forced Riccati equation with time-dependent forcing arising from the surface pressure applied to the fluid in the lock.
The results presented here are, to the best of our knowledge, the first to involve variable-inflow surface gravity currents with or without thermal enhancement and they relate to a variety of phenomena from leaking shoreline oil containers to spring runoff where the variable inflow must be taken into account to predict correctly the ensuing evolution of the flow.