P.M. Hui

Effects of Announcing Global Information in a Two-Route Traffic Flow Model

A two-route traffic model with a built-in decision-making process is proposed and studied numerically. The instantaneous average speeds on the routes are announced as global information. Two types of drivers, dynamic and static, are introduced. The dynamic drivers use the global information for making decisions. It is shown that announcing the instantaneous average speeds on the routes results in a better performance of the two-route system in terms of the traffic flux compared to announcing the transit time. When the static drivers randomly select a route, the presence of the dynamic drivers does not improve the traffic flux of the system. When the static drivers tend to select a particular route, the presence of dynamic drivers leads to a higher flux. Our model thus incorporates the effects of adaptability into the cellular automaton models of traffic flow.

Weighted scale-free networks with stochastic weight assignments.

We propose a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows, the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1-p. Numerical results show that the total weight exhibits a power-law distribution with an exponent sigma that depends on the probability p. The exponent sigma decreases continuously as p increases. For p=0, the scaling behavior is the same as that of the connectivity distribution. An analytical expression for the total weight is derived so as to explain the features observed in the numerical results. Numerical results are also presented for a generalized model with a fitness-dependent link formation mechanism.

The distribution and scaling of fluctuations for Hang Seng index in Hong Kong stock market

Abstract:The statistical properties of the Hang Seng index in the Hong Kong stock market are analyzed. The data include minute by minute records of the Hang Seng index from January 3, 1994 to May 28, 1997. The probability distribution functions of index returns for the time scales from 1 minute to 128 minutes are given. The results show that the nature of the stochastic process underlying the time series of the returns of Hang Seng index cannot be described by the normal distribution. It is more reasonable to model it by a truncated Lévy distribution with an exponential fall-off in its tails. The scaling of the maximium value of the probability distribution is studied. Results show that the data are consistent with scaling of a Lévy distribution. It is observed that in the tail of the distribution, the fall-off deviates from that of a Lévy stable process and is approximately exponential, especially after removing daily trading pattern from the data. The daily pattern thus affects strongly the analysis of the asymptotic behavior and scaling of fluctuation distributions.

Crowd–anticrowd theory of the minority game

The Minority Game is a simple yet highly non-trivial agent-based model for a complex adaptive system. Here, we provide an explanation of the games fluctuations which is both intuitive and quantitative, and which applies over the entire parameter range of interest. The physical idea behind our theory is to describe the interplay between crowds of like-minded agents and their anticorrelated partners (anticrowds).

Two-dimensional traffic flow problems in inhomogeneous lattices

Cellular automaton (CA) models are presented to simulate the traffic jam in a two-dimensional traffic flow. Effects of introducing inhomogeneities in the form of sites having different time scales and overpasses are studied using computer simulations. We present theoretical estimates of the critical car density and the average velocity at low car densities, and compare with numerical results. Results suggest that strategically adding these sites can help sustain a moving traffic at higher car densities.

Analytical results for the steady state of traffic flow models with stochastic delay

Exact mean field equations are derived analytically to give the fundamental diagrams, i.e., the average speed-car density relations, for the Fukui-Ishibashi one-dimensional traffic flow cellular automaton model of high speed vehicles (v max5M.1) with stochastic delay. Starting with the basic equation describing the time evolution of the number of empty sites in front of each car, the concepts of intercar spacings longer and shorter than M are introduced. The probabilities of having long and short spacings on the road are calculated. For high car densities ( r>1/M), it is shown that intercar spacings longer than M will be shortened as the traffic flow evolves in time, and any initial configurations approach a steady state in which all the intercar spacings are of the short type. Similarly for low car densities ( r<1/M), it can be shown that traffic flow approaches an asymptotic steady state in which all the intercar spacings are longer than M22. The average traffic speed is then obtained analytically as a function of car density in the asymptotic steady state. The fundamental diagram so obtained is in excellent agreement with simulation data. @S1063-651X~98!04709-6#

Enhanced winnings in a mixed-ability population playing a minority game

We study a mixed population of adaptive agents with small and large memories, competing in a minority game. If the agents are sufficiently adaptive, we find that the average winnings per agent can exceed that obtainable in the corresponding pure populations. In contrast to the pure population, the average success rate of the large-memory agents can be greater than 50%. The present results are not reproduced if the agents are fed a random history, thereby demonstrating the importance of memory in this system.

Topological properties of integer networks

Inspired by Pythagorass belief that numbers represent the reality, we study the topological properties of networks of composite numbers, in which the vertices represent the numbers and two vertices are connected if and only if there exists a divisibility relation between them. The network has a fairly large clustering coefficient C≈0.34, which is insensitive to the size of the network. The average distance between two nodes is shown to have an upper bound that is independent of the size of the network, in contrast to the behavior in small-world and ultra-small-world networks. The out-degree distribution is shown to follow a power-law behavior of the form k-2. In addition, these networks possess hierarchical structure as C(k)∼k-1 in accord with the observations of many real-life networks.

Self-segregation and enhanced cooperation in an evolving population through local information transmission

Effects of local information transmission and imitation among agents in an evolving population consisting of agents competing for limited resources are studied numerically through a model based on the evolutionary minority game (EMG). Enhanced cooperation is found to result from an effective self-segregation of the population into two groups with opposite characters. The self-segregation leads to an enhanced cooperation in that the winners per turn in the present model is higher than that in the minority game and EMG, and approaches the limiting value of (N−1)/2, where N is the number of agents in the population.

The asymptotic steady states of deterministic one-dimensional traffic flow models

Abstract The asymptotic steady state of deterministic Nagel–Schreckenberg (NS) traffic flow cellular automaton (CA) model for high-velocity cars ( v max =M>1 ) is studied. It is shown that the fundamental diagram, i.e., the relationship between the average car velocity and the car density, of the NS model in which the velocity of a car may increase by at most one unit per time step is exactly the same as that of the Fukui–Ishibashi (FI) traffic flow CA model in which a car may increase its velocity abruptly from zero to M or the maximum velocity allowed by the empty spacings ahead in one time step. This implies that for both gradual and abrupt accelerations, the self-organization of cars gives the same asymptotic behavior in one-dimensional traffic flow models.