Effect of signals on two-route traffic system with real-time information

We study the effect of signals on the vehicular traffic in the two-route system at the tour-time feedback strategy where the vehicles move ahead through a series of signals. The Nagel–Schreckenberg model is applied to the vehicular motion. The traffic signals are controlled by both cycle time and split. The tour times on two routes fluctuate periodically and alternately. The period increases with decreasing the split. Also, the tour time on each route varies with time by synchronizing with the density. The dependences of tour times and densities on both split and cycle time are clarified.     

Green-wave control of an unbalanced two-route traffic system with signals

We introduce the preference parameter into the two-route dynamic model proposed by Wahle et al. The parameter represents the driver’s preference for the route choice. When the driver prefers a route, the traffic flow on route A does not balance with that on route B. We study the signal control for the unbalanced two-route traffic flow at the tour-time feedback strategy where the vehicles move ahead through a series of signals. The traffic signals are controlled by both cycle time and phase shift (offset time). We find that the mean tour time can be balanced by selecting the offset time successfully. We derive the relationship between the mean tour time and offset time (phase shift). Also, the dependences of the mean density and mean current on the offset time are derived.     

Clustering and maximal flow in vehicular traffic through a sequence of traffic lights

We study the maximal current (maximum traffic capacity) of vehicular traffic through a sequence of traffic lights on a highway, where all signals turn on and off synchronously. The dynamical model of vehicular traffic controlled by signals is expressed in terms of a nonlinear map, where the excluded-volume effect is taken into account. The dynamical behaviors of vehicles are clarified by analyzing traffic patterns. The clustering of vehicles varies with the cycle time of signals. The maximum current is closely connected to vehicular clustering. Clustering of vehicles is controlled by varying both split and cycle time of signals. The dependence of the maximal current on both split and cycle time is derived.     

Vehicular traffic flow through a series of signals with cycle time generated by a logistic map

We study the dynamical behavior of vehicular traffic through a series of traffic signals. The vehicular traffic is controlled with the use of the cycle time generated by a logistic map. Each signal changes periodically with a cycle time, and the cycle time varies from signal to signal. The nonlinear dynamic model of the vehicular motion is presented by a nonlinear map including the logistic map. The vehicular traffic exhibits very complex behavior on varying both the cycle time and the logistic-map parameter a$a$. For a>3$a>3$, the arrival time shows a linear dependence on the cycle time. Also, the dependence of vehicular motion on parameter a$a$ is clarified.     

Realizing Wardrop equilibria with real-time traffic information

A Wardrop equilibrium for multiple routes from the same origin to the same destination requires equal travel time on each path used. With the advent of real-time traffic data regarding travel times on alternative routes, it becomes important to analyze how best to use the information provided to drivers. In particular, can a Wardrop equilibrium, which is a desired state, be realized? Simulations using a realistic traffic model (the three-phase model) on a two-route example are presented to answer this question. One route (the main line) is a two-lane highway with a stalled vehicle in the right lane and the other route is a low-speed bypass. For a critical incoming flow of vehicles, a phase transition between free flow and congested flow near the stalled vehicle is observed, making this a challenging example. In the first scenario, drivers choose routes selfishly on the basis of current travel times. The result is strong oscillations in travel time because of the inherent delay in the information provided. The second scenario involves a hypothetical control system that limits the number of vehicles on the main line to prevent the free-flow to congested-flow phase transition by diverting sufficient flow to the bypass. The resulting steady state is neither a Wardrop equilibrium nor a system optimum, but an intermediate state in which the main-line travel time is less than on the bypass but the average for all vehicles is close to a minimum. In a third scenario, anticipation is used as a driver-advice system to provide a fair indicator of which route to take. Prediction is based on real-time data comparing the number of vehicles on the main line at the time a vehicle leaves the origin to the actual travel time when it reaches the destination. Steady states that approximate Wardrop equilibria, or at least as close to them as can be expected, are obtained. This approach is also applied to an example with a low-speed boundary condition imposed at the destination in place of a stalled vehicle. The steady state flow approaches a Wardrop equilibrium because there is no abrupt change in travel time due to a phase transition.     

Nonlinear-map model for split effect on vehicular traffic through periodic signals

We study the effects of both split and cycle time on dynamical behavior of vehicles moving through a sequence of traffic lights on a highway, where the traffic lights turn on and off periodically. The dynamical model of vehicular traffic controlled by signals is expressed in terms of a nonlinear map. The vehicle exhibits complex behavior with varying split and cycle time. The tour time between signals shows a self-similar behavior. When split s_p is lower than 0.5, vehicular traffic shows a similar behavior as that of s_p=0.5, while vehicular traffic of s_p  >0.5 is definitely different from that of _sp?0.5$s_p?0.5$. The algebraic expression among the tour time, cycle time, and split is derived.     

Dynamics of traffic flows on crossing roads induced by real-time information

Traffic flows on crossing roads with an information board installed at the intersection have been simulated by a cellular automaton model. In the model, drivers have to enter the road with a shorter trip-time indicated on the information board, by making a turn at the intersection if necessary. The movement of drivers induces various traffic states, which are classified into six phases as a function of the car density. The dynamics of the traffic is expressed as the return map in the density–flow space, and analyzed on the basis of the car configuration on the roads.     

Randomness control of vehicular motion through a sequence of traffic signals at irregular intervals

We study the regularization of irregular motion of a vehicle moving through the sequence of traffic signals with a disordered configuration. Each traffic signal is controlled by both cycle time and phase shift. The cycle time is the same for all signals, while the phase shift varies from signal to signal by synchronizing with intervals between a signal and the next signal. The nonlinear dynamic model of the vehicular motion is presented by the stochastic nonlinear map. The vehicle exhibits the very complex behavior with varying both cycle time and strength of irregular intervals. The irregular motion induced by the disordered configuration is regularized by adjusting the phase shift within the regularization regions.     

Vehicular motion in counter traffic flow through a series of signals controlled by a phase shift

We study the dynamical behavior of counter traffic flow through a sequence of signals (traffic lights) controlled by a phase shift. There are two lanes for the counter traffic flow: the first lane is for east-bound vehicles and the second lane is for west-bound vehicles. The green-wave strategy is studied in the counter traffic flow where the phase shift of signals in the second lane has opposite sign to that in the first lane. A nonlinear dynamic model of the vehicular motion is presented by nonlinear maps at a low density. There is a distinct difference between the traffic flow in the first lane and that in the second lane. The counter traffic flow exhibits very complex behavior on varying the cycle time, the phase difference, and the split. Also, the fundamental diagram is derived by the use of the cellular automaton (CA) model. The dependence of east-bound and west-bound vehicles on cycle time, phase difference, and density is clarified.     

Vehicular motion in 2D city traffic network with signals controlled by phase shift

We study the dynamic behavior of vehicular traffic through the series of traffic lights controlled by phase shift in two-dimensional (2D) city traffic network. The nonlinear-map model is presented for the vehicular traffic. The city traffic network is made of one-way perpendicular streets arranged in a square lattice with traffic signals where vertical streets are oriented upwards and horizontal streets are oriented rightwards. There are two traffic lights for the movement to north or that to east at each crossing. The traffic lights are controlled by the cycle time, split, and phase shift. The vehicle moves through the series of signals on a path selected by the driver. The city traffic with a heterogeneous density distribution is also studied. The dependence of the arrival time on cycle time, split, phase shift, selected path, and density is clarified for 2D city traffic. It is shown that the vehicular traffic is efficiently controlled by the phase shift.     

Regularization and control of irregular vehicular motion through a series of signals at disordered intervals

We study the control and regularization of irregular motion of a vehicle moving through the series of traffic signals positioned at disordered intervals. All signals are controlled by both cycle time and phase shift. The nonlinear dynamic model of the vehicular motion controlled by signals is described in terms of the stochastic nonlinear map. The vehicle exhibits a very complex behavior with varying both cycle time and strength of disordered intervals. The delay or advance of tour time is compensated by synchronizing the phase shift with disordered intervals. The irregular motion induced by the disordered configuration of signals is regularized for various values of cycle time.     

Fluctuation and transition of vehicular traffic through a sequence of traffic lights

We study the dynamical behavior of N vehicles with no passing, but are moving through a sequence of traffic lights on a single-lane highway, where the traffic lights turn on and off periodically with the synchronized strategy. The dynamical model of N vehicles controlled by traffic lights is described in terms of coupled maps with three parameters. The motions of vehicles display a complex behavior, interacting with other vehicles through the sequence of traffic lights. Fluctuation of the leading vehicle is amplified to the following vehicles. The amplification of fluctuation changes with cycle time. The dynamical behavior of vehicles depends highly on their position of grouping vehicles. Signal traffic at a low density changes at specific values of cycle time. The complex dynamical transitions occur by varying three parameters.     

Effect of restart at signals on traffic flow through a series of signals

We study the effect of restart at signals on the vehicular traffic controlled by a series of signals. The Nagel–Schreckenberg model (NS model) and Fukui–Ishibashi model (FI model) are applied to the vehicular motion. In the FI model, the step-by-step acceleration is not taken into account but the acceleration effect is included in the NS model. It is shown that the difference between both models results in the restart effect at signals. The extended version of the NS model with signals is formulated by the difference equation. The restart at signals has an effective effect on the traffic flow. The fundamental diagram changes highly by the restart effect. The dependences of mean speed on the cycle time are shown.     

Complex motion in nonlinear-map model of elevators in energy-saving traffic

We have studied the dynamic behavior and dynamic transitions of elevators in a system for reducing energy consumption. We present a nonlinear-map model for the dynamics of M elevators. The motion of elevators depends on the loading parameter and their number M. The dependence of the fixed points on the loading parameter is derived. The dynamic transitions occur at 2(M−1) stages with increasing the value of loading parameter. At the dynamic transition point, the motion of elevators changes from a stable state to an unstable state and vice versa. The elevators display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates in a complex manner over various trips.     

Bunching and transition of vehicles controlled by a sequence of traffic lights

We study the dynamical behavior of many vehicles with different desired velocities, moving through a sequence of traffic lights on a single-lane highway, where the traffic lights turn on and off periodically with the synchronized strategy. The dynamics of vehicular traffic controlled by traffic lights is described in terms of the nonlinear maps. For specific values of cycle time, the group (cluster) of vehicles exhibits the bunching without extending over the highway. It is found that two types of traffic states appear: the one is the bunching traffic and the other is the extended traffic. In the bunching traffic, all vehicles move together with the same tour time, while vehicles spread over the highway in the extended traffic. The dynamical transition between two traffic states occurs at specific values of cycle time. The phase diagram (region map) is presented.     

Tipping news in information accumulation system

As a continuous opinion dynamics model, the information accumulation system (IAS) includes three basic mechanisms of the news, the inheritance and the diffusion as contributing to the information accumulation process of a system. A system is composed of agents who diffuse information through internal interaction, while each of them has incomplete memory or inheritance rate. The news comes from external sources of information, such as mass media. Previously the model IAS was studied only for the small news problems. In this study, a tipping news problem is considered. A key question of the problem is: what is the minimum strength of advertisement that can tip the minority opinion to a majority one? Dynamics of the IAS is briefly revisited with a special interest on nonlinear behavior of the model. In particular, it is shown that a discrete map of the IAS for a single color problem can be transformed into a logistic map, from which the dynamics of the IAS can be better understood. To show the applicability of the IAS model, the result is applied to explain the concept of the critical population size, which claims that there is a minimum population size for a social knowledge system to be continuously inherited without being lost. And critical size of the tipping news is found analytically in terms of IAS parameters. Some of the key results from the present study are compared in detail with the results from the Brownian particle model, which is believed to be the most similar model to the IAS. The concept of tipping news is used to show that a traditional society can tip at an exceptionally low inter-community exposure. Finally, the result was applied to the language competition problem.     

Dynamical model for retrieval of tram schedule

We present the dynamical model for retrieval of a tram schedule when trams arrive at stops slower or faster than the schedule. Trams speed up or stop shorter to retrieve the delay. The dynamics of the trams is expressed in terms of the nonlinear maps. We study the dynamical behavior of trams when they control the speed and stopping time to retrieve the schedule. The arrival times of trams exhibit the complex behavior with varying trips. The trams show the periodic and irregular (chaotic) motions even if there are no noises. The tram chaos is controlled by varying both stopping time and degree of speedup. The tram schedule is connected with the complex motions of trams. The region map (phase diagram) is shown to control the complex motions of trams.     

Passenger's fluctuation and chaos on ferryboats

We study the fluctuation of shipping passengers on a few ferryboats which shuttle between an origin and a destination repeatedly. We present the dynamical model for the ferryboats. The model is described in terms of nonlinear maps defined from the vectors T_i(n) and W_i(n), i=1, 2, …, N for N ferryboats where T_i(n) is the arrival time of ferryboat i at the origin on trip n and W_i(n) the number of passengers waiting at the origin on trip n. We clarify the fluctuations of shipping passengers and tour time for the ferry schedule. It is found that the dynamical transitions among the regular, periodic, and chaotic motions occur by varying the ferry's capacity F_max, headway T_min, and loading parameter ΓΠ. Even if the second ferryboat follows the leader (first ferryboat) keeping the constant headway, the passengers shipping on the second fluctuate highly when the parameters take specific values.     

Effect of speed fluctuations on a green-light path in a 2d traffic network controlled by signals

When a vehicle moves through a series of green lights, avoiding red signals in a two-dimensional (2d) city traffic network, the vehicle describes a characteristic trajectory (green-light path) and the travel time has a minimal value. The green-light path depends on the cycle time, split, signal-control strategy, and fluctuations of vehicular speed. We clarify the effect of speed fluctuations on a green-light path in a 2d traffic network controlled by signals. Even if an extremely small quantity of speed fluctuation is added, the green-light path changes greatly. It is shown that the root-mean square (RMS) of the deviation from the mean path depends highly on the cycle time. Also, the dependence of the green-light path on the speed-fluctuation strength is shown under a constant value of cycle time.     

Traffic dynamics in scale-free networks with tunable strength of community structure

In this paper we systematically investigate the impact of community structure on traffic dynamics in scale-free networks based on local routing strategy. A growth model is introduced to construct scale-free networks with tunable strength of community structure, and a packet routing strategy with a parameter α is used to deal with the navigation and transportation of packets simultaneously. Simulations show that the maximal network capacity stands at α=−1 in the case of identical vertex capacity and monotonously decreases with the strength of community structure which suggests that the networks with fuzzy community structure (i.e., community strength is weak) are more efficient in delivering packets than those with pronounced community structure. To explain these results, the distribution of packets of each vertex is carefully studied. Our results indicate that the moderate strength of community structure is more convenient for the information transfer of real complex systems.