HEADWAY DISTRIBUTION FOR NH-8 TRAFFIC AT VAGHASI VILLAGE LOCATION

Transcription

1 HEADWAY DISTRIBUTION FOR NH-8 TRAFFIC AT VAGHASI VILLAGE LOCATION Dr. L. B. Zala Associae Professor, Civil Engineering Deparmen, Kevin B. Modi M.Tech (Civil) Transporaion Sysem Engineering (Suden), Civil Engineering Deparmen, Dr. (Mrs.) T. A. Desai Professor and Head of Mahemaics Deparmen, Aakar N. Roghelia Assisan Professor, Mahemaics Deparmen, Absrac- The properies of vehicle ime headways are fundamenals in many raffic engineering applicaions, such as capaciy and level of service sudies on highways, unsignalized inersecions, and roundabous. In addiion, he vehicle generaion in raffic flow simulaion is usually based on some heoreical vehicle ime headway model. The saisical analysis of vehicle ime headways has been inadequae in hree imporan aspecs: 1) There has been no sandard procedure o collec headway daa and o describe heir saisical properies. 2) The fi goodness ess have been eiher powerless or infeasible. 3) Tes resuls from muli sample daa have no been combined properly. In his paper describe he sudy conduced on wo lane mid block secion of Naional Highway-8 (NH-8), beween Ahmedabad and Vadodara, a Vaghasi village o evaluae basic raffic flow parameers. Daa collecion was done using Video Recording Technique. The headway daa exraced and compared wih differen ype of vehicles in raffic sream. o examine he headways beween vehicles in he sream, and o search for saisical disribuion ha describe he frequencies of occurrence of headways. In normal erms, i is defined o be he ime difference beween he same poins (e.g. The fron bumper) on wo consecuive vehicles as hey pass an observaion poin on he road. This definiion holds for single or mulilane raffic. An imporan qualificaion from his definiion is ha i explicily ignores he physical lengh of he vehicles. Vehicles are regarded poins only. Then, under his definiion he reciprocal of he mean headway is equal o mean flow rae. Keywords- Headway; headway disribuion; capaciy; PCUs. I. INTRODUCTION The ime headway beween vehicles is an imporan microscopic flow characerisic ha affecs he safey, level of service, driver behavior and capaciy of ransporaion sysems. The capaciy of he sysem is governed primarily by he minimum ime headway an he ime headway disribuion under capaciy flow condiions. The elapsed ime beween pairs of vehicles is defined as he ime headway. A microscopic view of raffic flow is shown in figure 1, as several vehicles raverse a lengh of roadway in single file for a cerain period of ime. II. LITERATURE REVIEW A convenien way o describe he inheren variabiliy wihin a raffic sream is o consider i as a sochasic process, Figure 1. A microscopic view of raffic flow Source: May, A. D. Traffic flow fundamenals Prenice hall, 1990, pp-12 A. Headway Mehod The ime inerval beween successive vehicles in a raffic sream is used for deermining he volume of raffic. Traffic volume, (Q) Q = 3600 (1) Headway (h)

2 Where, Q = measured in vehicles per hour h = ime headway in seconds Consider a sream of raffic in which only wo caegories viz. cars, rucks, and scooers are presen. For his Guinn, Reilly and Seifer has suggesed following basic equaion. Then, basic equaion of headway mehod is: E = (h m / h c c) (2) Where, h c = ime headway beween wo cars in seconds for an all cars sream h m = ime headway beween wo vehicles in mixed flow sream (seconds) c = proporion of cars in he mixed sream = proporion of rucks in he mixed sream s = proporion of scooers in he mixed sream E = PCU of rucks The above equaion gives a simple basis for deerminaion of PCU facors when only cars, rucks, scooers and anoher ype of vehicles are presen. All ha is needed is o measure he average ime headway of a sample of all car samples and he average ime headway of he mixed raffic. Duraion of a leas one hour is desirable. The value so obained is valid only for he flow and speed condiions prevailing. The mehod is appropriae for plain errain and for low levels of service. The mehod does no consider he overaking phenomenon where faser vehicles end o overake he slower ones. B. Classificaion Of Headway Disribuion One can observe hree ypes of flow in he field. 1) Low Volume Flow: Headway follow a random process as here is no inersecion beween he arrivals of wo vehicles. The arrival of one vehicle is independen of he arrival of oher vehicle. The minimum headway is governed by he safey crieria. A negaive exponenial disribuion can be used o model such flow. 2) High Volume Flow This is characerized by near consan headway. The flow is very high and is near o capaciy. The mean is very low and so is he variance. A normal disribuion can be used o model such flow. 3) Inermediae Flow Some vehicle ravel independenly and some vehicle has ineracion. More difficul o analyzed and has more applicaion in he field. Pearson Type III disribuion can be used which is a very general case of negaive exponenial disribuion and normal disribuion. C. Negaive Exponenial Disribuion The negaive exponenial disribuion can be used o illusrae his headway sae. For ime headways o be ruly random, wo condiions o be me. Firsly, any poin in ime is likely o have a vehicle arriving as is any oher poin in ime. Secondly, he arrival of one vehicle a a poin in ime does no affec he arrival ime of any oher vehicle. The negaive exponenial disribuion can be derived from he Poisson coun disribuion. The paricular disribuion can be indicaed by he following form, P (x) = (m * e -m )/ x! (3) Where, P (x) = Probabiliy of arrival of x vehicles in any inerval of sec m= (average rae of arrival) * (ime inerval) Le us consider he special case when here is no vehicle. x=0 P( 0 ) = e -m (4) This means if here is no vehicle hen he individual ime headway mus be equal or greaer han. Therefore, P (0) = P (h ) (5) P (h ) = e -m (6) Now m is defined as he avg. no. of vehicles arriving in ime inerval. The hourly flow rae is V and in seconds. Then, m = (V/3600) (7) P (h ) = e -(V/3600) (8) The mean ime headway can be (μ) deermined easily so, P (h ) = e -/μ (9) To calculae probabiliy of a ime headway beween and +Δ P ( h + Δ) = P (h )-P (h + Δ) (10) Following he above menioned procedure i is possible o fi his disribuion ino differen flow levels o show he characerisics of he disribuion. The heoreical resuls are superimposed on he measured ime headway disribuion. Careful sudy will give some characerisics of he random disribuion o observed one. Some of he imporan observaions are:

3 The random disribuion has a characerisic of smalles headways occurring mos likely, probabiliies coninuously decrease wih he increase wih ime headway. The comparison is bes under lowes flow level. D. Pearson ype III Disribuion The inermediae headway sae lies beween he wo boundary condiions random, consan headway saes. This is he siuaion encounered almos every day. In his secion i is ried o describe Pearson ype III disribuion by which we can easily illusrae his headway sae. Pearson ype III disribuion is a generalized mahemaical model approach. f K K K1 e K1 K1 K 1 e if K 1 Neg. Exp. Where, λ is parameer ha is funcion of µ, K, and α; K = user specified parameer beween 0 and α = user seleced parameer greaer han 0 and called as he shif parameer = gamma funcion ( K= (K-1)!) Then, ph f d (11) Probabiliy of headway lying and +δ is e e K, R Pearson if if 0 Gamma K I Erlang Sudy Design Selecion of Locaion Mehodology of Daa Collecion Daa Collecion Daa Processing PCU Evaluaion Speed-Flow Relaionships Headway Analysis Conclusion Scope and Objecives Crieria for Selecion Spo-Speed Daa Volume Couns Headway Daa Preliminary Analysis Daa Enry Mehods of PCU Esimaion Regression Analysis Figure 2. Flow char of sudy mehodology Approximaing, (12) (13) Some of he imporan observaions are The probabiliy of he heoreical and measured disribuion is mos inconsisen when ime headways beween 1 and 4 sec. The comparison beween his and measured disribuion a four flow levels indicaes ha qualiaively he wo are abou he same. III. p p h f d f d h f STUDY METHODOLOGY The sudy objecive is measure headway values and develops analyical relaionship among headway and probabiliy of occurrence. The flow char of he mehodology is presened in figure 2. f 2 IV. HEADWAY DATA COLLECTION AND ANALYSIS In his survey, video recording mehod for o collec he daa of raffic parameers wih he help of Panasonic VHS Movie Camera (NV-M3000/HQ-VHS-PAL), 180 minues recording in he video cassee, video monior as a Videocon TV and video cassae player wih a sopwach were used. The raffic volume couns observed during sudy is presened in able-1. Headways for car follows car, ruck follows ruck and wo-wheeler follows wo-wheeler were recorded. Vehicle Types TABLE 1. TRAFFIC VOLUME COUNTS Cars LCVs Trucks /Buses Two- Wheelers Auo- Ricksh aws Vadodara o Ahmedabad Ahmedabad o Vadodara Toal Traco r/trail or The headways daa recorded have been fied for negaive exponenial disribuions. Table 2, 3, 4 show headway and probabiliy compued and figure 3, 4, 5 give observed and prediced probabiliies.

4 Lower TABLE 2. CAR FOLLOWS CAR HEADWAY ANALYSIS Car - Car µ P(<h) P(<h<+0.5) Prediced no. of H/W Toal Figure 4. Headway disribuion ruck follows ruck TABLE 4. TOW-WHEELER FOLLOWS TWO-WHEELER HEADWAY ANALYSIS 2-wheeler 2-wheeler Lower Figure 3. Headway disribuion car follows car TABLE 3. TRUCK FOLLOWS TRUCK HEADWAY ANALYSIS Truck - Truck µ P(<h) P(<h<+0.5) Prediced no. of H/W Lower µ P(<h) P(<h<+0.5) Prediced no. of H/W

5 Figure 5. Headway disribuion wo-wheeler follows wo-wheeler V. CONCLUSION AND RECOMMENDATIONS The following conclusion can be drawn from abular daa and plo. Headway daa for car follows negaive disribuion wihin range from 1.00 sec o 4.50 sec wih µ is sec. Headway daa for ruck follows negaive disribuion wihin range from 2.50 sec o sec wih µ is sec. Headway daa for wo-wheeler follows negaive disribuion wihin range from 1.50 sec o 8.00 sec wih µ is sec. The headway follows negaive disribuion up o sec in he heerogeneous raffic sream. The deailed headway daa for all vehicles can be sudied. The headway daa should be used for capaciy level of service analysis and evaluaion of PCUs. REFERENCES [1] Huber, M. J. (1982), Esimaion of Passenger Car Equivalens of Trucks in Traffic Sream, Transporaion Research Record No. 869, Washingon, D. C., pp [2] Kadyali, L. R. and Lal, N. B. (2007), Traffic Engineering and Transpor Planning, Khanna Publishers, Delhi-6. [3] Kremmes, R. A. (1987), and Crowly, K. W., Passenger Car Equaivalens for Trucks on Level Freeway Segmens, Transporaion Research Record (1901), TRB, Naional Research Council, Washingon, D. C., pp [4] May, A. D. (1990), Traffic Flow Fundamenals, Pranice Hall, Englewood Cliffs, New Jersey. [5] May, A. D. (1990), Traffic flow fundamenals Prenice hall, pp [6] Mahew, T. V. and Krishna Rao, K. V. K. (2009), Modelling Traffic Characerisics, [7] Road User Cos Sudy in India (1982), Final Repor, Cenral Road Research Insiue, New Delhi. [8] Transporaion Research Board (TRB) (1965), Highway Capaciy Manual, Special Repor 87. [9] Werner, A. and Morall, J. F. (1976), Passenger Car Equivalences of Trucks, Buses, and Recreaional vehicles for Two Lane Rural Highways, Transporaion Research Record 615, Naional Academic of Sciences, Washingon, D. C. [10] Zala, L. B. (1994), Traffic Flow Analysis on Heavily Trafficked Highway, Unpublished Disseraion Repor, ransporaion Engineering Secion, Civil Engineering Deparmen, Roorkee Universiy, Roorkee.