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УДК 656.025.2=111
A STOCHASTIC APPROACH TO EVALUATE THE RELIABILITY OF URBAN PASSENGER TRANSPORTATION SERVICES
D. Kopytkov, Ph. D. (Eng.), Kharkov National Automobile and Highway University
Abstract. An approach to estimate the reliability of urban passenger transport from the passengers' viewpoint has been presented, in which the parameter to be investigated is the fixed-route headway. The probability ofpassenger arrival to the destination point has been suggested as an indicator of the service reliability. The given approach makes it possible to evaluate the reliability of both single modes of the urban mass transit and the transportation system reliability as a whole.
Key words: urban mass transit, reliability, headway, law of distribution, arrival probability.
ВЕРОЯТНОСТНЫЙ ПОДХОД К ОПРЕДЕЛЕНИЮ НАДЕЖНОСТИ ПРЕДОСТАВЛЕНИЯ УСЛУГ ГОРОДСКОГО ПАССАЖИРСКОГО ТРАНСПОРТА
Д.М. Копытков, доц., к.п.н., Харьковский национальный автомобильно-дорожный университет
Аннотация. Предложена методика оценки надежности функционирования городского пассажирского транспорта с точки зрения пассажиров, в которой исследуемым параметром является интервал движения на маршрутах.
Ключевые слова: надежность, интервал движения, вероятность прибытия в пункт назначения, закон распределения.
1МОВ1РН1СНИЙ П1ДХ1Д ДО ВИЗНАЧЕННЯ НАД1ЙНОСТ1 НАДАННЯ ПОСЛУГ М1СЬКОГО ПАСАЖИРСЬКОГО ТРАНСПОРТУ
Д.М. Копитков, доц., к.п.н., Хар^вський нащональний автомобшьно-дорожнш ушверситет
Анотаця. Запропоновано методику оцтки надiйностi функщонування мiського пасажирсько-го транспорту з точки зору пасажирiв, в якт до^джуваним параметром е ттервал руху транспортних засобiв на маршрутах.
Ключов1 слова: надттсть, ттервал руху, iмовiрнiсть прибуття до пункту призначення, закон розподшу.
Introduction
The development of the urban passenger transportation (UPT) is of both economic and social significance. The economic consequences of urban passenger transportation functioning can be attributed to the effect obtained from the reduction of time losses in the material production and the non-productive sphere for the growth of social labor productivity, improving the quality
of products by reducing the transport fatigue of workers, saving recourses for the development of social infrastructure due to its high concentration rate. The social consequences of transportation services are taken to an increase in the free time of passengers, the opportunities for using the services of cultural and public institutions, improving people's health, etc.
One of the main goals of operation and further development of the mass transit industry is to improve the urban passenger transportation quality. The subjects to evaluate the service quality are the passengers, so, when assessing a task completion rate in the passenger transport operation, it is necessary to express the effect of qualitative changes from the passengers' viewpoint.
Analysis of publications
The issues of improving the customer service are closely related to the service quality problem. In the current market relations, it is proposed to introduce a consumer quality assessment for the service sector where a little experience has been accumulated yet.
In this area, the development of quality systems is limited to a technocratic approach in assessing the material resources, while the methods to evaluate the consumer effect have only begun to develop.
Concerning the urban passenger transportation, the need to ensure a high quality of passenger transport services is directly established by the regulations presented in [1, 2], most of which determine the complete satisfaction of the economy and population needs in passenger transportation as the main issue for mass transit operation.
If the reliability is considered as a single parameter of the urban transportation quality, then a technocratic approach prevails here, associated, first of all, with the reliability of technical systems, facilities or objects (for example, transportation systems, route network, vehicles or drivers) [3, 4]. In study [5] this value is considered as only a sum of average travel time and standard deviation. The papers [6, 7] give an approach from the consumer theory not explaining a stochastic nature of this quality indicator. Some authors say that parameter is considered as one of the components of transportation quality without giving the calculation technique [8]. The works [9-12] only demonstrate the indicator importance for passengers from various transport surveys but also not to provide any determination methodology. The earlier studies [13, 14] express this indicator as the «actual reliability values-to-normative ones» ratio that, in most cases, is difficult to be correctly determined.
Thus, the above-mentioned reliability assessment indicators, as a rule, describe the state and development of some urban transportation components and do not meet the passengers' requirements to the level of transportation services.
Purpose and problem statement
The objective of the study is to develop an approach to assess the reliability of urban passenger transportation services in current conditions for improving the system management efficiency.
To achieve this goal, it is necessary to conduct a full-scale survey to obtain the headways on the urban passenger transport routes.
Approach to the urban passenger transportation reliability determination
The functioning of urban passenger transportation is a stochastic process due to the influence of many disturbing effects, which are rather difficult to describe with strict analytical dependencies. In this case, good and consistent research results can be obtained by using the probabilistic approach and mathematical statistic methods including the public transportation reliability estimation [15].
From the above stated, the reliability of urban transportation is the probability for the passenger to arrive from the departure to the destination point within the expected time. On various routes the reliability of urban transport services must be assessed in the morning, «inter-peak» and evening peak-load periods j
The actual headway of the fixed-route public transportation is a stochastic value distributed with a probability distribution law of a continuous random variable. Until the present day, there is no a common opinion in respect to the exact distribution law value. Thus, the authors [16, 17] believe it to be normally distributed, although the paper [18] showed the consideration of the «peak» and «inter-peak» hours was of great importance in the distribution law selection that resulted in impossibility of its unambiguous confirmation within the data obtained.
For the case under consideration, during a bus route No. 265 survey the 211 values of headway were obtained. In order to determine the influence of the vehicle operating hours' assignment («peak» and «inter-peak» hours) on the value,
the null hypothesis was formulated that the gle-factor analysis of variance was done, the mathematical expectations of the headways for results of which are shown in table 1. various hours were the same. Due to this, a sin-
Table 1 Single-factor variance analysis results
Variation source Square sum Degree of freedom Mean square F-value calculated p-value F-critical value
Between groups 1,423 2 0,711
Within groups 799,72 205 3,901 0,182 0,833 3,039
Total 799,883 207 -
As can be seen in table 1, the calculated value of the Fisher test of 0,182 is much lower than the critical value of 3,039. Consequently, at the 95 % confidence limit, the null hypothesis on the equality of the mathematical expectations of the vehicle headway for different operating hours is to be accepted [19].
Thus, from the results of the variance analysis, in order to evaluate statistically there are no clear distinctions between the «peak» and «in-ter-peak» time windows.
For the headway values obtained, an attempt was made to fit the parameters of the normal distribution law in the Statistica software presented on fig. 1.
If the probability of the investigated event occurrence is equal to the integral of the probability density of the distribution, then
P(x) = J f (x)dx.
(1)
In case of the above-mentioned distribution, a stochastic value distributed in accordance with the normal law is described by the density [21]
f(x) =
> -J 2 n
_( x_a) 2a2
(2)
where a - the mathematical expectation of a random variable; c - the standard deviation of a random variable.
Due to this, it is necessary to determine that the probability of a continuous random variable, the measured actual vehicle headway, will take a value within the interval [a, P]. The probability is equal to a definite integral of the distribution density from a to P limits.
According to Laplace's theorem, this formula should be reduced to an equation that can be solved using the tables [21]
Fig. 1. Distribution fitting parameters
PH (a <Xj <ß) = F(■
a _ at,
ß_ j _ F(" "j
at,
a j
), (3)
1
As can be seen from the comparison of empirical and theoretical frequencies under the «chi-square» test shown on fig. 1 is equal to 2,254, and the probability is of 0,621, the hypothesis of the headway values to be normally distributed can be taken into consideration [20].
where pt - arrival probability at the destination point in the jth period; Xj - actual vehicle headway in the jth period, min; a, P - lower and upper headway limit, respectively, min; atj- -
headway mathematical expectation in the jth period, min; Oj - headway standard deviation in the jth period, min.
It is necessary to determine the [a, P] interval limits. In making the lower limit, we assume that a is the minimum route headway that can be provided taking into account the passenger traffic and the road network capacity, i.e. a = 1 minute [22]. Under the study [23] the upper limit should not exceed 15 minutes, since the waiting time that is more this value adversely affects the mental and emotional state of the passenger. Regarding the urban transportation, the dependence (2) can be presented in a general form
В - a, a, p, (0 < x, < 15) = F (^L ) + F (j (4)
Thus, this indicator comprises such significant components of the transport service quality as passenger-expected headway, mathematical expectation (the average headway value in case of large number of observations), and the headway standard deviation.
The probability to meet the headway for the 7th route of the jth urban transportation mode should be calculated for the characteristic hours of its operation that is for the «morning», «inter-» and «evening» peak-load. Then the resulting reliability factor can be presented as
kfel = P(Xj )mp ■ P(X, )p • P(X, )
j 'ep
(5)
For a single urban mass transit system
n
krel — I! krel , /—1
where n - number of routes in the jth mode. And for the urban mass transit as a whole
n
krel.UPT — PI kiel ' j—1
(6)
(7)
where n - number of the urban mass transit modes.
The example of the single bus route reliability evaluation using the 211 headway values is given in table 2 without peak hours fragmentation.
As can be seen in table 2 with the observed average headway, standard deviation and passenger-expected headway limits, the probability of a random variable to be within the range (or the
probability of arrival at the destination point) is 0,853. In our opinion, the obtained values of the arrival probability or the urban transportation reliability rate can be also ranked within the following scale: 0,9-1 - exemplary rate; 0,8-0,89 -sufficient rate; 0,7-0,79 - satisfactory rate; 0,69 and lower - unsatisfactory rate.
Table 2 Bus route reliability calculation
Parameter name Value
Lower headway limit, min 1
Upper headway limit, min 15
Headway expectation, min 10,93
Standard deviation, min 3,81
F (1) ratio 1,068
F (2) ratio -2,603
Laplace function F (1) 0,3577
Laplace function F (2) 0,4953
F (1) + F (2) total 0,853
The parameter value of 1 determines the formalized condition of a completely functioning public transport system in terms of the passenger transport service quality. This parameter can be measured in percents, but it can also be a relative value.
Conclusion
Analysis of sources on the quality of passenger transportation services showed the absence of a parameter that would take into account the requirements of passengers. Most of the existing evaluation criteria consider only the technological, technical or economic aspects of the passenger transportation process.
Taking into account the above-stated as an indicator of the service reliability, the probability of the passenger's arrival to the destination point has been suggested under actual limitations - the vehicle headway and its standard deviation. Resulting from of the technique, it is possible to evaluate the reliability of both single modes of the urban passenger transportation and the system reliability as a whole.
The further research is to perform a representative survey for, at least, one public transportation mode with aim of determining a general reliability indicator.
References
1. Роша О.М. Автомобшьний транспорт в Украш. Нормативна база / О.М. PoiHa. -К. : Атка, 2004. - 504 с.
2. Закон Украши «Про мюький електричний
транспорт»: Режим доступу: http: // zakon3.rada.gov.ua/laws/show/en/1914-15 (accessed 06.04.2016).
3. Поначугин В.А. Оценка надежности пере-
возочного процесса городского пассажирского транспорта / В.А. Поначугин.
- Н. Новгород: Нижегородский государственный архитектурно-строительный университет, 2008. - 92 с.
4. Мартынов Н.Г. Методологические аспекты
комплексной оценки эффективности работы транспорта / Н.Г Мартынов // ВИНИТИ. Обзорная информация. Транспорт, наука, техника, управление.
- 1999. - № 4. - С. 4-8.
5. Inta M. Researchs on reliability of urban pas-
senger transport in Sibiu / M. Inta, A. Mun-tean // Annals of the Oradea university. Fascicle of Management and Technological Engineering. - 2015. - Issue 1. - P. 79 - 82.
6. Tseng Y. Valuation of travel time reliability
in passenger transport / Y. Tseng. - Amsterdam: Rozenberg Publishers, 2008. - 187 p.
7. Vincent M. Measurement Valuation of Public
Transport Reliability / M. Vicent. - Wellington: Land Transport New Zealand, 2008. - 128 p.
8. Семчугова Е.Ю. Определение весомости
показателя надежности транспортных услуг в качестве перевозок / Е.Ю. Сем-чугова, В.В. Зырянов, П.П. Володькин // Науковедение: Интернет-журнал. -
2012. - № 4. - Режим доступу: http://cyberleninka.ru/article/n/opredelenie-vesomosti-pokazatelya-nadezhnosti-transportnyh-uslug-v-kachestve-perevozok.
9. Кужель В.П. Визначення рiвня якост па-
сажирських перевезень з позицп паса-жира / В.П. Кужель, А.П. 1щенко, М.О. Бишко // Вюник СНУ iм. В. Даля. -
2013. - № 15 (204). - С. 12-16.
10. Вшченко В.С. Аналiз факторiв i умов, як
впливають на якють пасажирських перевезень на мюькому пасажирському транспорт / В.С. Вшченко, 1.Ю. Тара-сюк // Комунальне господарство мют. -2011. - № 99. - С. 369-374.
11. Аулш В.В. Якють перевезень пасажирiв
як невщ'емна частина транспортного процесу / В.В. Аулш, Д.В. Голуб // Вюник КДПУ iм. Михайла Остроградсько-го. - 2008. - Вип. 5 (52). - С. 80-84.
12. Тлегенов Б.Н. Анализ методов оценки и
показателей качества системы городского пассажирского транспорта / Б.Н. Тле-
генов // Современные проблемы науки и образования. - 2012. - № 3. - С. 100-108.
13. Большаков А.М. Повышение качества обслуживания пассажиров и эффективности работы автобусов / А.М. Большаков, Е.А. Кравченко, С.Л. Черникова. -М.: Транспорт, 1981. - 206 с.
14. Цибулка Я. Качество пассажирских пере-
возок в городах / Я. Цибулка. - М.: Транспорт, 1987. - 240 с.
15. Kouwenhoven M. New values of time and
reliability in passenger transport in the Netherlands / M. Kouwenhoven, G.C. De Jong, P. Koster // Research in Transportation Economics. - 2014. - №. 47. -P. 37-49 .
16. Анохин С.А. Статистические методы оценки качества перевозочного процесса городского общественного автотранспорта / С.А. Анохин // Архитектура и строительство. Транспорт. - 2012. -№ 4 (42) - С. 35-43.
17. Гудков В.А. Технология, организация и
управление пассажирскими автомобильными перевозками / Л.Б. Миротин, В.А. Гудков - М.: Транспорт, 1997. -254 с.
18. Горбачов П.Ф. Дослщження iнтервалiв руху на мюькому автобусному маршрут / П.Ф. Горбачов, Д.М. Копитков // Коммунальное хозяйство городов. - 2007. -№ 76. - С. 336-344.
19. Минько А.А. Статистический анализ в MS Excel / А.А. Минько. - М.: Диалектика, 2004. - 448 с.
20. Халафян А.А. Statistica 6. Статистический
анализ данных / А.А. Халафян. - М.: Бином-Пресс, 2007. - 512 с.
21. Гмурман В.Е. Теория вероятностей и ма-
тематическая статистика / В.Е. Гмурман. - М.: Высшая школа, 2003. - 479 с.
22. Спирин И.В. Перевозки пассажиров городским транспортом / И.В. Спирин. -М.: Академкнига, 2004. - 413 с.
23. Горбачов П.Ф. Ощнка реакцп пасажира
на час очшування мюького пасажирсь-кого транспорту / П.Ф. Горбачов, Д.М. Копитков // Восточно-Европейский журнал передовых технологий. -2008. - № 2 (31). - С. 40-42.
References
1. Royina O.M. Avtomobil'nyy transport v Ukrayini. Normatyvna baza [Road transport in Ukraine. Normative base], Kiev, Atika Publ., 2004. 504 p.
2. Zakon Ukrayiny «Pro mis'kyy elektrychnyy
transport» [Law of Ukraine «On urban electric transport»]. Available at: http://zakon3.rada.gov.ua/laws/show/en/19 14-15 (accessed 03.04.2017).
3. Ponachugin V.A. Otsenka nadezhnosti perevozochnogo protsessa gorodskogo passazhirskogo transporta [The transportation process reliability evaluation of the urban mass transit], Nizhniy Novgorod, Nizhny Novgorod State University of Architecture and Civil Engineering Publ., 2008, 92 p.
4. Martynov N.G. Metodologicheskie aspekty
kompleksnoi otsenki effektivnosti raboty transporta [Methodological aspects of the integrated transport performance assessment], VINITI. Overview information. Transportation, science, technology, management, 1999, no. 4, pp. 4-8.
5. Inta M., Muntean A. Researchs on reliability
of urban passenger transport in Sibiu // Annals of the Oradea university. Fascicle of Management and Technological Engineering, 2015, no. 1, pp. 79-82.
6. Tseng Y. Valuation of travel time reliability
in passenger transport. Amsterdam, Rozen-berg Publishers, 2008. 187 p.
7. Vincent M. Measurement Valuation of Public
Transport Reliability. Wellington, Land Transport New Zealand, 2008. 128 p.
8. Semchugova E.Yu., Zyryanov V.V., Vo-
lod'kin P.P. Opredelenie vesomosti poka-zatelya nadezhnosti transportnykh uslug v kachestve perevozok [Determination of the reliability indicator weight in the transportation service quality]. Naukovedenie,
2012, no. 4. Available at: http:// cyber-leninka.ru/article/n/opredelenie-vesomosti-pokazatelya-nadezhnosti (accessed 29.03.2017).
9. Kuzhel' V P., Ishchenko A.P., Byshko M.O.
Vyznachennya rivnya yakosti pasa-zhyrs 'kykh perevezen' z pozytsiyi pasazhyra [Determination of the passenger transportation quality level from the passenger's viewpoint]. Visnyk SNU [SNU Bulletin],
2013, no. 15 (204). pp. 12-16.
10. Vinichenko V.S., Tarasyuk I.Yu. Analiz faktoriv i umov, yaki vplyvayut' na yakist' pasazhyrs'kykh perevezen' na mis'komu pasazhyrs'komu transporti [Analysis of factors and conditions affecting the quality of urban passenger transportation]. Komu-nal'ne hospodarstvo mist [Urban municipal engineering], 2011, no. 99, pp. 369-374.
11. Aulin V.V., Holub D.V. Yakist' perevezen' pasazhyriv yak nevid»yemna chastyna transportnoho protsesu [The passenger transportation quality as an integral part of the transportation process]. Visnyk KDPU im. Mykhayla Ostrohrads'koho. [Mykhaylo Ostrohrads'kyi KDPU Bulletin], 2008, no. 5 (52), pp. 80-84.
12. Tlegenov B.N. Analiz metodov otsenki i pokazatelei kachestva sistemy gorodskogo passazhirskogo transporta [Analysis of assessment methods and quality indicators of the urban passenger transport system]. Sov-remennye problemy nauki i obrazovaniya [Current problems of science and education], 2012, no. 3, pp. 100-108.
13. Bol'shakov A.M., Kravchenko E.A., Cher-
nikova S.L. Povyshenie kachestva obslu-zhivaniya passazhirov i effektivnosti raboty avtobusov [Improving the quality of passenger service and bus performance], Moscow, Transport Publ., 1981. 206 p.
14. Tsibulka Ya. Kachestvo passazhirskikh perevozok v gorodakh [Passenger urban transportation quality], Moscow, Transport Publ., 1987. 239 p.
15. Kouwenhoven M., De Jong G.C., Koster P.
New values of time and reliability in passenger transport in the Netherlands. Research in Transportation Economics, 2014, no. 47, pp. 37-49.
16. Anokhin S.A. Statisticheskie metody otsenki
kachestva perevozochnogo protsessa go-rodskogo obshchestvennogo avtotransporta [Statistical methods to evaluate the quality of the urban mass transit transportation process]. Arkhitektura i stroitel'stvo. Transport [Architecture and construction. Transport], 2012. no. 4 (42). pp. 35-43.
17. Gudkov V.A., Mirotin L.B. Tekhnologiya,
organizatsiya i upravlenie passazhirskimi avtomobil'nymi perevozkami [Technology, organization and management of passenger road transportation], Moscow, Transport Publ., 1997. 254 p.
18. Horbachov P.F., Kopytkov D.M. Doslid-zhennya intervaliv rukhu na mis'komu avtobusnomu marshruti [Headway study on the urban bus route]. Kommunal'noe khozyaystvo horodov [Urban municipal engineering], 2007, no. 76. pp. 336-344.
19. Min'ko A.A. Statisticheskii analiz v MS Ex-
cel [MS Excel Statistical Analysis], Moscow, Dialektika Publ., 2004. - 448 p.
20. Khalafyan A.A. Statistica 6. Statisticheskii
analiz dannykh [Statistica 6. Data statistical
analysis], Moscow, Binom-Press Publ., 2007. 512 p.
21. Gmurman V.E. Teoriya veroyatnostei i ma-
tematicheskaya statistika [Probability theory and mathematical statistic], Moscow, Vysshaya shkola Publ., 2003. 479 p.
22. Spirin I.V. Perevozki passazhirov gorodskim
transportom [Urban passenger transportations], Moscow, Akademkniga Publ., 2004. 413 p.
23. Horbachov P.F. Kopytkov D.M. Otsinka reaktsiyi pasazhyra na chas ochikuvannya mis'koho pasazhyrs'koho transportu [Passenger's response evaluation to the public
passenger transportation waiting time]. Vostochno-Evropeyskyy zhurnal peredo-vykh tekhnolohyy [Eastern-European Journal of Enterprise Technologies], 2008, no. 2 (31), pp. 40-42.
Рецензент: Е.В. Нагорный, профессор, д.т.н., ХНАДУ
