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– pp. 14-24.28 D’Ariano, A. A branch and bound algorithm for scheduling trains in a railway network [Text] / A. D’Ariano, D. Pacciarelli, M. Pranzo //European Journal of Operational Research, 183 (2) . – 2007. – pp. 643-665.29 Goverde,​R. M. P. Punctuality of Railway Operations and Timetable Stability Analysis [Text]: PhD Thesis / R. M. P. Goverde. – DelftUniversity of Technology, 2005.30 Goverde, R.

A delay propagation algorithm for large-scale railway traffic networks [Text] / R. Goverde // Transportation Research, Part C,18(3). – 2010. – pp. 269-287.31 Huisman, T. Running times on railway sections with heterogeneous train traffic [Text] / T. Huisman, R.J. Boucherie // TransportationResearch, Part B, 35. – 2001. – pp. 271-292.32 Keyhani, M.H. Reliability and Delay Distributions of Train Connections [Text] / M.H. Keyhani, M.

Schnee, K. Weihe, H-P. Zorn // In: D. Delling,L. Liberti (eds.), Proceedings of The 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems(ATMOS’12). – 2012. – pp. 35-46.33 Meester, L. E. Stochastic delay propagation in railway networks and phase-type distributions [Text] / L.E.

Meester, S. Muns //Transportation Research , Part B, 41. – 2007. – pp. 218-230.34 Muhlhans,​E. Berechnung der Verspatungsentwicklung bei Zugfahrten, Eisenbahntechn [Text] / E. Muhlhans // Rundschau ETR, 39 (7/8). –1990. – pp. 465-468.35 Tornquist, J. Computer-based decision support for railway traffic scheduling and dispatching: a review of models and algorithms [Text] /http://dvgups.antiplagiat.ru/ReportPage.aspx?docId=427.12578943&repNumb=121/2508.06.2015АнтиплагиатJ. Tornquist // In: Proceedings of The 5th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems,ATMOS 2005. – 2006.36 Krasemann, J. Design of an effective algorithm for fast response to the rescheduling of railway traffic during disturbances [Text] /J. Krasemann // Transportation Research, Part C, 20.

– 2012. – pp. 62-78.37 Quan L. Modeling Train Movements through Complex Rail Networks [Text] / L. Quan, M. Dessouky, R.C. Leachman // ACM Transactions onModeling and Computer Simulation, vol.14. – 2004. – pp. 32-76.38 Wendler, E. The scheduled waiting time on railway lines [Text] / E. Wendler // Transportation Research, Part B, 41 (2). – 2007.​– pp. 148158.39 Боровков А.А. Теория вероятностей.

– М.: Наука, 1986. – 431 с.40 Боровков А.А. Математическая статистика. – М.: Наука, 1984. – 472 с.41 Вентц ель Е.С. Теория вероятностей. – М.: Наука, 1998.42 Гмурман В.Е. Теория вероятностей и математическая статистика. – М.: Высшая школа, 1999.43 Гнеденко Б.В. Курс теории вероятностей. – М.: ​Наука, 1988. – 446 с.44 Колмогоров А.Н., Фомин С.В. Элементы теории функций и функционального анализа.

– М.: Наука, 1968.45[59]Чеботарев В.И. Теория вероятностей: учеб. пособие / В.И. Чеботарев. – Хабаровск: Изд-во ДВГУПС, 2014. – 233 с.ПРИЛОЖ ЕНИЕ АSection 1Mathematical model of train delaysСтудент гр.952 _______________________ К.С. Каблукова________________Консультант кафедры «Иностранные языки и меж культурная коммуникац ия»И.о. заведующ ей кафедрой,ст.

преподаватель _______________________ Е.Л. Рябкова________________1 Mathematical model of train delays1.1 Introduction. Description of models. The main resultsThe first model. Trains move one after another, along the same path in one direction from station A to station B with the same averagespeed: ahead train 1, behind him, in order, trains 2, 3, etc. We assume that the total number of trains equals n. Distance from train j to train(j – 1) is denoted by, where j = 2, 3, … , n, is the least safe distance between trains, X2, X3, … , Xn are random variables (while without anyassumptions with respect to their distributions).

Trains have the same destination station.We also denote , . Suppose that the train 1 departs from the station A at time​t = 0. Then the departure time of the train м сап Ье written as(see Figure 1.1). (1.1)Figure 1.1 – Scheduled departure times of trains 1, 2 and 3 from station ASuppose that the train 1 unplanned stopped at some time point.

Let the train 1 is delayed by the random time . If the time interval is largeenough, then the subsequent trains suffer from secondary delays. Assume that train stops, if the distance between the train and preceding(already standing) train was reduced to s0.

In this situation we assume that as soon as the preceding train starts moving, then the followingtrain will start moving immediately. Denote by the time interval between the arrivals of trains with numbers (к – 1) and к at the station B for .Note that the time interval has a random length. It is required to determine distribution functionof the random variable .The second model. For simplicity, we formulate the problem in an alternative form. Let trains 1, 2, … , n are in the way one after anotheraccording to their numbers. Trains depart from the station A at time points (see Figure 1.1).

Consider the sequence of n trains at some pointin time​.If the flow of trains moves in the normal mode (without unscheduled delays), we can assume that the intervals between trains will be thesame as at the beginning of their movement from the station A, i.e. distance from the train к to the train (к – 1) is equal to , namely the timeinterval between trains equals . We are interested in what will be with the time intervals between trains, if at the time train 1 due to someunforeseen circumstances stopped and was detained for a while ? In other words, it is needed to find the probability distribution of the timeintervals , between trains, provided that train 1 had been detained.

This problem is equivalent to the following.Let the train 1 was delayed at the station A at time t = 0 for a random time . If , then trains 2, 3, etc. depart at scheduled points in time , etc.,respectively. If , then the train 2 be delayed and starts moving at the moment . Train 3 departs by the same rule, depending on the delaytime of the train 2. Etc. Now is the time interval between the departure times of trains with the numbers (к – 1) and к. It is required todetermine the distribution functions of the random variables .An​example. If n = 5, Tk = 2, к = , t0 = 1, then departure times of trains satisfy the equalities T(к) = 3(к – 1), к = . Figure 1.2 shows intervals ,к = , depending on the six values of the interval .Figure 1.2 – The time intervals for someIn Figure 1.2 the dots indicate the actual departure times of trains that appeared as a result of delay of the train 1 for a time .Let us remind the basic assumptions:only the train 1 undergoes the primary delay ,.By the symbol R(к), in contrast to the T(к), we denote the real departure time of the train under the number к.Order of the train departures.

Let be a fixed integer.1. If, (1.2)then. (1.3)2. If, (1.4)then. (1.5)Next, we shall use the following notationhttp://dvgups.antiplagiat.ru/ReportPage.aspx?docId=427.12578943&repNumb=122/2508.06.2015Антиплагиатwhere A is an arbitrary set on the real line R.Assume that the total number of trains equals . Let for к > n.Theorem 1. 1. If , then.2. Let к Ье a fixed integer, . If, (1.6)then. (1.7)3. If(1.8)then(1.9)(1.10)Theorem 2. Let . The following formulas hold(1.11)(1.12).Let us​define(1.13)Then, in the right-hand side of eqn (1.12) for к = 2 we haveTherefore, the formula (1.12) coincides with formula (1.11) for к = 2.

Thus, Corollary 1 holds.Corollary 1. The formula (1.12) holds for .Let us formulate corollaries of Theorem 2 in terms of given probability density functions.Corollary 2. Let all be constants which are not necessarily equal to each other, is the density function of the random variable . Then, thefollowing formula holds(1.14), in particular, .Corollary 3.

Let all be constants which are equal to the same number T, is the density function of the random variable . Then, the followingformula holds(1.15), in particular,(1.16)Recall the definition of the convolution of the density functions. If and are two arbitrary probability density functions, the convolution of thesedensities is the integral which is denoted by . It is known that the operation of convolution is commutative. If we shall use the notation.By definition, we assume that . Recall also that if independent random variables are absolutely continuous, then the density function of their​sum is equal to the convolution of the original densities.Corollary 4.

Let be independent identically distributed random variables with the density function . Let has a density function and beindependent of . Then,(1.17)(1.18)Remark 1. Since random variables under consideration are positive, then in integrals of Corollary 4 lower limit of integration can be replacedby 0.Remark 2. We define 0-fold convolution as a generalized function with the following property: for any bounded continuous function theequality holds.

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