Research ArticleThe Theory of Dynamic Public Transit Priority with DynamicStochastic Park and Ride

Chengming Zhu,1,2 Yanyan Chen,1 and Changxi Ma3

1 Transportation Research Center, Beijing University of Technology, Beijing 100124, China2 College of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo, Henan 454000, China3 School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China

Correspondence should be addressed to Chengming Zhu; zhuchengming@hpu.edu.cn

Received 2 December 2013; Revised 24 January 2014; Accepted 10 February 2014; Published 12 March 2014

Academic Editor: Wuhong Wang

Copyright © 2014 Chengming Zhu et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Public transit priority is very important for relieving traffic congestion. The connotation of dynamic public transit priority anddynamic stochastic park and ride is presented. Based on the point that the travel cost of public transit is not higher than the travel costof car, how to determine the level of dynamic public transit priority is discussed.The traffic organizationmethod of dynamic publictransit priority is introduced. For dynamic stochastic park and ride, layout principle, scale, and charging standard are discussed.Traveler acceptability is high through the analysis of questionnaire survey. Dynamic public transit priority with dynamic stochasticpark and ride has application feasibility.

1. Introduction

There is a fact that public transit cannot compete with car andtravelers are not willing to initiatively reduce car use. Publictransit travelers make effort for relieving traffic congestion,but they do not benefit from their behaviors. Car travelersincrease traffic congestion degree and they benefit fromtheir behaviors. Because of the above reason, travelers arereluctant to actively cooperate with government and trafficadministration. For travel behavior intervention, there is alarge gap between actual effect and expected effect. Sometough intervention measures on car use are adopted forrelieving congestion, but tough intervention measures areeasily to cause traveler’s antipathy and cannot guide travelerto initiatively reduce car use.

The effective travel intervention measure should be ableto make public transit to compete with car. Also, it should beable to make government, traffic administration, and publictransit traveler (including travels who initiatively reduce caruse) to compete with traveler who do not reduce car use.Therefore, it is needed that public transit traveler are willingto actively cooperate with government and traffic adminis-tration. The premise of this cooperation is that public transit

travelers benefit from choosing public transit. But at presenttime, public transit traveler cannot benefit from choosingpublic transit because of very low comfort level and lowcarrying speed. Therefore, other travel behavior interventionmodel is needed to be studied based on enhancing publictransit travel service level. It should increase public transitcompetiveness with car and it should ensure that travelersare willing to accept it. It can promote traveler actively tocooperate with government and traffic administration. Thestart point of this interventionmodel is based on the fact thatpublic transit travel cost is not higher than car travel cost.

2. The Existing Problem

2.1. The Existing Problem of Current Public Transit Priority.There are many researches on public transit priority froma different point. Tirachini et al. [1] have studied restatingmodal investment prioritywith an improvedmodel for publictransport analysis. Eichler and Daganzo [2] have researchedBus lanes with intermittent priority. Koehler and Kraus Jr. [3]have studied simultaneous control of traffic lights and busdeparture for priority operation. Sun et al. [4] have studiedbus detection based on sparse representation for transit signal

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 525460, 7 pageshttp://dx.doi.org/10.1155/2014/525460

2 Mathematical Problems in Engineering

priority. Wahlstedt [5] analyzed the impacts of bus priorityin coordinated traffic signals. Liu et al. [6] proposed anElastic analysis on urban public transport priority in Beijing.Zyryanov and Mironchuk [7] studied intermittent bus laneand bus signal priority strategy by simulation. Vedagiri andArasan [8] discussed on estimating modal shift of car travel-ers to bus on introduction of bus priority system. The aboveresearches play an important role on public transit priority,but some problems exist. The above researches mainly focuson public transit prioritymeasures, but the research on publictransit priority level for specific city is absent. The researcheson public transit priority are not discussed from the pointof public transit travel cost comparing with car travel cost,which results in low acceptance level of car user on publictransit. Then the expected effect of public transit prioritycannot be achieved.

Public transit priority policy has been implemented inChina for more than ten years, it enhances public transittravel proportion in a certain extent, but traffic congestion isnot relieved and car travel proportion during peak period isstill increasing. Instead, public transit priority attracts slowtravel group to public transit. The nature reason of this resultlies in that public transit travel service level is far lower thancars during period. There is no reference point for publictransit priority and what priority extent should be achievedfor specific city is not discussed, which directly results in nogoal of public transit priority and little effect of easing trafficcongestion. The key reason is that how to attract car travelerto choose public transit is not considered from traveler point.Simply low fare is proved to be insufficient. Therefore, publictransit travel service level should be enhanced through publictransit priority. Since passenger crowd level is difficult to beeased in a short period, enhancing carrying speed of publictransit is an important goal of public transit priority. Also,carrying speed enhancement for public transit is relativeto car carrying speed, rather than simply comparing withcarrying speed of public transit itself. It is obvious that publictransit carrying speed should dynamic change accordingto car carrying speed and actual traffic volume. Therefore,dynamic public transit priority theory is needed.

2.2. The Present Situation and Existing Problem of Inter-vention on Car Use. The intervention on car use includespolicy intervention and driving behavior intervention. Fordriving behavior intervention, Wang et al. [9, 10] discussedmodel-based digital driving dependability and safety-basedbehavioural approaching model. This study focuses on pol-icy intervention. The current policy intervention measuresinclude restriction pass, congestion charging, and increasingparking fee. These measures play a certain role to ease trafficcongestion in a short period, but they are not suitable forlong period because they are difficult to make traveler toinitiatively voluntarily cooperate with traffic administration.Borjesson et al. [11] analyzed the Stockholm congestioncharges, 5 years on effects, acceptability, and lessons learnt.But current research neglects the study of traveler acceptanceon intervention measures. Traveler has low acceptability onintervention measures and is easy to form psychologicalresistance. These measures are not analyzed from convenient

travel perspective. Also, because public transit service level istoo low, there is no travel mode which car traveler can acceptwhen reducing car use is required or car use is restricted incertain time interval. Therefore, other intervention measureson car usewith higher traveler acceptability should be studiedand dynamic public transit priority combined with dynamicstochastic park and ride is an interventionmeasure with highstudying value.

2.3. The Present Situation and Existing Problem of Park andRide. There are many researches on park and ride from adifferent point. Holguın-Veras et al. [12] studied user ratio-nality and optimal park-and-ride location under potentialdemand maximization. Aros-Vera et al. [13] discussed p-Hub approach for the optimal park-and-ride facility locationproblem. Farhan and Murray [14] used a multiobjectivespatial optimization model for siting park-and-ride facilities.Meek et al. [15, 16] analyzed UK local authority attitudes topark and ride and evaluating alternative concepts of bus-based park and ride. Kepaptsoglou et al. [17] analyzed opti-mizing pricing policies in park-and-ride facilities: a modeland decision support system with application. Qin et al. [18]analyzed park-and-ride decision behavior based on DecisionFieldTheory. Hounsell et al. [19] studied enhancing park andride with access control.

The above researches focus on the layout around railtransit station of urban peripheral or some public transit hub.This layoutmodel plays a certain role for reducing car volumeof driving into city center, but it is not conducive for travelerto stochastic selecting park and ride according to their traveldemand. Therefore, it can influence the proportion of actualpark and ride to possible park and ride. The layout and scaleof park and ride should be hierarchical and classified in orderto be adapted to dynamic stochastic park and ride demandfor car traveler.

3. Dynamic Public Transit Priority Theory

3.1. The Connotation of Dynamic Public Transit Priority.Dynamic public transit priority dynamically adjusts space-time resources for public transit according to road trafficvolume and saturation, public transit vehicle volume, andintersection saturation. It includes public transit lane allo-cation on road, intersection entrance lane, and pass timeallocation for public transit at intersection. Its purpose isto ensure that public transit carrying speed is so high thatpublic transit can compete with car. When travelers selectpublic transit, their profits are not lower than car traveler,or public transit travel cost is not higher than car travel.The connotation of dynamic public transit priority can beconcretely expressed as follows.

(1) For unit travel distance, the proportion of publictransit travel profit to cost is not lower than car travel.

(2) For same travel distance, public transit travel cost isnot higher than car travel cost.

Dynamic public transit priority theory is conducive to pro-mote car traveler to reduce car use and shift to public transit.

Mathematical Problems in Engineering 3

3.2. The Level of Dynamic Public Transit Priority. The levelof dynamic public transit priority refers to what real-timedynamic priority level should be provided for public transitaccording to dynamic traffic demand under certain roadtraffic facilities conditions. That is how to dynamically allo-cate time and space for public transit priority pass. At thesame time, dynamic public transit priority is relative to cartravel service level (an average carrying speed of car). Thepurpose of dynamic public transit priority is to realize thatpublic transit travel cost is not higher than car travel cost.Therefore, the key of dynamic public transit priority is todetermine the proportion of public transit carrying speed tocar carrying speed. Because car carrying speed is influencedby the saturation of road and intersection, the carrying speedof public transit dynamic changes too. This is the essentialconnotation of dynamic public transit priority.

3.2.1. The Equilibrium Point of Public Transit Priority Carry-ing Speed (The Minimum Carrying Speed). Judging currentpublic transit priority, key factor influencing public transitpriority effect is carrying speed. Enhancing public transitcarrying speed is a powerful measure for enhancing publictransit competitiveness. Therefore, dynamic public transitshould ensure that public transit carrying speed is higher thancar carrying speed. Because car speed is influenced by trafficsaturation, the carrying speed of dynamic transit priority alsoshould be depended on specific traffic saturation.

Assume that public transit travel and car travel havesame travel OD and approximate same travel path. That istravel distance of two travel modes is approximately equal.From the point of travel cost, what carrying speed should beprovided for public transit is analyzed under certain road-traffic facilities and traffic saturation.

The travel cost of choosing public transit is𝐶𝑃. It includes

time cost 𝐶𝑡𝑃(including walking time of arriving at station,

away from station, transfer, and waiting time) and ticket cost𝐶𝑒

𝑃, the energy consumption cost caused by the crowd in

public transit and energy consumption cost per unit time𝐶𝑛

𝑃, without considering energy consumption cost of walking

(this walking can be regarded as a kind of physical training).The travel cost of choosing car is 𝐶

𝐶. It includes time cost

𝐶𝑡

𝐶, fuel cost 𝐶𝑓

𝐶, and parking cost 𝐶𝑝

𝐶.

Note that travel distances are 𝐿, walking distance ofchoosing public transit is 𝐿

𝑊, walking speed is 𝑉

𝑊, public

transit carrying speed is𝑉𝑃, car carrying speed is𝑉

𝐶, and fuel

cost of per km is 𝐶𝑓0.

For the same traveler, per time cost of choosing publictransit and car is equal. Assume that Per time cost is 𝐶𝑡

0, then

travel cost of choosing public transit is as shown in (1):

𝐶𝑃= 𝐶𝑡

𝑃+ 𝐶𝑒

𝑃+ 𝐶𝑛

𝑃⋅𝐿 − 𝐿𝑊

𝑉𝑃

= 𝐶𝑡

0⋅ (𝐿𝑊

𝑉𝑊

+ 𝑇𝑊+𝐿 − 𝐿𝑊

𝑉𝑃

) + 𝐶𝑒

𝑃+ 𝐶𝑛

𝑃⋅𝐿 − 𝐿𝑊

𝑉𝑃

.

(1)

Travel cost of choosing car is as shown in (2):

𝐶𝐶= 𝐶𝑡

𝐶+ 𝐶𝑓

𝐶+ 𝐶𝑝

𝐶= 𝐶𝑡

0⋅𝐿

𝑉𝐶

+ 𝐶𝑓

0⋅ 𝐿 + 𝐶

𝑝

𝐶. (2)

Under real-time dynamic traffic flow conditions, the relation-shipmodel between𝑉

𝑃and𝑉

𝐶is obtained in (3) according to

𝐶𝑃= 𝐶𝐶:

𝑉𝑃=

(𝐶𝑡

0+ 𝐶𝑛

𝑃) ⋅ (𝐿 − 𝐿

𝑊) 𝑉𝑊𝑉𝐶

𝐶𝑡

0𝐿𝑉𝑊+ [(𝐶

𝑓

0𝐿 + 𝐶

𝑝

𝐶− 𝐶𝑒

𝑃− 𝐶𝑡

0𝑇𝑊)𝑉𝑊− 𝐶𝑡

0𝐿𝑊]𝑉𝐶

.

(3)

Car speed is average speed and it is related to road traffic flowdensity and waiting time at intersection. The model between𝑉𝐶and road traffic flow density 𝐾 and waiting time 𝑇

𝐷at

intersection will be constructed. Assume that speed is a linearrelationship with density, which is shown in (4). LimitationAssume that high speed of urban road is 𝑉

𝑓, jam density is

𝐾𝑗, and the travel speed of car is 𝑉

𝑅, then

𝑉𝑅= 𝑉𝑓(1 −

𝐾

𝐾𝑗

) , (4)

𝑉𝐶=

𝐿𝑉𝑓(𝐾𝑗− 𝐾)

𝐿𝐾𝑗+ 𝑇𝐷𝑉𝑓(𝐾𝑗− 𝐾)

. (5)

Put (5) to (3), then

𝑉𝑃= ((𝐶

𝑡

0+ 𝐶𝑛

𝑃) ⋅ (𝐿 − 𝐿

𝑊) 𝑉𝑊⋅

𝐿𝑉𝑓(𝐾𝑗− 𝐾)

𝐿𝐾𝑗+ 𝑇𝐷𝑉𝑓(𝐾𝑗− 𝐾)

)

× (𝐶𝑡

0𝐿𝑉𝑊+[(𝐶𝑓

0𝐿 + 𝐶

𝑝

𝐶− 𝐶𝑒

𝑃− 𝐶𝑡

0𝑇𝑊)𝑉𝑊− 𝐶𝑡

0𝐿𝑊]

⋅

𝐿𝑉𝑓(𝐾𝑗− 𝐾)

𝐿𝐾𝑗+ 𝑇𝐷𝑉𝑓(𝐾𝑗− 𝐾)

)

−1

.

(6)

From the above model, it is shown that if parking cost 𝐶𝑝𝐶,

walking distance 𝐿𝑊, walking speed 𝑉

𝑊, and fuel cost 𝐶𝑓

0of

per km and ticket cost are invariable, when the travel costof choosing public transit and choosing car is equal for thesame travel distance, public dynamic 𝑉

𝑃is determined by

car flow density, car waiting time at intersection, and energyconsumption cost per unit time. Energy consumption costper unit time is the function of crowding degree 𝐽 in publictransit. Therefore, 𝑉

𝑃is the level of dynamic public transit

priority.

3.2.2. The Public Transit Priority Demand Based on MinimumCarrying Speed. According to above priority level, roadlane numbers of one direction, intersection form, entrancelane, and passing time for public transit priority can bedetermined. For public transit, the necessary driving speedon road and allowable waiting time at intersection can be

4 Mathematical Problems in Engineering

Bus lane

Social vehicleSocial vehicle

Prestop line LT

Figure 1: Traffic organization design sketch of dynamic publictransit priority.

deduced from public route number 𝑁, departure interval𝜏, stop time 𝑆

𝑇at station, and average spacing between

intersection. Necessary public transit lane number can bedetermined by the necessary driving speed on road andpublic transit volume.The pass rule for public transit prioritycan be determined by allowable waiting time at intersection.

For public transit, the available passing time 𝑇𝑅on road

and waiting time 𝑇𝐽at intersection are analyzed firstly:

𝑇𝑅+ 𝑇𝐽=𝐿

𝑉𝑃

−𝐿

𝑑⋅ 𝑆𝑇. (7)

Actually, the travel speed of public transit on public transitlane can reach 𝑉

𝑅, thus,

𝑇𝐽=𝐿

𝑉𝑃

−𝐿

𝑑⋅ 𝑆𝑇− 𝑇𝑅. (8)

It is obvious that available waiting time 𝑇𝐽at intersection is

related to carrying speed 𝑉𝑃and stop time 𝑆

𝑇. The longer

𝑇𝑅and 𝑆𝑇are, the shorter 𝑇

𝐽is. Intersection signal timing is

mainly determined by 𝑇𝐽.

Generally, one public transit lane is enough on roadand two public transit lanes is needed at intersection undergeneral condition. Stop line in advance is designed for publictransit and car. Specific traffic organization and design isshowed as Figure 1.

3.3. Dynamic Traffic Organization and Design of DynamicPublic Transit Priority. The dynamic traffic organization anddesign of dynamic public transit priority mainly includevariable public transit lane design, pass space, and stop ruledesign at intersection and signal timing design. Variablepublic transit lane design is deduced from above model,with setting variable public transit lane sign and releasinginformation about variable public transit lane in advancein order to enable car traveler to select appropriate path orpark and ride in advance. Two stop lines are adopted atintersection entrance lane. Vehicle firstly stops at stop linefar away intersection for prewaiting. Vehicle which will passintersection in next green signal waits before stop line nearintersection. Specific organizational design is as shown inFigure 1.

The distance 𝐿𝑇between two stop lines is determined by

public transit vehicle volume 𝑄𝐵, which needs to pass inter-

section during one green time and entrance lane numbers 𝑛(relating to permit through rule influenced by signal timing).

The space way of public transit vehicle queue is 𝑙𝐵. Themodel

used to determine 𝐿𝑇is as shown in (9):

𝐿𝑇=𝑄𝐵𝑙𝐵

𝑛. (9)

3.4. Model Analysis. The equation of 𝐶𝑃= 𝐶𝐶is the basic

requirement of dynamic public transit priority. The aim ofdynamic public transit priority is to make traveler initiativeto choose public transit, but the equation of 𝐶

𝑃= 𝐶𝐶

cannot make sure that traveler will prefer to choose publictransit, therefore, the equation of 𝐶

𝑃= 𝐶𝐶is adjusted as

𝐶𝑃= 𝐾𝐶

𝐶. Here, 𝐾 is a coefficient. In order to determine

𝐾, questionnaire survey is carried out in Jiaozuo city. Thequestion is that when the total travel cost including traveleconomic cost, travel time, and comfort is considered, 𝑅is the ratio of public transit travel cost and car travel cost,what value is 𝑅? you will prefer to choose public transit.Two hundred questionnaires are carried out. Questionnairesurvey shows that 60% of travelers choose 70 percentage and22% of travelers choose 80 percentage.Therefore, it is rationalto let 𝐾 = 0.7, then 𝐶

𝑃= 0.7𝐶

𝐶. That is,

𝐶𝑡

0⋅ (𝐿𝑊

𝑉𝑊

+ 𝑇𝑊+𝐿 − 𝐿𝑊

𝑉𝑃

) + 𝐶𝑒

𝑃+ 𝐶𝑛

𝑃⋅𝐿 − 𝐿𝑊

𝑉𝑃

= 0.7 (𝐶𝑡

0⋅𝐿

𝑉𝐶

+ 𝐶𝑓

0𝐿 + 𝐶

𝑝

𝐶) .

(10)

Here, 𝐿 is average travel distance, 𝑇𝑊

is waiting time. ForJiaozuo city, average travel distance is 6 km, 𝐿

𝑊is 0.6 km, 𝑇

𝑊

is 12min, 𝐶𝑒𝑃is 1 yuan, 𝐶𝑓

0is 0.7 yuan, 𝑉

𝐶is 22.9 km, 𝐶𝑝

𝐶is

5 yuan, 𝐶𝑡0is 10 yuan, and 𝐶𝑛

𝑃is 8 yuan. Then according to

(10), 𝑉𝑃can be calculated. 𝑉

𝑃= 25.116 km/h. It is the level of

dynamic public transit priority when the car carrying speedis 22.9 km.

But according to survey, actual𝑉𝑃is 12.92 km/h. Now, 𝑉

𝑃

is difficult to be increased in Jiaozuo city; according to (10),𝐶𝑝

𝐶should be raised to 10 yuan.

4. Dynamic Stochastic Park and Ride Theory

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, itis necessary to encourage traveler to reduce car use as faras possible, secondly, park and ride should be provided fortraveler who have selected car when they feel too crowd.Also when dynamic public priority is carried out, sometraveler of using car will want to park and ride because carcarrying 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 publictransit station, with smaller scale comparing with generalpark and ride facility. Therefore, it is different from generalpark and ride. When dynamic public priority is carried out,not only public transit carrying speed is guaranteed, but alsoother choices are provided for car traveler on road. Thisintervention measures can be willingly accepted by traveler.

Mathematical Problems in Engineering 5

Congestion area

Public transit station

Figure 2: The layout sketch of dynamic stochastic park and ride.

When traveler has selected car and drives on road, at thebeginning stage of travel, traveler is not sure that park andride is necessary. If park and ride is needed, which site willbe selected is not clear too. These are related to real-timedynamic traffic condition. That is, whether park and ride isneeded and which park and ride site is selected is determinedby dynamic traffic condition, which means that this park andride has dynamic. Also it is obvious that this park and ridehas uncertainty, which means it is stochastic. Therefore, thispark and ride is called dynamic stochastic park and ride. Atthe same time, the above dynamic public transit priority willpromote travel behavior of dynamic stochastic park and ride.

4.2. The Layout and Scale of Dynamic Stochastic Park andRide. Dynamic stochastic park and ride layout is generallyclose to public transit station and corresponding road withmore traffic volumewill be priority selected. Figure 2 is layoutsketch.

For dynamic stochastic park and ride, the closer it is tocongestion area, the smaller the scale is.The diminishing sizemethod mainly lies in two reasons. First, the closer it is tocongestion area, the greater the difficulty of arranging parkand ride land is. Second, traveler is encouraged and guidedto park and ride in advance as far as it is possible in orderto release traffic pressure of road and intersection close tocongestion area.

The specific size of dynamic stochastic park and ride isdetermined by car volume of peak period and correspondingtraffic volume with travel destination in congestion area.The corresponding traveler is investigated for park and rideproportion and site. Then, the park and ride volume foreach station can be obtained and the park and ride scalefor park and ride facility is determined. For car traveldestination investigation, license plate photo can be adopted.Each road with park and ride facility should be investigatedby license plate photo.The car volume with travel destinationat congestion area is analyzed and for each car, whetherpark and ride will be adopted and which station will beselected are analyzed. If the station number with park andride facility is 𝑁, corresponding road section number is 𝑁and corresponding intersection number is 𝑁. The layoutsketch and charging standard for different site of dynamicstochastic park and ride are shown for car traveler duringinvestigation (delivering card and feedback).

When investigation is completed, the car volume withpassing road Section 1 and travel destination at congestionarea are obtained, the park and ride volume at each parkand ride facility of this volume, respectively, is 𝑃𝑄

1𝑗(𝑗 =

1, 2, . . . , 𝑁). Car volume entering investigation road section

from 𝑖 (𝑖 = 2, . . . , 𝑁) intersection combined with traveldestination at congestion area is investigated and its ridevolume at each park and ride facility is 𝑃𝑄

𝑖𝑗(𝑗 = 𝑖, . . . , 𝑁),

then the park and ride volume of 𝑖 park and ride facility is asshown in (11):

𝑃𝑅𝑖= 𝑃𝑄𝑖=

𝑖

∑

𝑗=1

𝑃𝑄𝑗𝑖 (𝑖 = 1, . . . , 𝑁) . (11)

Therefore, the 𝑖 park and ride facility scale can be preliminarydetermined as ashown in (11).

After 𝑃𝑅𝑖 is determined, the car volume of each roadsection during peak period is 𝑄𝑖 = (𝑖 = 1, . . . , 𝑁); when cartraveler selects park and ride, the car volume of 𝑖 road sectionreduces to as shown in (12):

𝑄𝑖

𝑃= 𝑄𝑖−

𝑖

∑

𝑗=1

𝑃𝑄𝑗𝑖 (𝑖 = 1, . . . , 𝑁) . (12)

This model can be directly used to analyze 𝑉𝑃of dynamic

public transit; that is the relationship between dynamic publictransit priority and dynamic stochastic park and ride volumeis established.

4.3. Charging Standard of Dynamic Stochastic Park and Ride.The charging principle of dynamic stochastic park and rideis lower than charging standard of central area. For park andride facility, the closer it is to congestion area, the higher thecharging standard is. Charging standards of park and ride canbe based on the charge standard of congestion area and it isreduced according to the distance of park and ride apart fromcongestion area. The charging standard of congestion area is𝐹𝐽yuan per hour. The charging standard of the park and ride

with large scale at urban peripheral is 𝐹𝐸yuan per hour and

its distance apart from congestion area is 𝐿𝐸𝐽

km; dynamicstochastic park and ride distance apart from congestion areais𝐿𝑃𝐽km, then corresponding charging standard for park and

ride is as shown in (13):

𝐹𝑃𝐽= 𝐹𝐽−𝐹𝐽− 𝐹𝐸

𝐿𝐸𝐽

⋅ 𝐿𝑃𝐽

yuan per hour. (13)

4.4.The Guidance for Dynamic Stochastic Park and Ride. Theguidance for dynamic stochastic park and ride includes twoaspects. On the one hand, it is needed to guide travelers topark and ride in advance as far as possible based on reducingcar volume on road; on the other hand, the closer it is tocongestion area, the smaller the scale of park and ride is, so,it is needed to guide travelers to park and ride in advanceas far as possible based on park and ride capacity. Whendynamic public transit priority is carried out, the closer it isto congestion area, the greater the car travel resistance is, andthe parking cost is very high in area close to congestion areaor in congestion area. The above two factors prompt travelerto park and ride in advance. At the same time, marked signis set before each park and ride and propaganda slogan areadopted with showing the benefits and charge standard ofpark and ride. In order to provide convenience for park and

6 Mathematical Problems in Engineering

90%

10% Traveler without owning car

Fully acceptAccept with a certain extent

(a)

31%

50%

19%

Traveler owning car

Reducing car useChoosing dynamic stochastic park and rideWithout changement

(b)

Figure 3: Traveler acceptability on dynamic public transit priority with dynamic stochastic park and ride.

ride traveler to transfer to public transit, public transit stationis set at dynamic stochastic park and ride with bigger transferdemand.

5. Traveler Acceptability Analysis

The traveler acceptability on dynamic public transit prioritywith dynamic stochastic park and ride includes public transittraveler acceptability on dynamic public transit priority andcar traveler acceptability on dynamic public transit prioritywith dynamic stochastic park and ride. Acceptability analysisis conducted by questionnaire investigation. The goal ofdynamic public transit priority and charging standard ofdynamic stochastic park and ride is stated in questionnaire.300 questionnaires are handed out. One hundred respon-dents own cars. The result from investigating on travelerwithout owning car at present shows that ninety percent ofthem fully accept dynamic public transit priority and tenpercent of them, who prepare to buy car recently, accept witha certain extent.

The result from investigating on traveler owning carshows that thirty-one percent of them intend to reduce caruse by choosing public transit in peak period, fifty percentof them intend to choose dynamic stochastic park and ride,and nineteen percent of them do not intend to change car usepattern. The result is showed as in Figure 3.

It can be observed from above survey result that travelerhas higher acceptability on dynamic public transit prioritywith dynamic stochastic park and ride. Therefore, dynamicpublic transit priority with dynamic stochastic park and ridehas a good application prospect and it can relieve trafficcongestion.

6. Further Discussion on Dynamic PublicTransit Priority

The above discussion on dynamic public transit priority ismainly from the point of carrying speed, which is mainlyfrom the point of dynamic space-time priority. But some-times, the expected level of dynamic public transit priority

cannot be achieved because of many factors, such as roadand traffic condition and car user acceptance. Then, othermeasures should be adopted in order to achieve the expectedlevel of dynamic public transit priority. Other measures canalso be obtained from the point that the travel cost of usingpublic transit is not higher than travel cost of using car. Ifcongestion charging 𝐶𝑐

𝐶is considered, the travel cost of using

car can be modified as follows:

𝐶𝐶= 𝐶𝑡

𝐶+ 𝐶𝑓

𝐶+ 𝐶𝑝

𝐶+ 𝐶𝑐

𝐶= 𝐶𝑡

0⋅𝐿

𝑉𝐶

+ 𝐶𝑓

0⋅ 𝐿 + 𝐶

𝑝

𝐶+ 𝐶𝑐

𝐶.

(14)

According to 𝐶𝑃= 𝐶𝐶,

𝐶𝑡

0⋅ (𝐿𝑊

𝑉𝑊

+ 𝑇𝑊+𝐿 − 𝐿𝑊

𝑉𝑃

) + 𝐶𝑒

𝑃+ 𝐶𝑛

𝑃⋅𝐿 − 𝐿𝑊

𝑉𝑃

= 𝐶𝑡

0⋅𝐿

𝑉𝐶

+ 𝐶𝑓

0⋅ 𝐿 + 𝐶

𝑝

𝐶+ 𝐶𝑐

𝐶.

(15)

In this equation, 𝐿𝑊, 𝑉𝑃, 𝐶𝑒𝑃, 𝐶𝑛𝑃, 𝑉𝐶, 𝐶𝑝𝐶, and 𝐶𝑐

𝐶can be

dynamically adjusted.At present time, for most cities, the adjustable range of

𝐿𝑊, 𝐶𝑒𝑃, 𝐶𝑛𝑃is very small; that is, in order to achieve the

equation of 𝐶𝑃= 𝐶𝐶, 𝑉𝑃, 𝑉𝐶, 𝐶𝑝𝐶, 𝐶𝑐𝐶should be key dynamic

adjustment parameter.Based on traveler acceptance, 𝑉

𝑃and 𝑉

𝐶should be firstly

adjusted. When the equation of𝐶𝑃= 𝐶𝐶cannot be achieved,

𝐶𝑝

𝐶should be adjusted. The last adjustment parameter is 𝐶𝑐

𝐶.

For traffic management, the key of dynamic public transitpriority is how to achieve the balance among 𝑉

𝑃, 𝑉𝐶, 𝐶𝑝𝐶, and

𝐶𝑐

𝐶tomake traveler to initiative accept it.This is the emphasis

of future research.

7. Conclusion

Based on the point that the travel cost of choosing publictransit is not higher than the travel cost of choosing car, thereal-time dynamic relationship model among public transit

Mathematical Problems in Engineering 7

carrying speed, car carrying speed, and traffic density isestablished. The model of determining the level of dynamicpublic transit priority is constructed. For dynamic publictransit priority, if parking cost and congestion charge do notreach a certain level, public transit carrying speed must behigher than car carrying speed. Dynamic stochastic park andride is amatchingmeasure for dynamic public transit priorityand its layout and scale have feasibility, with promoting cartraveler to dynamic stochastic transfer to public transit. Ques-tionnaire survey shows that traveler has higher acceptabilityon dynamic public transit priority with dynamic stochasticpark and ride and it illustrates that the application of dynamicpublic transit priority with dynamic stochastic park andride is feasible. How to achieve the balance among publictransit carrying speed, car carrying speed, parking cost, andcongestion charging is the emphasis of future research.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This research is sponsored by Science and Technology Plan-ning Project of Beijing Municipal Science and TechnologyCommission (no. Z1211000003120100) and the Natural Sci-ence Foundation of China (no. 61164003).

References

[1] A. Tirachini, D. A. Hensher, and S. R. Jara-Dı́az, “Restatingmodal investment priority with an improved model for publictransport analysis,” Transportation Research E, vol. 46, no. 6, pp.1148–1168, 2010.

[2] M. Eichler and C. F. Daganzo, “Bus lanes with intermittentpriority: strategy formulae and an evaluation,” TransportationResearch B, vol. 40, no. 9, pp. 731–744, 2006.

[3] L. A. Koehler and W. Kraus Jr., “Simultaneous control of trafficlights and bus departure for priority operation,” TransportationResearch C, vol. 18, no. 3, pp. 288–298, 2010.

[4] X. . Sun, H. P. Lu, and J. Wu, “Bus detection based on sparserepresentation for transit signal priority,” Neurocomputing, vol.118, pp. 1–9, 2013.

[5] J. Wahlstedt, “Impacts of bus priority in coordinated trafficsignals,” Procedia, vol. 16, pp. 578–587, 2011.

[6] M. J. Liu, J. Yang, L. L. Yang, and Z. Zhangb, “An elastic analysison urban public transport priority in Beijing,” Procedia, vol. 42,pp. 79–85, 2012.

[7] V. Zyryanov and A. Mironchuk, “Simulation study of intermit-tent bus lane and bus signal priority strategy,” Procedia, vol. 48,pp. 1464–1471, 2012.

[8] P. Vedagiri and V. T. Arasan, “Estimating modal shift ofcar travelers to bus on introduction of bus priority system,”Journal of Transportation Systems Engineering and InformationTechnology, vol. 9, no. 6, pp. 120–129, 2009.

[9] W. H. Wang, H. W. Guo, H. Bubb, and K. Ikeuchi, “Numericalsimulation and analysis procedure for model-based digitaldriving dependability in intelligent transport system,” KSCEJournal of Civil Engineering, vol. 15, no. 5, pp. 891–898, 2011.

[10] W. H. Wang, W. Zhang, H. W. Guo, H. Bubb, and K. Ikeuchi,“A safety-based approaching behavioural model with variousdriving characteristics,” Transportation Research C, vol. 19, no.6, pp. 1202–1214, 2011.

[11] M. Borjesson, J. Eliasson, M. B. Hugosson, and K. Brundell-Freij, “The Stockholm congestion charges—5 years on. Effects,acceptability and lessons learnt,” Transport Policy, vol. 20, pp.1–12, 2012.

[12] J. Holguın-Veras, W. F. Yushimito, F. Aros-Vera et al., “Userrationality and optimal park-and-ride location under potentialdemand maximization,” Transportation Research B, vol. 46, pp.949–970, 2012.

[13] F. Aros-Vera, V. Marianov, and J. E. Mitchell, “p-hub approachfor the optimal park-and-ride facility location problem,” Euro-pean Journal of Operational Research, vol. 226, no. 2, pp. 277–285, 2013.

[14] B. Farhan and A. T. Murray, “Siting park-and-ride facilitiesusing a multi-objective spatial optimization model,” Computers& Operations Research, vol. 35, no. 2, pp. 445–456, 2008.

[15] S. Meek, S. Ison, and M. Enoch, “UK local authority attitudesto Park and Ride,” Journal of Transport Geography, vol. 18, no. 3,pp. 372–381, 2010.

[16] S.Meek, S. Ison, andM. Enoch, “Evaluating alternative conceptsof bus-based park and ride,” Transport Policy, vol. 18, no. 2, pp.456–467, 2011.

[17] K. Kepaptsoglou, G. K. Matthew, and Z. Z. Li, “Optimizingpricing policies in Park-and-Ride facilities: a model and deci-sion support systemwith application,” Journal of TransportationSystems Engineering and Information Technology, vol. 10, no. 5,pp. 53–65, 2010.

[18] H. M. Qin, H. Z. Guan, and Y. J. Wu, “Analysis of park-and-ride decision behavior based on Decision Field Theory,”Transportation Research F, vol. 18, pp. 199–212, 2013.

[19] N. Hounsell, B. Shrestha, and J. N. Piao, “Enhancing Parkand Ride with access control: a case study of Southampton,”Transport Policy, vol. 18, no. 1, pp. 194–203, 2011.

Submit your manuscripts athttp://www.hindawi.com

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttp://www.hindawi.com

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Journal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

CombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com

Volume 2014 Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Stochastic AnalysisInternational Journal of