Markov Birth Research Articles

Accounting for passenger loss in bus bunching reduction: a robust real-time speed control method

ABSTRACT Bus bunching is a common phenomenon resulting from the inherent instability influenced by factors such as traffic and passenger behaviour. However, the issue of passenger loss caused by extended waiting time, is often overlooked despite being a significant concern for passengers. This paper addresses this problem by modelling passenger arrival and loss as a Markov birth–death process. We present a transit route model that incorporates passenger loss while considering additional factors, such as stochasticity, overtaking, passenger alighting, and bus capacity constraints. The primary objective of our model is to minimise passenger loss. To achieve this, we conduct an analysis about the characteristics of passenger loss. Under mild assumptions, we prove that passenger loss increases as the headways between buses exhibit greater variance. We also develop a robust optimisation (RO) method and corresponding algorithms to minimise passenger loss. To validate the effectiveness of our control method, we conduct numerical experiments using both computer-generated and real-world data. The results demonstrate that our method effectively reduces bus bunching, passenger loss, and waiting time compared to the existing literature.

Process modeling for decomposition unit of a UFP for reliability indices subject to fail-back mode and degradation

PurposeEnsuring safe operation of a urea fertilizer plant (UFP) is a vital aspect for its functioning and production. Clearly the safe operation of such systems can only be archived with proper and effective maintenance scheduling and through controlling its failures as well as repairs of the components. Also for this, the concern plant management must have the information regarding the failures that affects the system's performance most/least. The objective of this study is to analyze mathematically the factors that are responsible for the failure/degradation of the decomposition unit of UFP.Design/methodology/approachThe considered system has been modeled by the aid of Markov's birth–death process with two types of failures for its components: variable (which are very similar in practical situations) and constant. The mathematical model is solved by the help of Laplace transform and supplementary variable technique.FindingsIn the present paper, the availability, reliability and mean time to failure (MTTF) are computed for the decomposition unit of the UFP. The critical components that affect the reliability and MTTF of the decomposition unit are identified through sensitivity analysis.Originality/valueIn this paper, a mathematical model based on the working of the decomposition unit of a UFP has been developed by considering two types of failure, namely, variable failures rates and constant failure rates (which has not been done in the literature for the decomposition unit). Conclusions in this paper are good references for the improvement of the same.

Reliability, Availability, Maintainability, and Dependability Analysis of Cold Standby Series-Parallel System

This paper dealt with the evaluation reliability, availability, maintainability, dependability, mean time between failures, and mean time to failure of series-parallel system. The system under investigation has four subsystems, namely subsystem A containing two units in cold standby, subsystem B and C possess one unit each, and subsystem D has two units in cold standby. Through the transition diagram of each subsystem and the Markov birth–death process, Chapman Kolmogorov forward equations are derived. Both failure and repair rates of units in each subsystem are assumed to follow exponential distribution. The objective is to derive the corresponding reliability models of dependability, availability, maintainability, and reliability and capture the effect of system parameters on reliability, availability, maintainability, and dependability and to determine the critical subsystems. On the basis of numerical results obtained, the system’s performance has been evaluated. Moreover, the outcome of this study shows that the ideal system reliability can be achieved when the overall system failure rate is low and the supporting units are activated.

Performance Modeling and Availability Analysis of Screw Manufacturing Plant

In this research, we focus at the deviation of availability, which is used as a performance measure of screw plant with respect to time. This plantconsistsofnumerous units, viz., header, slotting, thread roller and burnishing unit. These units are operating in sequence. Working, partial failure and absolute fault are the system's three states. We originated the mathematical model of the plant Using Markov birth - death Process and we solve the differential equation by implementing the matlab tool to determine the availability of the system. Appropriate maintenance planning must be devised, which can be controlled after assessing availability variances over time. The theory of availability analysis will help to increase output and increase screw plant uniformity. We use data and graphical representation to depict the availability of the screw plant as it evolves over time the numerical data are provided for different configurations which are successful in enhancing the availability of the system..

Measurement and improvement of efficiency of Library by mathematical modelling and finding reliability

Here in this paper we have developed the mathematical model of the library server using Markov birth – death process assuming that library system server system is based on exponential distribution. The model so developed by victimisation Chapman Kolmogorov differential equation and is solved by using Mathematica. The solution so obtained is analysed for various rates of failures and repair. The finding so obtained are discussed with the concerned authorities of the library to boost the efficiency of the library.

Reliability and Maintainability Investigation of Generator in Steam Turbine Power Plant using RAMD analysis

Generator is key unit of steam turbine power plant which is used to convert mechanical energy into electrical energy. This energy is further used for completing the requirement generated by various sectors of country. Generator is one of the most important component of steam turbine power plant configured with seven subsystems in series configuration. So, it is necessary to ensure its smooth functioning which is attain by the proper functioning of its subcomponents. It is important to increase operational availability of subsystem. Hence, present study is proposed to investigate various reliability measures of generator used in STP through RAMD approach at component level. For this purpose, mathematical models using Markovian birth death process have been developed for all subsystems of generator. These models are very helpful in reliability, maintainability, and availability analysis of generators. RAMD analysis will play significant role in this direction. This will help to find critical component of system so that proper maintenance strategies can be proposed. It is assumed that all failure and repair rates associated with each component followed exponential distribution and adequate repair facility always remains available with system. Various system performance measures like reliability function, maintainability function, dependability function and steady state availability for different components as well as system have been evaluated. The numerical results have been derived to highlight the importance of study.

Investigation of performance measures of power generating unit of sewage treatment plant

The main objective of present study to investigate the availability and profit of power generation systems established in sewage treatment plants. The sewage treatment plant is an industry in which waste sewage water has been treated and waste is used to generate power. For this purpose, a mathematical model has been proposed by considering constant failure and repair rates. The power generating unit in sewage treatment plant comprises six subsystems as sludge digester, gas holding tank, gas burner, gas scrubber, gas engine and power generation. By using appropriate redundancy technique in model development Chapman-Kolmogorov differential equations has been drawn with the help of the Markov birth death process. Availability and profit have been analysed based on making variation in the failure and repair rates. The numerical and graphical results have been depicted for a particular case. The derived results have been discussed with system designers and found useful.

RAM analysis and availability optimization of thermal power plant water circulation system using PSO

This paper presents reliability, availability, and maintainability (RAM) analysis framework for evaluating the performance of a circulation system of water (WCS) used in a coal-fired power plant (CFPP). The performance of WCS is evaluated using a reliability block diagram (RBD), fault tree analysis (FTA), and Markov birth–death probabilistic approach. In this work, the system under study consists of five subsystems connected in series and parallel configuration namely condensate extraction pump (CEP), low-pressure feed water heater (LPH), deaerator (DR), boiler feed pump (BFP), high-pressure feed water heater (HPH). The reliability block diagram (RBD) and fault tree approach (FTA) have been employed for the performance evaluation of WCS. The Markov probabilistic approach based simulation model is developed. The transition diagram of the proposed model represented several states with full working capacity, reduced capacity, and failed state. The ranking of critical equipment is decided on the basis of criticality level of equipment. The study results revealed that the boiler feed pump affects the system availability at most, while the failure of deaerator affects it least. The availability of the system is optimized using the particle swarm optimization method. The optimized availability parameter (TBF, TTR) based modified maintenance strategy is recommended to enhance the availability of the plant system. The optimized failure rate and repair rate parameters of the subsystem are used to suggest a suitable maintenance strategy for the water circulation system of the thermal power plant. The proposed RAM framework helps the decision-makers to plan the maintenance activity as per the criticality level of subsystems and allocate the resources accordingly.

Modeling and availability analysis of data center: a fuzzy approach

Data Centers are the backbone of any industry that provides a specialized environment to safeguard the company's valuable equipment and intellectual property. The successful operation of company's Data Center is typically shared among multiple departments and personnel. But, the involvement of multiple personal and departments make its configuration complex. In such situations, reliability of data center become a necessary factor. But, the traditional theory of reliability is based on the Bernoulli trials, i.e., either operative or failure. But this situation is unrealistic in case of complex systems like data center. To rectify this problem, here a mathematical model has been developed using the concept of fuzzy reliability. All the failure and repair rates are exponential distributed along with coverage factor. Chapman-Kolmogorov differential equations have been developed for the fuzzy system using Markov birth–death process. A new methodology Runge–Kutta method of order four has been used to solve Chapman-Kolmogorov differential equations using MATLAB (Ode 45 function).

Operational availability analysis of generators in steam turbine power plants

The main aim of this study is to explore the availability and profitability of generators, which are key units of steam turbine power plants, considering exponential failure and arbitrary repair time distributions. A Markov birth–death process and supplementary variable technique are used to evaluate system effectiveness measures. Such a generator mainly consists of seven repairable components arranged in a series configuration. A stochastic model of the generator is developed, and the Chapman–Kolmogorov differential difference equation of the system derived. Finally, the results for the steady-state availability and profitability of the system are obtained for a particular case that will be helpful to system designers to enhance the performance of plants to some extent.

A study of microprocessor systems using RAMD approach

The aim of the present study is to offer results of reliability, availability, maintainability and dependability analysis of a microprocessor system. A microprocessor is designed with the help of seven subsystems including input, terminal, processor, main memory disk, addressing modes, disk controller and disk drives. Reliability, availability, maintainability and dependability analysis has been performed for all the subsystems. For analysis purpose, state transition diagram has been designed for all subsystems and using Markov birth–death process governing equations has been derived. All random variables are exponentially distributed, i.e., follows constant failure rate. Mean time between failures, mean time to repair, availability, reliability, maintainability and dependability ratio parameters for all the subsystems are computed. The reliability and maintainability are estimated at various time instants.

Short-Term Parking Demand Prediction Method Based on Variable Prediction Interval

With the rapid economic development, parking problems have become increasingly prominent due to the city's development model and the emergence of a large number of private cars. Parking management departments around the world focus on intelligent parking system in order to solve parking problems, but most of them are limited to upgrading the parking infrastructure. There is no effective solution from a perspective of the fundamental cause to solve the parking problem. At present, it is generally believed that parking guidance systems can effectively alleviate parking problems and provide drivers and traffic managers with real-time and accurate parking information. As one of the prerequisites of the parking guidance system, the accuracy of the short-term parking demand prediction method determines whether the implementation of the parking guidance scheme can effectively solve the parking problem in a certain area. Based on this, we have studied a short-term parking demand prediction in this paper. First, focusing on the distribution of typical parking arrivals and departures regular pattern, a parking demand prediction model was constructed utilizing the Markov birth and death process, and model parameters were calibrated utilizing curve fitting method and undetermined coefficients method. The simulation environment was set up utilizing the Markov process to verify the accuracy of the availability of parameter estimation method. Secondly, a method for determining the prediction interval based on the parking trend was given for different situations with the parking rush hours and ordinary hours which parking arrival and departure parameters were different. In order to verify the effectiveness of the model in practical applications, parking arrival and departure data from June 17 to June 23, 2019 in Jilin University of Nanling Campus was used to verify the short-term parking demand prediction method proposed in this paper. The results show that the parking demand prediction model proposed in this paper can accurately calibrate model parameters, predict parking demand quickly and effectively and provide theoretical reference and technical support for parking planning and management.

Modeling and analysis of concrete mixture plant subject to coverage factor and profust reliability approach

The main objective of the present study is to analyze the effect of coverage factor, failure rates and repair rates on the availability and performance of a concrete mixture plant by considering profust reliability approach. Concrete mixture plant comprises seven subsystems installed in series configuration. In most of the plants, some units of subsystems named mixer and cement silo are used in redundancy. In the present model, both subsystems are configured as 2-out-of-2: G with one cold standby. Rest of the subsystems are single-unit systems. Sufficient repair facilities remain available with system to do repair activities. All failure and repair rates are exponentially distributed. Using Markov birth–death model, differential equations have been derived and solved by Runge–Kutta method of fourth order. The result of the proposed model verifies the theory and would prove beneficial for system designers.

Reliability, maintainability and sensitivity analysis of physical processing unit of sewage treatment plant

India is facing radical change in perspective of inadequate water resources which can reduce by using treated water. In this direction, sewage treatment plants play a key role. Sewage treatment plant comprises three units namely physical processing, chemical processing and biological process. The physical process is the most important part and it has five component arranged in series configuration. It becomes necessary to perform this process with high efficiency and reliability, availability, maintainability, and dependability (RAMD) is the methodology to analyze the performance. The failure and repair rates of the subsystems has been considered exponentially distributed. Chapman–Kolmogorov differential equations are derived using Markovian birth–death process and several measures like mean time between failures, mean time to repair and dependability ratio are derived. The sensitivity analysis of reliability of the plant has also been performed. RAMD investigation shows that: availability of system is 0.952177, reliability of the system after 20 days is 0.2018 and after 60 days 0.00823, maintainability of the plant is 0.999948, dependability ratio is 0.9541 and raw sewage sump is the most sensitive subsystem of the plant with reliability 0.382893. This work is projected to support as an informative exertion in steering a RAMD analysis of physical processing unit and vary few work is available in literature related to the performance features of physical processing units of the sewage treatment plants. The main findings may be very useful for sewage treatment plants designers.

Analysis and performance of coded symbol recovery loop using oversampling

In this work, we propose a closed-loop analog system to detect the source information of a binary data stream coded by a flexible finite automaton. We initially consider the dual sideband suppressed-carrier modulation of a base band binary amplitude waveform. The automaton introduces a symbol redundancy as phase contribution of the modulated signal by a simple mapping scheme. The proposed recovery system performs a coherent demodulation, presenting the base-band binary wave to a maximum likelihood hard detector, a simple analog trigger that estimates the source data within the symbol period. This wave is over-sampled, and the final decision comes by counting the positive samples and a majority vote. We prove our approach is valid answering the most important concerns: the stability of the closed loop, a first analytical expression of the error rate when a Markov birth process models the counting phase, and finally the role of this last loop to lower the bit error rate compared to a simple Costas loop. The analysis continues by solving the problem of carrier and symbol rate recovery and the impact of non-linearity and noise in the basic analog blocks. Behavioral simulations describe a competitive scenario in terms of error rate, comparing the proposed approach to the Costas Loop and the basic convolutional decoding strategies based on Viterbi algorithm both in the hard (Hamming metrics) and soft (Euclidean metrics) versions.

Performance analysis of evaporation system in sugar industry using RAMD analysis

The main aim of this study is to analyze the application of reliability, availability, maintainability and dependability in identification of most sensitive subsystem of evaporation system in sugar plant. For this analysis, transition diagram of all subsystems is drawn and respective Chapman–Kolmogorov differential equations are derived using Markov birth–death process. All failure and repair rates of each subsystem are exponentially distributed. Various measures of system effectiveness like mean time between failures, mean time to repair and dependability ratio for all the three subsystems are also computed. Sensitivity analysis of system reliability is also performed. The reliability and maintainability are estimated at various time instants. Analysis of all the subsystems shows that sulphited syrup is highly sensitive from reliability point of view. The derived measures are shared with system designers for their active deliberation.

Mathematical modeling and performance evaluation of A-pan crystallization system in a sugar industry

In this paper, an effort has been made to formulate a mathematical model of A-pan crystallization system of a sugar plant using fuzzy reliability approach. The sugar plant comprises eight subsystems. A-pan crystallization system is one of the most important representative among sugar plant systems. The A-pan crystallization system has four subsystems arranged in a series. The configuration of first and second subsystems is 2-out-of-2: G with two cold standby while third and fourth subsystems are in single-unit configuration. A mathematical model has been proposed by considering exponential distribution for failure and repair rates. By considering fuzzy reliability approach and Markov birth–death model differential equations have been derived. These equations are then solved by Runge–Kutta method of fourth order using MATLAB (Ode 45 function) to obtain the fuzzy availability. The results of the proposed model are beneficial for system designers.

Mathematical modeling of sugar plant: a fuzzy approach

Conventional reliability of a system is defined as the probability that it can perform a pre-specific function without failure in a pre-fixed time interval under a predefined environment. It is based on the assumption that system’s failure behavior is characterized in probabilistic context and binary-state assumption for the demonstration of the states. At any time, the system is either in failed or operative state. But, this assumption seems unrealistic for large complex industrial systems. The uncertainty of each component enhances the uncertainty of the whole system. In this paper, the concept of fuzzy reliability has been used for the analysis of fuzzy availability of a sugar plant. The effect of coverage factor, failure and repair rates of subsystems on systems fuzzy availability had been analyzed. Chapman–Kolmogorov differential equations have been derived with the help of Markov birth–death process. The governing differential equations are solved by Runge–Kutta method of order four using MATLAB (Ode 45 function).

A discrete log-Sobolev inequality under a Bakry–Émery type condition

We consider probability mass functions $V$ supported on the positive integers using arguments introduced by Caputo, Dai Pra and Posta, based on a Bakry--\'{E}mery condition for a Markov birth and death operator with invariant measure $V$. Under this condition, we prove a modified logarithmic Sobolev inequality, generalizing and strengthening results of Wu, Bobkov and Ledoux, and Caputo, Dai Pra and Posta. We show how this inequality implies results including concentration of measure and hypercontractivity, and discuss how it may extend to higher dimensions.

Analytical Modeling of LTE-based Network Capacity for Public Safety Communications

In this paper, an analytical approach for estimating the network capacity for voice communications on LTE-based public safety networks is presented. The network is modeled using Markov birth and death process. In order to provide the required Grade of Service for LTE-based public safety users, the minimum number of channels required for different levels of users' priority is calculated. The results for some performance metrics such as throughput, delay probability, and channel utilization are obtained. The results obtained from the simulation is compared with the existing network model such as Erlang C. Results show that the existing network model show similarities and differences in predicting the channel estimation of the deployed LTE networks for public safety communications. The results can help the network designer in the proper dimensioning of LTE-based public safety network.