Author details

Alexey Markov<sup>1</sup> \*, Alexander Barabanov<sup>2</sup> and Valentin Tsirlov<sup>2</sup>

\*Address all correspondence to: mail@cnpo.ru


## References

[1] Gokhale SS, Marinos PN, Trivedi KS. Important milestones in software reliability modeling. In: Proceedings of Software Engineering and Knowledge Engineering (SEKE 96); Lake Tahoe; 1996. pp. 345-352

[15] Anniprincy B, Sridhar S. Prediction of software reliability using COBB-Douglas model in SRGM. Journal of Theoretical and Applied Information Technology. 2014;62(2):355-363

Models for Testing Modifiable Systems http://dx.doi.org/10.5772/intechopen.75126 167

[16] Bubnov VP, Sergeev SA. Non-stationary models of a local server of the automated system for monitoring artificial structures. SPIIRAS Proceedings. 2016;2(45):102-115. DOI:

[17] Krymsky VG, Ivanov IV. Application of interval-valued probabilities and unified scheme of non-homogeneous Poisson process models to software failure prognostics. In: Podofillini L, Sudret B, Stojadinovic B, Zio E, Kröger W, editors. Safety and Reliability of Complex Engineered Systems: ESREL 2015. Balkema: CRC Press; 2015. pp. 2403-2411 [18] Tamura Y, Yamada S. Cost optimization based on decision-making and reliability modeling for big data on cloud computing. Communications in Dependability and Quality

[19] Wang LJ, Hu QP, Xie M. Bayesian analysis for NHPP-based software fault detection and correction processes. In: 2015 IEEE International Conference on Industrial Engineering

[20] Zeephongsekul P, Jayasinghe CL, Fiondella L, Nagaraju V. Maximum-likelihood estimation of parameters of NHPP software reliability models using expectation conditional maximization algorithm. IEEE Transactions on Reliability. 2016;65(3):1571-1583. DOI:

[21] Zhao C, Qiu J, Liu G, Lv K. Planning, tracking and projecting method for testability growth based on in time correction. Proceedings of the Institution of Mechanical Engi-

[22] Teyer TA, Lipow M, Nelson EC. Software Reliability. A Study of Large Project Reality, TRW Systems and Energy. Amsterdam/Lausanne/New York: Elsevier; 1978. p. 326 [23] Markov A. Nonmonotone models of reliability and security of software in the early stages of testing. Voprosy kiberbezopasnosti [Cybersecurity Issues]. 2014;2(3):10-17. DOI: 10.21681/

[24] Lloyd DK, Lipow M. Reliability Management, Methods, and Mathematics. 2nd ed. Mil-

[25] Gnedenko B, Pavlov IV. Ushakov IA. Statistical Reliability Engineering, New York: Wiley-

[26] Junhong G, Xiaozong Y, Hongwei L. Software reliability nonlinear modeling and its fuzzy evaluation. In: 4th WSEAS International Conferernce on Non-Linear Analysis, Non-Linear Systems and Chaos (NOLASC'05); 27–29 October 2005; Sofia: ACM; 2005. pp. 49-54

[27] Kumar R, Khatter K, Kalia A. Measuring software reliability: A fuzzy model. ACM SIGSOFT Software Engineering Notes. 2011;36(6):1-6. DOI: 10.1145/2047414.2047425 [28] Vorobiev EG, Petrenko SA, Kovaleva IV, Abrosimov IK. Organization of the entrusted calculations in crucial objects of informatization under uncertainty. In: Proceedings of 2017 20th IEEE International Conference on Soft Computing and Measurements (SCM 2017); 24–26 May 2017; St. Petersburg: IEEE; 2017. 17039917. DOI: 10.1109/SCM.2017.7970566

and Engineering Management (IEEM); IEEE; 2015. pp. 1046-1050

neers, Part O: Journal of Risk and Reliability. 2015;230(2):228-236

10.15622/sp.45.6

Management. 2015;18(4):5-19

10.1109/TR.2016.2570557

2311-3456-2014-2-10-17 (in Russia)

Interscience; 1999. p. 528

waukee: American Society for Quality; 1984. p. 589


[15] Anniprincy B, Sridhar S. Prediction of software reliability using COBB-Douglas model in SRGM. Journal of Theoretical and Applied Information Technology. 2014;62(2):355-363

Author details

Alexey Markov<sup>1</sup>

References

\*Address all correspondence to: mail@cnpo.ru

2 NPO Echelon, Moscow, Russia

166 Probabilistic Modeling in System Engineering

Lake Tahoe; 1996. pp. 345-352

nique. SEBIT; 2004. p. 32

0471028959.sof329

ken: Wiley; 2008. p. 616

2004. p. 632

1306.1958.pdf [Accessed: February 5, 2018]

1 Bauman Moscow State Technical University, Moscow, Russia

\*, Alexander Barabanov<sup>2</sup> and Valentin Tsirlov<sup>2</sup>

[1] Gokhale SS, Marinos PN, Trivedi KS. Important milestones in software reliability modeling. In: Proceedings of Software Engineering and Knowledge Engineering (SEKE 96);

[2] Markov A. Software testing models against information security requirements. Cornell University Library [Internet]. 2013. Available from: http://arxiv.org/ftp/arxiv/papers/1306/

[3] Andersson B, Persson M. Software reliability prediction—An evaluation of a novel tech-

[4] Bondi AB. Performance Engineering: Process, Performance Modeling, Requirements, Testing, Scalability, and Practice. 1st ed. Harlow: Addison-Wesley Professional; 2014. p. 426 [5] Kapur PK, Pham H, Gupta A, Jha PC. Software Reliability Assessment with OR Applica-

[6] Karanta I. Methods and problems of software reliability estimation. VTT WP. 2006;63:57 [7] Lyu MRT. Software Reliability Theory. John Wiley & Sons Inc.; 2002. p. 43. DOI: 10.1002/

[8] Musa JD. More Reliable Software Faster and Cheaper. 2nd ed. New York: McGraw-Hill;

[9] Naik S, Tripathy P. Software Testing and Quality Assurance: Theory and Practice. Hobo-

[10] Shooman ML. Reliability of Computer Systems and Networks: Fault Tolerance, Analysis

[11] Subburaj R. Software Reliability Engineering. New York: McGraw Hill Education; 2014. p. 458 [12] Tian J. Software Quality Engineering: Testing, Quality Assurance and Quantifiable

[13] Xie M, Dai Y-S, Poh K-L. Computing Systems Reliability. Models and Analysis. Dordrech:

[14] Yamada S. Software Reliability Modeling: Fundamentals and Applications. Japan: Springer;

Improvement. Hoboken: Wiley-IEEE Computer Society Press; 2005. p. 440

Kluwer Academic Publishers; 2004. 293p. DOI: 10.1007/b100619

tions. London: Springer; 2013. p. 548. DOI: 10.1007/978-0-85729-204-9

and Design. New York: Wiley-Interscience; 2002. p. 560

2014. p. 90. DOI: 10.1007/978-4-431-54565-1


[29] Iqbal J, Quadri SMK. Software reliability simulation: Process, approaches and methodology. Global Journal of Computer Science and Technology. 2011;1(8):1-8

**Section 5**

**Modeling of Transport and Cosmic Systems**


**Modeling of Transport and Cosmic Systems**

[29] Iqbal J, Quadri SMK. Software reliability simulation: Process, approaches and methodol-

[30] Utkin LV, Zatenko SI, Coolen FPA. New interval Bayesian models for software reliability based on non-homogeneous Poisson processes. Automation and Remote Control. 2010;

[31] Danilov AI, Khomonenko AD, Danilov AA. Dynamic software testing models. In: Proceedings of International Conference on Soft Computing and Measurements (SCM 2015); 19–21 May 2015; St. Petersburg: IEEE; 2015. pp. 72-74. DOI: 10.1109/SCM.2015.7190414

[32] Ivannikov V, Gaissaryan S, Avetisyan A, Padaryan V, Leontyev H. Dynamic analysis and trace simulation for data parallel programs in the parjava environment. In: Avances en la

[33] Ivutin AN, Larkin EV, Perepelkin DA. Software errors and reliability of embedded software. In: 2016 IEEE Conference on Quality Management, Transport and Information Security, Information Technologies (IT&MQ&IS); 4–11 October 2016; Nalchik: IEEE; 2016.

[34] Kostogryzov A. Modeling software tools complex for evaluation of information systems operation quality (CEISOQ). Lecture Notes in Computer Science. 2001;2052:90-101. DOI:

[35] Smagin VA, Novikov AN, Smagin SY. A probabilistic model of the control of technical systems. Automatic Control and Computer Sciences. 2010;44(6):324-329. DOI: 10.3103/

[36] Rana R, Staron M, Berger C, Hansson J, Nilsson M, Meding W. Analyzing defect inflow distribution and applying Bayesian inference method for software defect prediction in large software projects. Journal of Systems and Software. 2016;117:229-244. DOI: 10.1016/j.

[37] Stieber HA. Estimating the total number of software faults reliability models and mutation testing a Bayesian approach. In: 2015 IEEE 39th Annual Computer Software and Applications Conference; 1–5 July 2015. Taichung: IEEE; 2015. pp. 423-426. DOI: 10.1109/

[38] Bisi M, Goyal NK. Artificial Neural Network Applications for Software Reliability Predic-

[39] Kaswan KS, Choudhary S, Sharma K. Software reliability modeling using soft computing techniques: Critical review. Journal of Information Technology and Software Engineering.

[40] Maevsky D, Kharchenko V, Kolisnyk M, Maevskaya E. Software reliability models and assessment techniques review: Classification issues. In: 2017 9th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS); 21–23 Sept. 2017; Bucharest: IEEE; 2017. pp. 894-899. DOI:

tion, Performability Engineering Series. Wiley-Scrivener; 2017. p. 303

2015;5:144. DOI: 10.4172/2165-7866.1000144

10.1109/IDAACS.2017.8095216

ogy. Global Journal of Computer Science and Technology. 2011;1(8):1-8

Ciencia de la Computacion (ENC'04); Colima; 2004. pp. 481-488

71(5):935-944. DOI: 10.1134/S0005117910050218

pp. 69-71. DOI: 10.1109/ITMQIS.2016.7751926

10.1007/3-540-45116-1\_12

168 Probabilistic Modeling in System Engineering

S0146411610060027

jss.2014.08.033

COMPSAC.2015.180

**Chapter 8**

Provisional chapter

**Probabilistic Model of Delay Propagation along the**

DOI: 10.5772/intechopen.75494

In this chapter, we propose a probabilistic model for train delay propagation. There are deduced formulas for the probability distributions of arrival headways and knock-on delays depending on distributions of the primary delay duration and the departure headways. We prove some key mathematical statements. The obtained formulas allow to predict the frequency of train arrival delays and to determine the optimal traffic adjustments. Several important special cases of initial probability distributions are considered. Results of the theoretical analysis are verified by comparison with statistical data on the

Keywords: train traffic, stochastic model, train delay propagation, probabilistic modeling,

The trains' movement is subject to a variety of random factors which leads to unplanned delays. This causes the scattering of the arrival times, hence, the inconvenience to passengers and consignees. Knowledge of the arrival times' distribution properties leads to the possibility of predicting the characteristics of the train traffic and making correct decisions on the transportation process management. This makes it possible to improve the punctuality of train

The properties of the arrival headways distributions allow us to estimate the probability of delays emergence and theirs characteristics, which are important from a practical point of

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Probabilistic Model of Delay Propagation along the

**Train Flow**

Train Flow

Kseniya Kablukova

Kseniya Kablukova

Abstract

Vladimir Chebotarev, Boris Davydov and

Vladimir Chebotarev, Boris Davydov and

http://dx.doi.org/10.5772/intechopen.75494

train traffic at the Russian railways.

traffic and save resources, in particular, electric power.

operative management

1. Introduction

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Probabilistic Model of Delay Propagation along the Train Flow** Probabilistic Model of Delay Propagation along the Train Flow

DOI: 10.5772/intechopen.75494

Vladimir Chebotarev, Boris Davydov and Kseniya Kablukova Vladimir Chebotarev, Boris Davydov and Kseniya Kablukova

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75494

#### Abstract

In this chapter, we propose a probabilistic model for train delay propagation. There are deduced formulas for the probability distributions of arrival headways and knock-on delays depending on distributions of the primary delay duration and the departure headways. We prove some key mathematical statements. The obtained formulas allow to predict the frequency of train arrival delays and to determine the optimal traffic adjustments. Several important special cases of initial probability distributions are considered. Results of the theoretical analysis are verified by comparison with statistical data on the train traffic at the Russian railways.

Keywords: train traffic, stochastic model, train delay propagation, probabilistic modeling, operative management
