Jiang Qian Ying

Sensitivity Analysis for Stochastic User Equilibrium Network Flows-- A Dual Approach

Recently, extensive studies have been conducted on the computational methods of sensitivity analysis for the Wardropian equilibrium modeling of traffic networks and their applications. But the same problems in the context of the stochastic user equilibrium modeling seem not to have been addressed. In this paper, we present a method for sensitivity analysis for network flows at stochastic user equilibrium. Our method is developed from a dual formulation of the stochastic user equilibrium analysis. By adopting Dials algorithm for stochastic traffic assignment, we are able to formulate a computationally efficient link-based algorithm for the sensitivity analysis. Since the Wardropian equilibrium in a traffic network is an extreme case of stochastic user equilibrium with ? ? 8, ? being a dispersion parameter in the expected utility function for stochastic route choice, the method presented here can also be used for sensitivity analysis of the Wardropian equilibrium by setting ? large enough.

An algorithm for local continuous optimization of traffic signals

In this paper, an algorithm for sensitivity analysis for equilibrium traffic network flows with link interferences is proposed. Based on this sensitivity analysis algorithm, a general algorithm is provided for solving the optimal design and management problems for traffic networks. In particular, this algorithm is applied to the optimal traffic signal setting problem. A numerical example is given to demonstrate the effectiveness of our algorithm.

An algebraic approach to strong stabilizability of linear nD MIMO systems

Although some necessary conditions for the strong stabilizability of linear multidimensional (nD) multiple-input-multiple-output (MIMO) systems have been available recently, very little is known about sufficient conditions for the same problem. This note presents two sufficient conditions for strong stabilizability of some classes of linear nD MIMO systems obtained using an algebraic approach. A simple necessary and sufficient condition is also given for the strong stabilizability of a special class of linear nD MIMO systems. An advantage of the proposed algebraic approach is that a stable stabilizing compensator can be constructed for an nD plant satisfying the sufficient conditions for the strong stabilizability presented in this note.

Factorizations for nD polynomial matrices

In this paper, a constructive general matrix factorization scheme is developed for extracting a nontrivial factor from a givennD (n>2) polynomial matrix whose maximal order minors satisfy certain conditions. It is shown that three classes ofnD polynomial matrices admit this kind of general matrix factorization. It turns out that minor prime factorization and determinantal factorization are two interesting special cases of the proposal general factorization. As a consequence, the paper provides a partial solution to an open problem of minor prime factorization as well as to a recent conjecture on minor prime factorizability fornD polynomial matrices. Three illustrative examples are worked out in detail.

On the Strong Stabilizability of MIMO n -Dimensional Linear Systems

A plant is strongly stabilizable if there exists a stable compensator to stabilize it. Based on some theorems in complex analysis of several variables proved in this paper, we present necessary conditions for the strong stabilizability of complex and real n-D multi-input multi-output (MIMO) shift-invariant linear plants. For the real case, the condition is a generalization of the parity interlacing property of Youla, Bongiorno, and Lu [ Automatica J. IFAC, 10 (1974), pp. 159--173] for the strong stabilizability of a real one-dimensional MIMO plant. These conditions are also sufficient for the cases of n-D plants with a single output (MISO) or with a single input (SIMO). For general n-D MIMO plants, we do not know if the conditions are sufficient or not. A useful sufficient, but not necessary, condition for the strong stabilizability of a class of n-D

A Simulation Model for Traffic Behavior at Merging Sections in Highways

(n\geq 2)

Sensitivity Analysis Based Method for Optimal Road Network Pricing

MIMO plants is given.

Comments on "Stability tests of N-dimensional discrete time systems using polynomial arrays

In this paper, a novel lane change model is introduced. By combining this model with intellegent driver model proposed by Treiber and Helbing a simulation model for describing the traffic flow behavior in the merging sections in highways is proposed. By numerical simulation experiments, this model is shown to be able to reproduce typical traffic behavior patterns in the highway.

Some algebraic aspects of the strong stabilizability of time-delay linear systems

Abstract Road pricing is an important economic measure for optimal management of transportation networks. The optimization objectives can be the total travel time or total cost incurred by all the travelers, or some other environmental objective such as minimum emission of dioxide, an so on. Suppose a certain toll is posed on some link on the network, this will give an impact on flows over the whole network and brings about a new equilibrium state. An equilibrium state is a state of traffic network at which no traveler could decrease the perceived travel cost by unilaterally changing the route. The aim of the toll setting is to achieve such an equilibrium state that a certain objective function is optimized. The problem can be formulated as a mathematical program with equilibrium constraints (MPEC). A key step for solving such a MPEC problem is the sensitivity analysis of traffic flows with respect to the change of link characteristics such as the toll prices. In this paper a sensitivity analysis based method is proposed for solving optimal road pricing problems.

A Computational Method for Determining Strong Stabilizability of n-D Systems

For original paper see X. Hu, ibid., vol.42, p.261-8 (1995). In this brief, we wish to point out that Hu overlooked a mistake in the stability test procedure for N-dimensional (N-D, N>2) systems proposed in the above paper, which made the polynomial array approach not general. It is shown that Hus test procedure applies only to a very restricted class of N-D stability test problems, and for a general case, instead of necessary and sufficient conditions, it provides only sufficient conditions. A counterexample is also given.