^{1}

^{1}

^{2}

^{2}

^{1}

^{2}

The merge control models proposed for work zones are classified into two types (Hard Control Merge (HCM) model and Soft Control Merge (SCM) model) according to their own control intensity and are compared with a new model, called Individual Subjective Initiative Merge (ISIM) model, which is based on the linear lane-changing probability strategy in the merging area. The attention of this paper is paid to the positive impact of the individual subjective initiative for the whole traffic system. Three models (ISIM, HCM, and SCM) are established and compared with each other by two order parameters, that is, system output and average vehicle travel time. Finally, numerical results show that both ISIM and SCM perform better than HCM. Compared with SCM, the output of ISIM is 20 vehicles per hour higher under the symmetric input condition and is more stable under the asymmetric input condition. Meanwhile, the average travel time of ISIM is 2000 time steps less under the oversaturated input condition.

Over the past several decades, many methods and rules [

In next sections, three models with different lane-changing rules and a vehicle input method are introduced. Simulation results and analyses are presented after that. Conclusions and further studies are given in the last section.

We introduce Cellular Automaton (CA) [

The basic updating rules are introduced according to NS model [

Accelerating at the

Safety breaking at the

Random decelerating at the

Moving at the

where

The basic model is presented in Figure

The basic work zone system.

We introduce three different kinds of lane-changing rules into the basic model and then get three models: (1) ISIM, (2) HCM, and (3) SCM.

(1)

Lane-changing probability of ISIM.

With the linear lane-changing probability, we try to perform a more realistic simulation and find out the impact of the individual subjective initiative on the whole system.

(2)

Lane-changing probability of HCM.

The probability of the vehicle on Lane 1 changing to Lane 2 is

Lane-changing probability of SCM.

The difference between ISIM and SCM is the lane-changing probability of the vehicle on Lane 2. When the traffic demand is light, vehicles on Lane 1 can easily change lane at the upstream of the DL model (like the static early merge in [

We introduce the probability distribution function here to obtain the quantity of the arriving vehicle per time step. According to the traffic flow theory, the Poisson distribution function is adaptive under the light traffic condition and the binomial distribution function is chosen under the congested condition [

The Poisson distribution function is

After getting the quantity of arriving vehicles, we do not input them into the model directly. Instead, we put them into a stack and set the serial number and arriving time for them. Then we input them into the model in turn (according to the First-In-First-Out principle) with the consideration of the real-time conditions of the lane and the stack.

We performed simulations based on the three models described above with

We simulate two other basic models for comparison: a 200-lattice long SL model and a 200-lattice long DL model. Briefly, the work zone model is composed of a SL model and a DL model, so the simulation of SL and DL model helps us to get the theoretical limitations of the output of the work zone system in Figure

(a) Output of SL and DL model; (b) the fitting line of SL and DL model.

We simulate the three models individually, and the results are illustrated in Figure

(a) Output results of three models; (b) fitting lines of three models and the theoretical value (

Next, we run three models under asymmetric input conditions as (

The results are presented as in Figure

Output results of three models under asymmetric input conditions (a) ISIM, (b) HCM, and (c) SCM.

From Figure

Output of HCM in the section where

It is obvious from the Figure

Similar to the discussion of output, we simulate SL and DL model to obtain the theoretical travel time and the results of SL and DL model and other three models are presented in Figure

The travel time results of SL model, DL model, and three models.

When the input increases to their respective

The travel time results of ISIM and SCM.

In Figure

Area A:

Area B:

In Area A, the input is smaller than the theoretical value, and the travel time results of both models are about 58 time steps, so the mean velocity at which the vehicle passes through the system is about 3.4 lattice per time step. According to the maximum velocity (4 lattice per time step), it is a satisfactory value. In Area B, once the input is larger than the theoretical value, the travel time result of SCM increases dramatically. The result of ISIM is obviously better. The circled point (after which the result increases rapidly) of ISIM is about 1350 vph which is about 200 vph higher than the theoretical value and that of SCM. Furthermore, the travel time of ISIM is 2000 time steps less when the input reaches to 1500 vph, and this is a huge advantage to move vehicles in less time. It is noticed that the individual subjective initiative in ISIM can improve the velocity and capacity of the traffic.

In this paper, we try to make a comparison between the three models: ISIM, HCM, and SCM. HCM model performs unsatisfactorily in both output and average travel time, because its control method is purely mechanical. The vehicle in it has to slow down or even stop for the signal, and the individual subjective initiative is not considered. When HCM is implemented, many factors should be taken into consideration, such as the careful input control, and the interval between the signal changes. Meanwhile, SCM model, owing to the passive performance of DL model, performs better than HCM model when the traffic is heavy. ISIM model performs the best among the three models under different traffic conditions due to the well-designed individual subjective initiative. The huge advantage in travel time results compared with SCM cannot be ignored. Vehicles in it can balance themselves more actively, and this makes the system perform the best in both output results, and travel time results. The individual subjective initiative is helpful for the vehicle to make a good use of system resources and make the system more flexible.

In further studies, we will try to take more details of ISIM model into consideration, such as the complex driver-vehicle behavior [

This work is partially supported by the National Natural Science Foundation of China (70631002, 10774112) and the Program for New Century Excellent Talents in University (NCET-08-0406).