The Theory of Dynamic Public Transit Priority with Dynamic Stochastic Park and Ride

2.1. The Existing Problem of Current Public Transit Priority

There are many researches on public transit priority from a different point. Tirachini et al. [1] have studied restating modal investment priority with an improved model for public transport analysis. Eichler and Daganzo [2] have researched Bus lanes with intermittent priority. Koehler and Kraus Jr. [3] have studied simultaneous control of traffic lights and bus departure for priority operation. Sun et al. [4] have studied bus detection based on sparse representation for transit signal priority. Wahlstedt [5] analyzed the impacts of bus priority in coordinated traffic signals. Liu et al. [6] proposed an Elastic analysis on urban public transport priority in Beijing. Zyryanov and Mironchuk [7] studied intermittent bus lane and bus signal priority strategy by simulation. Vedagiri and Arasan [8] discussed on estimating modal shift of car travelers to bus on introduction of bus priority system. The above researches play an important role on public transit priority, but some problems exist. The above researches mainly focus on public transit priority measures, but the research on public transit priority level for specific city is absent. The researches on public transit priority are not discussed from the point of public transit travel cost comparing with car travel cost, which results in low acceptance level of car user on public transit. Then the expected effect of public transit priority cannot be achieved.

Public transit priority policy has been implemented in China for more than ten years, it enhances public transit travel proportion in a certain extent, but traffic congestion is not relieved and car travel proportion during peak period is still increasing. Instead, public transit priority attracts slow travel group to public transit. The nature reason of this result lies in that public transit travel service level is far lower than cars during period. There is no reference point for public transit priority and what priority extent should be achieved for specific city is not discussed, which directly results in no goal of public transit priority and little effect of easing traffic congestion. The key reason is that how to attract car traveler to choose public transit is not considered from traveler point. Simply low fare is proved to be insufficient. Therefore, public transit travel service level should be enhanced through public transit priority. Since passenger crowd level is difficult to be eased in a short period, enhancing carrying speed of public transit is an important goal of public transit priority. Also, carrying speed enhancement for public transit is relative to car carrying speed, rather than simply comparing with carrying speed of public transit itself. It is obvious that public transit carrying speed should dynamic change according to car carrying speed and actual traffic volume. Therefore, dynamic public transit priority theory is needed.

2.2. The Present Situation and Existing Problem of Intervention on Car Use

The intervention on car use includes policy intervention and driving behavior intervention. For driving behavior intervention, Wang et al. [9, 10] discussed model-based digital driving dependability and safety-based behavioural approaching model. This study focuses on policy intervention. The current policy intervention measures include restriction pass, congestion charging, and increasing parking fee. These measures play a certain role to ease traffic congestion in a short period, but they are not suitable for long period because they are difficult to make traveler to initiatively voluntarily cooperate with traffic administration. Borjesson et al. [11] analyzed the Stockholm congestion charges, 5 years on effects, acceptability, and lessons learnt. But current research neglects the study of traveler acceptance on intervention measures. Traveler has low acceptability on intervention measures and is easy to form psychological resistance. These measures are not analyzed from convenient travel perspective. Also, because public transit service level is too low, there is no travel mode which car traveler can accept when reducing car use is required or car use is restricted in certain time interval. Therefore, other intervention measures on car use with higher traveler acceptability should be studied and dynamic public transit priority combined with dynamic stochastic park and ride is an intervention measure with high studying value.

2.3. The Present Situation and Existing Problem of Park and Ride

There are many researches on park and ride from a different point. Holguın-Veras et al. [12] studied user rationality and optimal park-and-ride location under potential demand maximization. Aros-Vera et al. [13] discussed p-Hub approach for the optimal park-and-ride facility location problem. Farhan and Murray [14] used a multiobjective spatial optimization model for siting park-and-ride facilities. Meek et al. [15, 16] analyzed UK local authority attitudes to park and ride and evaluating alternative concepts of bus-based park and ride. Kepaptsoglou et al. [17] analyzed optimizing pricing policies in park-and-ride facilities: a model and decision support system with application. Qin et al. [18] analyzed park-and-ride decision behavior based on Decision Field Theory. Hounsell et al. [19] studied enhancing park and ride with access control.

The above researches focus on the layout around rail transit station of urban peripheral or some public transit hub. This layout model plays a certain role for reducing car volume of driving into city center, but it is not conducive for traveler to stochastic selecting park and ride according to their travel demand. Therefore, it can influence the proportion of actual park and ride to possible park and ride. The layout and scale of park and ride should be hierarchical and classified in order to be adapted to dynamic stochastic park and ride demand for car traveler.

3.1. The Connotation of Dynamic Public Transit Priority

3.2. The Level of Dynamic Public Transit Priority

The level of dynamic public transit priority refers to what real-time dynamic priority level should be provided for public transit according to dynamic traffic demand under certain road traffic facilities conditions. That is how to dynamically allocate time and space for public transit priority pass. At the same time, dynamic public transit priority is relative to car travel service level (an average carrying speed of car). The purpose of dynamic public transit priority is to realize that public transit travel cost is not higher than car travel cost. Therefore, the key of dynamic public transit priority is to determine the proportion of public transit carrying speed to car carrying speed. Because car carrying speed is influenced by the saturation of road and intersection, the carrying speed of public transit dynamic changes too. This is the essential connotation of dynamic public transit priority.

3.2.2. The Public Transit Priority Demand Based on Minimum Carrying Speed

According to above priority level, road lane numbers of one direction, intersection form, entrance lane, and passing time for public transit priority can be determined. For public transit, the necessary driving speed on road and allowable waiting time at intersection can be deduced from public route number N, departure interval τ, stop time S_T at station, and average spacing between intersection. Necessary public transit lane number can be determined by the necessary driving speed on road and public transit volume. The pass rule for public transit priority can be determined by allowable waiting time at intersection.

For public transit, the available passing time T_R on road and waiting time T_J at intersection are analyzed firstly:

$$ (7)

Actually, the travel speed of public transit on public transit lane can reach V_R, thus,

$$ (8)

It is obvious that available waiting time T_J at intersection is related to carrying speed V_P and stop time S_T. The longer T_R and S_T are, the shorter T_J is. Intersection signal timing is mainly determined by T_J.

Generally, one public transit lane is enough on road and two public transit lanes is needed at intersection under general condition. Stop line in advance is designed for public transit and car. Specific traffic organization and design is showed as Figure 1.

3.3. Dynamic Traffic Organization and Design of Dynamic Public Transit Priority

The dynamic traffic organization and design of dynamic public transit priority mainly include variable public transit lane design, pass space, and stop rule design at intersection and signal timing design. Variable public transit lane design is deduced from above model, with setting variable public transit lane sign and releasing information about variable public transit lane in advance in order to enable car traveler to select appropriate path or park and ride in advance. Two stop lines are adopted at intersection entrance lane. Vehicle firstly stops at stop line far away intersection for prewaiting. Vehicle which will pass intersection in next green signal waits before stop line near intersection. Specific organizational design is as shown in Figure 1.

3.4. Model Analysis

But according to survey, actual V_P is 12.92 km/h. Now, V_P is difficult to be increased in Jiaozuo city; according to (10), $$ should be raised to 10 yuan.

4.1. The Connotation of Dynamic Stochastic Park and Ride

Current park and ride generally lies in urban peripheral. For urban center with serious traffic congestion, firstly, it is necessary to encourage traveler to reduce car use as far as possible, secondly, park and ride should be provided for traveler who have selected car when they feel too crowd. Also when dynamic public priority is carried out, some traveler of using car will want to park and ride because car carrying speed is lower than public transit carrying speed, then it is needed to provide parking facility for park and ride. This park and ride facility is located around general public transit station, with smaller scale comparing with general park and ride facility. Therefore, it is different from general park and ride. When dynamic public priority is carried out, not only public transit carrying speed is guaranteed, but also other choices are provided for car traveler on road. This intervention measures can be willingly accepted by traveler. When traveler has selected car and drives on road, at the beginning stage of travel, traveler is not sure that park and ride is necessary. If park and ride is needed, which site will be selected is not clear too. These are related to real-time dynamic traffic condition. That is, whether park and ride is needed and which park and ride site is selected is determined by dynamic traffic condition, which means that this park and ride has dynamic. Also it is obvious that this park and ride has uncertainty, which means it is stochastic. Therefore, this park and ride is called dynamic stochastic park and ride. At the same time, the above dynamic public transit priority will promote travel behavior of dynamic stochastic park and ride.

4.2. The Layout and Scale of Dynamic Stochastic Park and Ride

Dynamic stochastic park and ride layout is generally close to public transit station and corresponding road with more traffic volume will be priority selected. Figure 2 is layout sketch.

For dynamic stochastic park and ride, the closer it is to congestion area, the smaller the scale is. The diminishing size method mainly lies in two reasons. First, the closer it is to congestion area, the greater the difficulty of arranging park and ride land is. Second, traveler is encouraged and guided to park and ride in advance as far as it is possible in order to release traffic pressure of road and intersection close to congestion area.

The specific size of dynamic stochastic park and ride is determined by car volume of peak period and corresponding traffic volume with travel destination in congestion area. The corresponding traveler is investigated for park and ride proportion and site. Then, the park and ride volume for each station can be obtained and the park and ride scale for park and ride facility is determined. For car travel destination investigation, license plate photo can be adopted. Each road with park and ride facility should be investigated by license plate photo. The car volume with travel destination at congestion area is analyzed and for each car, whether park and ride will be adopted and which station will be selected are analyzed. If the station number with park and ride facility is N, corresponding road section number is N and corresponding intersection number is N. The layout sketch and charging standard for different site of dynamic stochastic park and ride are shown for car traveler during investigation (delivering card and feedback).

4.3. Charging Standard of Dynamic Stochastic Park and Ride

4.4. The Guidance for Dynamic Stochastic Park and Ride

The guidance for dynamic stochastic park and ride includes two aspects. On the one hand, it is needed to guide travelers to park and ride in advance as far as possible based on reducing car volume on road; on the other hand, the closer it is to congestion area, the smaller the scale of park and ride is, so, it is needed to guide travelers to park and ride in advance as far as possible based on park and ride capacity. When dynamic public transit priority is carried out, the closer it is to congestion area, the greater the car travel resistance is, and the parking cost is very high in area close to congestion area or in congestion area. The above two factors prompt traveler to park and ride in advance. At the same time, marked sign is set before each park and ride and propaganda slogan are adopted with showing the benefits and charge standard of park and ride. In order to provide convenience for park and ride traveler to transfer to public transit, public transit station is set at dynamic stochastic park and ride with bigger transfer demand.