Non-homogeneous Poisson Research Articles

A spline function method for modelling and generating a nonhomogeneous poisson process

ABSTRACT This paper presents a spline-based input modelling method for inferring the rate function of a nonhomogeneous Poisson process (NHPP) given arrival-time observations and a simple method for generating arrivals from the resulting rate function. Splines are a natural choice for modelling rate functions as they are smooth by construction, and highly flexible. Although flexibility is an advantage in terms of reducing the bias with respect to the true rate function, it can lead to overfitting. Our method is therefore based on maximising the penalised NHPP log-likelihood, where the penalty is a measure of rapid changes in the spline-based representation. A controlled empirical comparison of the spline-based method against two recently developed input modelling techniques is presented considering the recovery of the rate function, the propagation of input modelling error, and the performance of methods given data that are under or over-dispersed in comparison to a Poisson process.

Detecting clusters of transcription factors based on a nonhomogeneous poisson process model.

Rapidly growing genome-wide ChIP-seq data have provided unprecedented opportunities to explore transcription factor (TF) binding under various cellular conditions. Despite the rich resources, development of analytical methods for studying the interaction among TFs in gene regulation still lags behind. In order to address cooperative TF binding and detect TF clusters with coordinative functions, we have developed novel computational methods based on clustering the sample paths of nonhomogeneous Poisson processes. Simulation studies demonstrated the capability of these methods to accurately detect TF clusters and uncover the hierarchy of TF interactions. A further application to the multiple-TF ChIP-seq data in mouse embryonic stem cells(ESCs) showed that our methods identified the cluster of core ESC regulators reported in the literature and provided new insights on functional implications of transcrisptional regulatory modules. Effective analytical tools are essential for studying protein-DNA relations. Information derived from this research will help us better understand the orchestration of transcription factors in gene regulation processes.

Modelling of NHPP Based Software Reliability Growth Model from the Perspective of Testing Coverage, Error Propagation and Fault Withdrawal Efficiency

This paper presents a software reliability growth model framework modeled from a non-homogenous poisson process (NHPP). Invariably, software testing continues to be a paramount measure for validating the standard of software. Test coverage measures appraise and estimate the proportion and gradation of testing in software. Therefore, presenting a correct picture of the test coverage becomes a prime requisite to guarantee software reliability. As an enhancement over the existing models, the proposed model integrates testing coverage (TC), error propagation, and fault withdrawal efficiency while keeping the number of parameters restrained to make the framework more reliable for parameter estimation. A relative analysis to assess the efficacy of the proposed model and some existing models has been carried out on the failure data obtained from three real-world software applications using six comparison criteria. Finally, the weighted criteria rank method has been used to rank the models and assess their performance. In addition, sensitivity analysis has been carried out to demonstrate the effect of the parameters of the proposed model on the mean value function.

Spatiotemporal nonhomogeneous poisson model with a seasonal component applied to the analysis of extreme rainfall

This paper develops an extension of spatiotemporal models that handle count data using nonhomogeneous Poisson processes. In this new proposal, we incorporate a seasonal cycle component in the definition of the intensity function to control possible effects produced by the occurrence of the event of interest in regular periods. The seasonal cycle can cause problems in estimating the shape parameter of the Weibull and generalized Goel intensity functions. This shape parameter serves to confront the research hypothesis that seeks to identify a trend in the occurrence rate of an event of interest. In the case of the Weibull intensity function, a value significantly equal to one of the shape parameters indicates a constant rate of occurrence, less than one indicates a decreasing rate, and greater than one indicates an increasing rate. In the case of the Goel intensity function, parameter values less than or equal to one indicate a decreasing occurrence rate, and values greater than one indicate the presence of a change point. We also built a spatial model using the Musa-Okumoto intensity function as an alternative to approximate counting processes for which there is a decreasing trend in the occurrence rate of the event of interest. We estimated the parameters of the proposed method from a Bayesian perspective. Finally, we fitted the proposed model and compared it with other approximations to analyze the frequency of extreme rainfall in the northern region of the states of Maranhão and Piauí in northeastern Brazil over ten years. Among the main results, we found that (1) the proposed method has proven superior in terms of fit and prediction performance than the other models, and (2) unlike other approximations, the proposed model does not detect changes in the rate of extreme rainfall occurrences.

On the second-order excess wealth order and its properties

AbstractIn the literature, some stochastic orders have been extended to the higher orders in different scenarios. In this paper, inspired by interesting properties of the excess wealth order and its wide range application particularly in comparing the tail variability of risks, we consider the second-order excess wealth order and study its main properties. We obtain two results characterizing the proposed order. We also investigate its relationship with other well-known variability orders and criteria to compare risks. An application of the results in comparing the epoch times of two nonhomogeneous poisson processes is also given.

Nonhomogeneous poisson process model of summer high temperature extremes over China

In this study, nonhomogeneous Poisson process (NHPP) models arising from the extreme value theory have been fitted to summer high temperature extremes (HTEs) at 321 meteorological stations over China. The seasonality and six prominent atmospheric teleconnection patterns in Northern Hemisphere are incorporated in the NHPP models reflecting the non-stationarity of occurrence rate in Poisson process of HTEs. In addition, Poisson regression model has also been applied to link HTEs and these teleconnection patterns. The linkages of HTEs and teleconnection patterns have been identified in both NHPP modeling and Poisson regression. Composite maps of differences of 500-hPa geopotential height and wind fields in the positive and negative phases of teleconnection patterns are constructed to show the impacts of atmospheric circulation patterns on extreme heat events. The spatial pattern of the associated anticyclonic or cyclonic circulations with teleconnection patterns partly explains the spatial variability of the occurrences of summer HTEs over China.

Performance evaluation of a distributed energy model with compound Poisson arrivals on an improvised forked network: A detailed analysis

Performance evaluation of a distributed energy model with compound poisson arrivals on an improvised forks network discusses the usage and operations on communication networks, the utilization of these network models had changed the scenario of communication around the world. Establishment and working with these networks lead to work efficiently and effectively for various modes of communications like voice transmission and data transmission. In the current network model, we had considered and developed the network model for the arrival of packets to the network model following non-homogeneous compound poisson arrivals with a uniform distribution pattern. The current model compares with the other homogeneous arrival of packets which follow the Duane process of arrival of packets to the network. When considering energy preservation, it is possible to enhance end-user performance while simultaneously decreasing energy consumption for the mean number of packets, throughput, network node utilization, and dynamic bandwidth utilization. After Implementation of the model, it is observed that energy reservation of the network nodes had increased a lot. During high traffic, our model demonstrates that its emptiness with the comparison of the homogenous model like poisson process and duan process was more efficient with a percentage increase of 16 % and 19 % respectively for a homogeneous network, mean number of packets with a rise of 10 % and 37 %, utilization of packets with 11 % and 18 %, mean delay of packets with 16 % and 5% and throughput of the network with 47 % and 38 %. The results obtained from the equation models were derived and developed with the help of the software MATLAB and MATHCAD. Comparing our heterogeneous model with the results of the homogenous network model had enormously decreased the computational time of the network. Thus, we can clearly state that our proposed model outperformed than remaining other homogenous models.

A fluid approximation for the single-leg fare allocation problem with nonhomogeneous poisson demand

Fare allocation for legs and O&D pairs plays a crucial role in airline revenue management. Despite a large number of dynamic pricing studies, there are only a few widely adopted studies in which assumptions affect most tactical decisions with potentially large impacts on airline profitability. These decisions involve approximating future pricing schemes, allocation of fare classes, and setting booking limits. We propose a fare allocation model for a single leg in the presence of a realistic nonhomogeneous Poisson demand with an increasing rate. We aim to compute when and how to markup the price for an airfare product (switch to an upper fare class) to maximize the expected revenue. We study a fluid approximation of the underlying stochastic problem considering independent demand from each customer segment and examine different properties that lead to several important insights. Finally, we propose a dynamic look-ahead pricing scheme to compare our fluid approximation results against the well-known EMSRb heuristic and a dynamic programming solution on randomly generated booking request data. Numerical examples illustrate the effectiveness of our proposed approach.

Agricultural drought periods analysis by using nonhomogeneous poisson models and regionalization of appropriate model parameters

Precipitation has a dominant role in agriculture, and a regular rain pattern is usually vital to agriculture; excessive or inadequate rainfall can be harmful. In this paper, an agricultural drought index is utilized to study the agricultural drought periods and analyze them with their intensities at various locations. Some nonhomogeneous Poisson models are also used to calculate the probability of agricultural droughts (number of times occurred) in a time interval of interest. It is to be assumed that the number of agricultural drought event occurrences is a Nonhomogeneous Poisson Process (NHPP) has a rate function, which depends on some parameters that must be estimated. Two cases of these functions are considered: the Weibull and linear intensity function. The Bayesian approach with Gibbs sampling under the Markov Chain Monte Carlo (MCMC) algorithm is used to estimate the parameters of these functions. The most appropriate fitted model is selected by using Deviance Information Criteria (DIC) and use that appropriately fitted model to calculate the accumulated events of agricultural drought in a time interval of interest at each location. Ordinary Kriging (OK) is used to regionalize the parameters and present its spatial behavior. The results based on the DIC indicate that the Power Law Process (PLP) performs better than the linear intensity function, NHPP model. The interpolated parameter values for the appropriate model, their patterns, and fluctuations for the study area are efficiently presented using contour maps. It is a novel and straightforward approach to assess the selected model parameter values used to predict the accumulated drought events at un-sampled locations. The proposed framework might also help to analyze other spatial variables of interest and can be used for climate-change study, ecosystem modeling, etc. The findings can also help to make decisions for sustainable environmental management in Pakistan.

Compound intervened poisson distribution through one server queuing model with non-homogeneous compound poisson arrivals in bulk and its service rates

Queuing models are used to determine the pragmatic approach in different fields of engineering, sciences, and allied areas. Most of these, the arrivals are dependent on time and would be described by a Poisson process which is non-homogeneous. In this research paper, a one-server queuing model with model with non-homogeneity compound Poisson bulk arrivals has been studied with Compound Intervention Poisson distribution (CIPD). It is observed that the system performance measures are highly influenced by non-homogeneous bulk arrivals rate and batch size distribution parameters. Simulated studies presented that the intervened and compound intervened parameter increases the service rate in terms of utilization, the mean number of customer who undertakes service and emptiness pattern in the queue. Sensitivity analysis has been carried out for the developed model. Non-Homogeneous Poisson process, bulk arrivals, state dependent service rates, Compound Intervened Poisson distribution

Research on the software reliability quantitative evaluation of nuclear power plant digital control system based on non-homogeneous poisson process model

With the application of digital technology, the software used in various systems has become increasingly important, as well as complex. This increase in complexity and scale has led to an increase in the probability of software failure. Quantitative reliability evaluation of the digital instrumentation and control system software used in nuclear power plants represent a significant challenge. This study uses a non-homogeneous Poisson process model for quantitative evaluation of the software reliability of a nuclear power plant safety digital control system (DCS), which is the research object. To analyse the research object, a software test environment is established, and the research object is tested to obtain the software failure data. The software reliability growth model, which is widely used in other industries, is combined with data on nuclear power plant DCS software defects that obey a non-homogeneous Poisson process, to construct a non-homogeneous Poisson process model. The formulas for software reliability indicators such as total failures, remaining failures, failure rate (failures per week), reliability, and time to next failure(s) are derived. The software failure data obtained from the test are used to determine the variables of the model based on maximum likelihood estimation; the estimates are then used to quantitatively evaluate software reliability-related indicators. Finally, the minimum correlation error method is used to analyse the error by comparing the actual and model prediction results. The model can evaluate the current reliability level of software and predict the impact of subsequent reliability test results. The findings from this study can provide data support for evaluating the reliability of nuclear power plant DCS software. Therefore, this study can be significant for further research on the reliability of nuclear power plant DCS software.

Thinning process algorithms for compound poisson process having nonhomogeneous poisson process (NHPP) intensity functions

One stochastic process that is often used to model real phenomena is the compound Poisson process (CPP). CPP is a process in which a component in the process of the events occurred is assumed to be a Poisson process with a certain intensity function (homogeneous or nonhomogeneous). Thinning process algorithm is usually used to generate events that occurred in the Poisson process, but not yet in CPP. This study aims to find out the algorithm to produce CPP which has the function of Poisson nonhomogeneous (NHPP) intensity, where in addition to knowing the process of events that occur, it also takes into account the extent of the consequences of these events. The value of the load caused by the Poisson process is assumed to be a family of i.i.d random variables and the variables are also independent of the Poisson process. The results of this study have obtained the thinning process algorithm and its generalizations for compound Poisson process having nonhomogeneous Poisson process (NHPP) intensity functions. This algorithm is the result of theoretical development and analysis of computational simulations that can be applied in various fields of science such as the analysis of reliability and risk models.

Research on the Behavior of the Shill Bidding with Affiliated Values

On-line auction provides convenience, as well as causes the frequent occurrence of many deceits, the passage mainly provides the concealed conditions for the seller’s shill bidding behavior based on the anonymity of on-line auction, it discusses the bidder’s optimal decision quotation when the shill bidding behavior happens or nor in the affiliated value pattern. To establish the bidder and seller’s incomplete information dynamic game model when occurring the shill bidding and analyze the probability of shill bidding can provide the reference for bidder’s quotation. To consider the time, reserved price (price accepted by the seller) and the current highest auction price which affect the shill bidding and match the relevant nonhomogeneous poisson process and exponent distribution can provide the reference for bidders to judge if the shill bidding behavior occurs by sellers.

Critical fault-detecting time evaluation in software with discrete compound Poisson models

Software developers predict their product’s failure rate using reliability growth models that are typically based on nonhomogeneous Poisson (NHP) processes. In this article, we extend that practice to a nonhomogeneous discrete-compound Poisson process that allows for multiple faults of a system at the same time point. Along with traditional reliability metrics such as average number of failures in a time interval, we propose an alternative reliability index called critical fault-detecting time in order to provide more information for software managers making software quality evaluation and critical market policy decisions. We illustrate the significant potential for improved analysis using wireless failure data as well as simulated data.

ENB Selection for Machine Type Communications Using Reinforcement Learning Based Markov Decision Process

Machine type communication (MTC), as one of the most promising technologies in the future wireless communication, has brought mobile communication network into a new level. The breakthrough of cutting-edge technology and broad coverage of cellular networks in long term evolution advanced network constitute an ideal platform for ubiquitous MTC service provisioning on a large scale. However, under the traditional attach approach, the massive MTC devices always select the evolved NodeB (eNB) with the best signal quality for the attachment, thereby causing the network congestion and overload. As a result, it is necessary to design an efficient eNB selection scheme to avoid overload issue. In this paper, by modeling MTC arrivals using nonhomogeneous poisson process with the memoryless property, we formulate the eNB selection problem as a Markov decision process (MDP) and try to compute an optimal solution. Since the network parameters for MDP are not obtained easily, a learning-based algorithm with value-difference based exploration (VDBE) policy who could leverage both present conditions and expected future demands is further proposed. The performances of the proposed reinforcement learning (RL) VDBE, other RL-based, the legacy best-signal-quality, and MDP without RL eNB-selection schemes are analyzed in terms of blocking probability, transmission rate, and load balancing. The simulation results show that our scheme has the best performance on the blocking probability and loading balancing while an acceptable result on the transmission rate. It is suitable for the MTC environment with a highly changed number of MTC arrivals while without high requirement on the transmission rate.

Maximum-Likelihood Estimation of Parameters of NHPP Software Reliability Models Using Expectation Conditional Maximization Algorithm

Since its introduction in 1977, the expectation maximization (EM) algorithm has been one of the most important and widely used estimation method in estimating parameters of distributions in the presence of incomplete information. In this paper, a variant of the EM algorithm, the expectation conditional maximization (ECM) algorithm, is introduced for the first time and it provides a promising alternative in estimating the parameters of nonhomogeneous poisson (NHPP) software reliability growth models (SRGM). This algorithm circumvents the difficult M-step of the EM algorithm by replacing it by a series of conditional maximization steps. The utility of the ECM approach is demonstrated in the estimation of parameters of several well-known models for both time domain and time interval software failure data. Numerical examples with real-data indicate that the ECM algorithm performs well in estimating parameters of NHPP SRGM with complex mean value functions and can produce a faster rate of convergence.

Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach

In a heavily congested metro line, unexpected disturbances often occur to cause the delay of the traveling passengers, infeasibility of the current timetable and reduction of the operational efficiency. Due to the uncertain and dynamic characteristics of passenger demands, the commonly used method to recover from disturbances in practice is to change the timetable and rolling stock manually based on the experiences and professional judgements. In this paper, we develop a stochastic programming model for metro train rescheduling problem in order to jointly reduce the time delay of affected passengers, their total traveling time and operational costs of trains. To capture the complexity of passenger traveling characteristics, the arriving ratio of passengers at each station is modeled as a non-homogeneous poisson distribution, in which the intensity function is treated as time-varying origin-to-destination passenger demand matrices. By considering the number of on-board passengers, the total energy usage is modeled as the difference between the tractive energy consumption and the regenerative energy. Then, we design an approximate dynamic programming based algorithm to solve the proposed model, which can obtain a high-quality solution in a short time. Finally, numerical examples with real-world data sets are implemented to verify the effectiveness and robustness of the proposed approaches.

Wireless sensor network reliability modelling based on masked data

This paper studies the reliability modelling of wireless sensor networks WSNs with the masked data that are often observed in practice. The masked data are the system failure data when exact subsystems or components causing system failures cannot be identified. When the masked data are observed, however, it is difficult to estimate the WSN reliability since the failure processes of the subnets cannot be decomposed into simple subsystem processes. In this paper, an additive non-homogeneous poisson process NHPP model is proposed to describe the failure process of the WSN with subnets. The maximum likelihood estimation MLE procedure is developed to estimate the parameters in the proposed model. By applying the given procedure, the WSN reliability estimate can be relatively easy to obtain. A numerical example based on simulation data with random masking is also provided to illustrate the applicability of the methodology.

A non-homogeneous poisson model with spatial anisotropy applied to ozone data from Mexico City

In this work we consider a non-homogenous Poisson model to study the behaviour of the number of times that a pollutant’s concentration surpasses a given threshold of interest. Spatial dependence is imposed on the parameters of the Poisson intensity function in order to account for the possible correlation between measurements in different sites. An anisotropic model is used due to the nature of the region of interest. Estimation of the parameters of the model is performed using the Bayesian point of view via Markov chain Monte Carlo (MCMC) algorithms. We also consider prediction of the days in which exceedances of the threshold might occur at sites where measurements cannot be taken. This is obtained by spatial interpolation using the information provided by the sites where measurements are available. The prediction procedure allows for estimation of the behaviour of the mean function of the non-homogeneous Poisson process associated with those sites. The models considered here are applied to ozone data obtained from the monitoring network of Mexico City.

The Lifetime Model of the One-Unit-System with Two Kinds of Wear-Out

A system at inception is endowed with a random amount of resource, the process of the lapse of system life can be viewed as that of the depletion of random resource caused by the wear-out effect. This thesis considers the wear-out process of the system as the sum of an additive compound nonhomogeneous poisson shock wear-out and a continuous routine wear-out in time t. With the introduction of the concept of random resource, a wear-out model is built. Moreover, the aging properties of the system lifetime are studied in this model.