Natural Test for Random Numbers Generator Based on Exponential Distribution

Tanackov, Ilija; Sinani, Feta; Stanković, Miomir; Bogdanović, Vuk; Stević, Željko; Vidić, Mladen; Mihaljev-Martinov, J

doi:10.3390/math7100920

Cited by 5 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We collected passengers' ticket-purchasing data of partial OD sections during the pre-sale period on a certain date in January 2022. According to the method of testing random numbers based on an exponential distribution [40], we verified that the statistics satisfied the randomness requirement. Figure 4 indicates that the daily ticket-purchasing rates are different in different OD sections.…”

Section: Basic Datamentioning

confidence: 82%

Joint Optimization of Ticket Pricing and Allocation on High-Speed Railway Based on Dynamic Passenger Demand during Pre-Sale Period: A Case Study of Beijing–Shanghai HSR

et al. 2022

View full text Add to dashboard Cite

Against the background of the gradual deepening of China Railway’s market-oriented reform, and in order to improve the revenue and competitiveness for high-speed railway (HSR) passenger transport, this paper studies the joint optimization problem of the high-speed railway ticket pricing and allocation considering the dynamic demand characteristics of passengers during the pre-sale period. Firstly, we use the compound non-homogeneous Poisson process to describe the passengers' ticket-purchasing process and use the sparse method to simulate the passengers' ticket demand during the pre-sale period. Secondly, taking the ticket pricing and allocation as the decision variables and considering the full utilization of the train seat capacity, a stochastic nonlinear-programming mathematical model is established with the goal of maximizing the train revenue. A particle swarm algorithm is designed to solve the model. Finally, this study takes the G19 train running on the Beijing–Shanghai HSR in China as a case study to verify the effectiveness of the model and algorithm. The results show that the joint optimization scheme of ticket pricing and allocation considering dynamic demand yields a revenue of CNY 601,881, which increases the revenue by 1.01% with a small adjustment of the price compared with the fixed ticket price and pre-allocation scheme. This study provides scientific support for the decisions made by railway transportation enterprises, which is conducive to further increasing the potential ticket revenue and promoting sustainable development.

show abstract

Section: Basic Datamentioning

confidence: 82%

Joint Optimization of Ticket Pricing and Allocation on High-Speed Railway Based on Dynamic Passenger Demand during Pre-Sale Period: A Case Study of Beijing–Shanghai HSR

et al. 2022

View full text Add to dashboard Cite

show abstract

“…In this sense, all probabilistic systems based on the exponential distribution are indeterminate to the greatest extent, which is the foundation of discrete processes based on Denis Poison’s distribution (1781–1840), and Cony Pelma’s theorem (1907–1951) proves the elementary importance of exponential distribution in Poison’s processes. This fact is contained in the “memoryless” property of exponential distribution, which has already found application in the field of tests for generating independent random numbers [ 50 ].…”

Section: Model Of Heterogeneous Queuing Systemmentioning

confidence: 99%

Model for Risk Calculation and Reliability Comparison of Level Crossings

Ercegovac

Stojić

Kopić

et al. 2021

Entropy

View full text Add to dashboard Cite

There is not a single country in the world that is so rich that it can remove all level crossings or provide their denivelation in order to absolutely avoid the possibility of accidents at the intersections of railways and road traffic. In the Republic of Serbia alone, the largest number of accidents occur at passive crossings, which make up three-quarters of the total number of crossings. Therefore, it is necessary to constantly find solutions to the problem of priorities when choosing level crossings where it is necessary to raise the level of security, primarily by analyzing the risk and reliability at all level crossings. This paper presents a model that enables this. The calculation of the maximal risk of a level crossing is achieved under the conditions of generating the maximum entropy in the virtual operating mode. The basis of the model is a heterogeneous queuing system. Maximum entropy is based on the mandatory application of an exponential distribution. The system is Markovian and is solved by a standard analytical concept. The basic input parameters for the calculation of the maximal risk are the geometric characteristics of the level crossing and the intensities and structure of the flows of road and railway vehicles. The real risk is based on statistical records of accidents and flow intensities. The exact reliability of the level crossing is calculated from the ratio of real and maximal risk, which enables their further comparison in order to raise the level of safety, and that is the basic idea of this paper.

show abstract

“…The first algorithm is presented as Algorithm 3. In this algorithm, rnorm(µ, σ) denotes the function that generates normally distributed random numbers with mean µ and standard deviation σ [42]. The function mean() is the arithmetic mean of its list of arguments.…”

Section: Quasi-random Generation Algorithm (I)mentioning

confidence: 99%

Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding

Huang

2020

Mathematics

View full text Add to dashboard Cite

The capacity is a powerful tool with exponential coefficients to represent the interaction phenomenon among decision criteria, but its random generation becomes a tough issue for dealing with the monotonicity with all inclusion subsets as well as the complex constraints of decision preference. In this paper, we adopt a kind of explicit interaction index, the nonadditivity index, to construct two types of quasi-random generation methods of capacity under a given decision interaction preference. Compared to the existing random generation algorithms, the methods have relatively satisfactory performance on the statistics characteristic of generated capacities but need rather less calculation effort on the generation process. We also show the effectiveness of proposed quasi-random generation methods by an illustrative decision example.

show abstract

Natural Test for Random Numbers Generator Based on Exponential Distribution

Cited by 5 publications

References 27 publications

Joint Optimization of Ticket Pricing and Allocation on High-Speed Railway Based on Dynamic Passenger Demand during Pre-Sale Period: A Case Study of Beijing–Shanghai HSR

Joint Optimization of Ticket Pricing and Allocation on High-Speed Railway Based on Dynamic Passenger Demand during Pre-Sale Period: A Case Study of Beijing–Shanghai HSR

Model for Risk Calculation and Reliability Comparison of Level Crossings

Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding

Contact Info

Product

Resources

About