《Car Delay Time near a Curbside Stop under Mixed Traffic.doc》由会员分享，可在线阅读，更多相关《Car Delay Time near a Curbside Stop under Mixed Traffic.doc（7页珍藏版）》请在三一文库上搜索。
1、精品论文Car Delay Time near a Curbside Stop under Mixed TrafficCondition5YANG Xiaobao, HUAN Mei, FAN Aihua, DONG Ling, LI Ming(MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology,Beijing Jiaotong University, Beijing 100044)Abstract: This paper proposes a delay model to cars
2、 under mixed traffic flow near the curbside stop based on queuing theory. Bus stream system is described by an M/M/k queue and the service counter is10the bus stop. The conflict between different streams at the stop is developed by the advanced Markovian model with unequal arrival rates and unequal
3、service rates for customers of two major types. The delay to cars near the stop under mixed traffic flow can be derived by the queuing models. Theaverage car delay is estimated as the sum of the average delay at the conflict points between differentstreams, and the delay resulting from following the
4、 slower bicycles that merged into the motorized lane.15Car delay model is the function of three types of traffic streams with buses, cars and bicycles. The proposed model may be applicable to design and operational analysis of bus stops in other Asiandeveloping countries.Key words: Delay time; bus s
5、top; mixed traffic flow; queuing theory200IntroductionAs the first point of contact between the passenger and the public transit service, the bus stop is a critical element in a transit systems overall goal of providing timely, safe, and convenient transportation. In recent decades, many studies hav
6、e been conducted on the the location 1, design2-3 and operations 3-4 of bus stops and obtained many useful achievements. In addition, other25researchers mainly focused on the effects of bus stops on traffic flow 5-8. On the bus stop, unfortunately, little information has been published concerning bu
7、s stops with non-motor vehicles.As a developing country, China has her own traffic characteristics. Mixed traffic between non-motor vehicles and motor vehicles is an important traffic type in China. Some survey show that non-motor vehicles, mainly bicycle is still one of the more sustainable modes t
8、han motor30vehicle travel in China. Typically, there are three types of bus stops in urban areas: the curbside stops, bus bays, and bus boarders 9. And curbside stops are the most common bus stops in many Chinese cities. Fig. 1 presents a sketch map for mixed traffic streams at a typical curbside st
9、op and will be referred to in the following discussions. Firstly, there are two lanes on the urban roadway: one is the bicycle lane and the other is the motor lane. Secondly, there are three types of traffic35streams: bicycle stream, bus stream, and car stream. Thirdly, bus stop is usually located o
10、n the bicycle lane. When a bus dwells at the curbside stop, bicycles will change to the motor lane and round the stopped bus. Thus, the presence of a stopped bus creates a temporary conflict between bicycles and cars, reducing the road capacity and increasing the vehicles travel time. Similar phenom
11、ena may be found in other Asian developing countries, for example, India, Malaysia,40Vietnam, Cambodia, etc.Foundations: Specialized Research Fund for the Doctoral Program of Higher Education of China (No.20090009120015), National Natural Science Foundation of China (No. 70901005, 71131001), Nationa
12、l BasicResearch Program of China ( No. 2012CB725401)Brief author introduction:Yang Xiaobao(1981-), male, associate professor. His research interest is including transportation engineering, traffic behavior and safety. E-mail: - 7 -Fig. 1 Curbside stop with mixed traffic streams among buses, cars and
13、 bicyclesDue to the special features of mixed traffic, the existing traffic models of bus stops developed45according to the traffic conditions in developed cities might not be applicable to developing cities.Therefore, it is necessary to deeply study mixed traffic flow between motor vehicle and non-
14、motor vehicle. In recent years, some researchers have realized this particularity, and correlative work is being done, but it still has a long way to go. KOSHY and ARASAN 9 used simulation technique to study the impact of bus stop type on the speeds of other vehicles under heterogeneous50conditions.
15、 YANG et al. 10-11 established capacity models near the curbside stop with bicyclesbased on gap acceptance theory and conflict technique. However, no information was found in the literature on delay time at the bus stop with mixed traffic flow. Because no traffic streams near a bus stop under mixed
16、traffic condition possess the absolute priority of driving, the conflict between different streams (e.g. the car-bicycle conflict and the car-bus conflict) at the stop can be55described by the queuing model with no priorities but unequal service rates for customers of two major types. This paper inv
17、estigates delay time to cars near the bus stop with mixed traffic flow. Firstly, mixed traffic flow characteristics on bus stops are analyzed. Then, the delay model based on queuing theory is proposed. Next, the delay model is validated by field data in Beijing. Finally, conclusions and future resea
18、rches are given.601Mixed Traffic Flow Characteristics at the Curbside Stop1.1Bus stream: M/M/k queuing modelConsider a road link near the bus stop as shown in Figure 1. A sophisticated queuing theory model can be developed by the assumption that the simple bus stream system can be represented by an
19、M/M/k queue. The service counter is the bus stop. The input of the queuing system in65equilibrium, as well as the output, is formed by the buses approaching from upstream which are assumed to be negative exponentially distributed arrival headways with mean 1/ lb . The dwelling time at the stop is th
20、e service time, which is also assumed to be independent and negative exponential distributed random variables with mean sb . Finally, the “k” in M/M/k stands for k identical servers, i.e. the number of existing berths at the bus stop.70For the M/M/k system as a general property, the probability of t
21、he busy system is given by thefollowing equation. That is, the probability of one or more buses at the stop is-1ps = 1 - k -1 r j br k k + b (1) j =0 j !k ! k - rb Note that, here, rb = lb sb , and for the existence of a steady-state solution,lb m1 ). Here, service rate ( m ) is the reciprocal value
22、 of the meanservice time ( s ), that is,m1 = 1/ s1 , m2 = 1/ s2 . Then, the expected waiting time for each type ofcustomers in queue at steady state 12 is(l + l) s2 1 - l s(1 - s/ s )W = 1 2 1 2 2 2 1 95q1(1 - l s- l s )(3)(l + l) s21 1 2 2s2 / s2 + (1 - s/ s ) (l s )W =1 2 1 2 1 2 1 1 2q2 (1 - l s-
23、 l s )(4)1001051 1 2 22Delay model for car stream near the stop under mixed traffic flowThe delay to cars near the stop under mixed traffic flow is calculated as the sum of a) the delay because of the car-bicycle conflict at the point B, b) the delay of a car following its leading bicycle from point
24、 B to point C, c) the delay because of the car-bus conflict at the point C.2.1Delay at the point B because of the car-bicycle conflictThe car-bicycle conflict may take place only when one or more buses berth the stop. The car delay time at the point B is equal to the expected waiting time in the que
25、ue system for mixed streams between cars and bicycles. According to Equation (3), the car delay caused by thecar-bicycle conflict at the point B can be given asd = W= s2 (l+ l p ) 1 - (1 - sn / sc ) ln ps snB c, B c c n s1 - l s- l p s(5)where,ln psand lcc c n s nare the arrival rate of bicycle stre
26、am and car stream approaching theconflicting point B, respectively. snand scare the mean service time of bicycle stream and car110stream passing the point B, respectively.2.2Delay of a car following its leading bicycle from point B to point CThe car-bicycle conflict takes place only when one or more
27、 buses berth the stop and meanwhile at least one bicycle approach the stop. Accordingly, the car-bicycle conflict probability for car stream ispc = ps rn = ps ln sn(6)115where,ps is the probability of one or more buses at the stop.rn is the traffic intensity forbicycle stream and is equal to the pro
28、bability of finding at least one bicycle approaching the stop.According to the equation (2), the distance from B to C can be obtained by the formulae:l = lr kk ! L = l b bk rb(1 - p ) + r (7)BCbb(k -r )2 s b where,lBCis the distance from B to C. lbis the minimum headway distance of successively120st
29、opped buses at the stop, and L is the expected number of buses at the stop at steady state.Combined with Equations (6) and (7), the delay of a car following its leading bicycle can be written asd = p l 1 - 1r kk != p l s l b k rb 1 1 (1 - p ) + r - (8)BC c BC v vs n n b(k - r )2s b v v 1n1c b 1n1c w
30、here,v1candv1nare the normal velocity for car stream and bicycle stream without the125interruption of other streams, respectively.2.3Delay at the point C because of the car-bus conflictSimilar to the delay caused by the car-bicycle conflict, on the basis of Equation (4), the car delay caused by the
31、car-bus conflict at the point C can be given asd = W= s2 (l2 2+ l ) s/ sb+ (1 - sc / sb ) lb sccC c,C b c b1 - lb sb - lc sc(9)130where, lband lcare the arrival rate of bus stream and car stream, respectively.sb and sc135140145are the mean service time of bus stream and car stream passing the point
32、C, respectively.3Model Validation and ComparisonIn order to calibrating the proposed model of car delay at the curbside stop under mixed traffic flow, field data collected at bus stops in Beijing were employed. Video cameras were used to record traffic operations at the bus stop. Vehicle type, and f
33、lows, travel times were recorded for each vehicle passing through the stop. In addition, the dwell time of bus stream, the headways in the conflicting area were also recorded. Data were collected in the spring of 2008 in one direction over 3 minutes categorized into a group.3.1Estimation of the Crit
34、ical ParametersThe basic parameters used to compute car delay at a stop under mixed traffic is the service time for each stream. The service time was directly measured for each vehicle at the conflicting point using video during this study. The service time in this paper is the follow-up headway for
35、 vehicles in this approach if no vehicle is waiting on the conflicting approach, and is equal to the minimum saturation headway. On the basis of field survey and video process, the minimum saturation headways for bicycle stream, car stream and bus stream are 0.90, 2.04 and 4.27,respectively. Here, t
36、he relatively low value for bicycle stream is the result of cycling parallelbehavior and group behavior. In addition, curbside stops in Beijing.lb =12 m,v1n =4.5m/s, andv1c =10m/s on the surveyed1501551601651701751803.2Modeled travel time and Comparison with the measured valueThe data collected in f
37、ield study are used to validate the model, as shown in Fig. 2. To facilitate comparison, the line where the measured average travel time equals to the estimated average travel time is superimposed on each figure. And it is found that scatter dots fluctuates narrowly around the line. In addition, the
38、 mean percent error between the estimated travel times and the measured times is -5.1%, and the mean absolute percentage error is 14.8%. Thus, the proposed delay model at the stop with mixed traffic flow is desirable.Fig. 2 Comparison of measured average travel time and estimated average travel time
39、4ConclusionDelay time to cars at a curbside stop with mixed traffic flow is investigated on the basis of queuing theory. Bus stream system can be represented by an M/M/k queue. Meanwhile, the conflict between different streams at the stop can be described by the advanced Markovian model with no prio
40、rities but unequal service rates for customers. The analysis shows that both bus stream and bicycle stream have significant effects on car delay. Car delay near the stop under mixed traffic condition is the function of three types of traffic streams with buses, cars and bicycles. The proposed model may be applicable to de