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A queueing system with an SIR-type infection 具有 SIR 型感染的排队系统
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2024-01-16 DOI: 10.1017/s0269964823000256
Claude Lefèvre, Matthieu Simon
{"title":"A queueing system with an SIR-type infection","authors":"Claude Lefèvre, Matthieu Simon","doi":"10.1017/s0269964823000256","DOIUrl":"https://doi.org/10.1017/s0269964823000256","url":null,"abstract":"<p>We consider the propagation of a stochastic SIR-type epidemic in two connected populations: a relatively small local population of interest which is surrounded by a much larger external population. External infectives can temporarily enter the small population and contribute to the spread of the infection inside this population. The rules for entry of infectives into the small population as well as their length of stay are modeled by a general Markov queueing system. Our main objective is to determine the distribution of the total number of infections within both populations. To do this, the approach we propose consists of deriving a family of martingales for the joint epidemic processes and applying classical stopping time or convergence theorems. The study then focuses on several particular cases where the external infection is described by a linear branching process and the entry of external infectives obeys certain specific rules. Some of the results obtained are illustrated by numerical examples.</p>","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139476167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Game-theoretic policy computing and simulation for blockchained buffering system via diffusion approximation 通过扩散近似实现区块链缓冲系统的博弈论策略计算与仿真
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2024-01-12 DOI: 10.1017/s026996482300027x
Wanyang Dai
{"title":"Game-theoretic policy computing and simulation for blockchained buffering system via diffusion approximation","authors":"Wanyang Dai","doi":"10.1017/s026996482300027x","DOIUrl":"https://doi.org/10.1017/s026996482300027x","url":null,"abstract":"We study 2-stage game-theoretic problem oriented 3-stage service policy computing, convolutional neural network (CNN) based algorithm design, and simulation for a blockchained buffering system with federated learning. More precisely, based on the game-theoretic problem consisting of both <jats:italic>“win-lose”</jats:italic> and <jats:italic>“win-win”</jats:italic> 2-stage competitions, we derive a 3-stage dynamical service policy via a saddle point to a zero-sum game problem and a Nash equilibrium point to a non-zero-sum game problem. This policy is concerning users-selection, dynamic pricing, and online rate resource allocation via stable digital currency for the system. The main focus is on the design and analysis of the joint 3-stage service policy for given queue/environment state dependent pricing and utility functions. The asymptotic optimality and fairness of this dynamic service policy is justified by diffusion modeling with approximation theory. A general CNN based policy computing algorithm flow chart along the line of the so-called <jats:italic>big model</jats:italic> framework is presented. Simulation case studies are conducted for the system with three users, where only two of the three users can be selected into the service by a zero-sum dual cost game competition policy at a time point. Then, the selected two users get into service and share the system rate service resource through a non-zero-sum dual cost game competition policy. Applications of our policy in the future blockchain based Internet (e.g., metaverse and web3.0) and supply chain finance are also briefly illustrated.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139464797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Equilibrium analysis of the fluid model with two types of parallel customers and incomplete fault 具有两种并行客户和不完全故障的流体模型的平衡分析
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2024-01-12 DOI: 10.1017/s0269964823000244
Yitong Zhang, Xiuli Xu, Pei Zhao, Mingxin Liu
{"title":"Equilibrium analysis of the fluid model with two types of parallel customers and incomplete fault","authors":"Yitong Zhang, Xiuli Xu, Pei Zhao, Mingxin Liu","doi":"10.1017/s0269964823000244","DOIUrl":"https://doi.org/10.1017/s0269964823000244","url":null,"abstract":"This article considers the individual equilibrium behavior and socially optimal strategy in a fluid queue with two types of parallel customers and incomplete fault. Assume that the working state and the incomplete fault state appear alternately in the buffer. Different from the linear revenue and expenditure structure, an exponential utility function can be constructed to obtain the equilibrium balking thresholds in the fully observable case. Besides, the steady-state probability distribution and the corresponding expected social benefit are derived based on the renewal process and the standard theory of linear ordinary differential equations. Furthermore, a reasonable entrance fee strategy is discussed under the condition that the fluid accepts the globally optimal strategies. Finally, the effects of the diverse system parameters on the entrance fee and the expected social benefit are explicitly illustrated by numerical comparisons.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139464975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the dynamic residual measure of inaccuracy based on extropy in order statistics 基于订单统计外熵的不准确性动态残差测量
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2024-01-11 DOI: 10.1017/s0269964823000268
M. Mohammadi, M. Hashempour, O. Kamari
{"title":"On the dynamic residual measure of inaccuracy based on extropy in order statistics","authors":"M. Mohammadi, M. Hashempour, O. Kamari","doi":"10.1017/s0269964823000268","DOIUrl":"https://doi.org/10.1017/s0269964823000268","url":null,"abstract":"<p>In this paper, we introduce a novel way to quantify the remaining inaccuracy of order statistics by utilizing the concept of extropy. We explore various properties and characteristics of this new measure. Additionally, we expand the notion of inaccuracy for ordered random variables to a dynamic version and demonstrate that this dynamic information measure provides a unique determination of the distribution function. Moreover, we investigate specific lifetime distributions by analyzing the residual inaccuracy of the first-order statistics. Nonparametric kernel estimation of the proposed measure is suggested. Simulation results show that the kernel estimator with bandwidth selection using the cross-validation method has the best performance. Finally, an application of the proposed measure on the model selection is provided.</p>","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139421156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shock models governed by an inverse gamma mixed Poisson process 由反伽马混合泊松过程控制的冲击模型
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2023-12-15 DOI: 10.1017/s0269964823000232
Antonella Iuliano, Barbara Martinucci, Verdiana Mustaro
{"title":"Shock models governed by an inverse gamma mixed Poisson process","authors":"Antonella Iuliano, Barbara Martinucci, Verdiana Mustaro","doi":"10.1017/s0269964823000232","DOIUrl":"https://doi.org/10.1017/s0269964823000232","url":null,"abstract":"We study three classes of shock models governed by an inverse gamma mixed Poisson process (IGMP), namely a mixed Poisson process with an inverse gamma mixing distribution. In particular, we analyze (1) the extreme shock model, (2) the <jats:italic>δ</jats:italic>-shock model, and the (3) cumulative shock model. For the latter, we assume a constant and an exponentially distributed random threshold and consider different choices for the distribution of the amount of damage caused by a single shock. For all the treated cases, we obtain the survival function, together with the expected value and the variance of the failure time. Some properties of the inverse gamma mixed Poisson process are also disclosed.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138692444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Precise large deviations for a multidimensional risk model with regression dependence structure 具有回归依赖结构的多维风险模型的精确大偏差
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2023-12-01 DOI: 10.1017/s0269964823000220
Yang Liu, Ke-Ang Fu, Zhenlong Chen
{"title":"Precise large deviations for a multidimensional risk model with regression dependence structure","authors":"Yang Liu, Ke-Ang Fu, Zhenlong Chen","doi":"10.1017/s0269964823000220","DOIUrl":"https://doi.org/10.1017/s0269964823000220","url":null,"abstract":"In this paper, we consider a nonstandard multidimensional risk model, in which the claim sizes <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0269964823000220_inline1.png\" /> <jats:tex-math>${vec{X}_k, kge 1}$</jats:tex-math> </jats:alternatives> </jats:inline-formula> form an independent and identically distributed random vector sequence with dependent components. By assuming that there exists the regression dependence structure between inter-arrival time and the claim-size vectors, we extend the regression dependence to a more practical multidimensional risk model. For the univariate marginal distributions of claim vectors with consistently varying tails, we obtain the precise large deviation formulas for the multidimensional risk model with the regression size-dependent structure.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a retrial queue with negative customers, passive breakdown, and delayed repairs 在有负面客户、被动故障和延迟维修的重审队列上
3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2023-10-20 DOI: 10.1017/s0269964823000219
Yunna Han, Ruiling Tian, Xinyu Wu, Liuqing He
{"title":"On a retrial queue with negative customers, passive breakdown, and delayed repairs","authors":"Yunna Han, Ruiling Tian, Xinyu Wu, Liuqing He","doi":"10.1017/s0269964823000219","DOIUrl":"https://doi.org/10.1017/s0269964823000219","url":null,"abstract":"Abstract This paper studies an M/M/1 retrial queue with negative customers, passive breakdown, and delayed repairs. Assume that the breakdown behavior of the server during idle periods is different from that during busy periods. Passive breakdowns may occur when the server is idle, due to the lack of monitoring of the server during idle periods. When the passive breakdown occurs, the server does not get repaired immediately and enters a delayed repair phase. Negative customers arrive during the busy period, which will cause the server to break down and remove the serving customers. Under steady-state conditions, we obtain explicit expressions of the probability generating functions for the steady-state distribution, together with some important performance measures for the system. In addition, we present some numerical examples to illustrate the effects of some system parameters on important performance measures and the cost function. Finally, based on the reward-cost structure, we discuss Nash equilibrium and socially optimal strategy and numerically analyze the influence of system parameters on optimal strategies and optimal social benefits.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135565467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Jensen- divergence measure 詹森散度测度
3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2023-10-19 DOI: 10.1017/s0269964823000189
Omid Kharazmi, Narayanaswamy Balakrishnan
{"title":"On Jensen- divergence measure","authors":"Omid Kharazmi, Narayanaswamy Balakrishnan","doi":"10.1017/s0269964823000189","DOIUrl":"https://doi.org/10.1017/s0269964823000189","url":null,"abstract":"Abstract The purpose of this paper is twofold. The first part is to introduce relative- $chi_{alpha}^{2}$ , Jensen- $chi_{alpha}^{2}$ and ( p , w )-Jensen- $chi_{alpha}^2$ divergence measures and then examine their properties. In addition, we also explore possible connections between these divergence measures and Jensen–Shannon entropy measure. In the second part, we introduce $(p,eta)$ -mixture model and then show it to be an optimal solution to three different optimization problems based on $chi_{alpha}^{2}$ divergence measure. We further study the relative- $chi_{alpha}^{2}$ divergence measure for escort and arithmetic mixture densities. We also provide some results associated with relative- $chi_{alpha}^{2}$ divergence measure of mixed reliability systems. Finally, to demonstrate the usefulness of the Jensen- $chi_{alpha}^{2}$ divergence measure, we apply it to a real example in image processing and present some numerical results. Our findings in this regard show that the Jensen- $chi_{alpha}^{2}$ is an effective criteria for quantifying the similarity between two images.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dependence among order statistics for time-transformed exponential models 时变指数模型阶统计量间的相关性
3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2023-10-05 DOI: 10.1017/s0269964823000190
Subhash Kochar, Fabio L. Spizzichino
{"title":"Dependence among order statistics for time-transformed exponential models","authors":"Subhash Kochar, Fabio L. Spizzichino","doi":"10.1017/s0269964823000190","DOIUrl":"https://doi.org/10.1017/s0269964823000190","url":null,"abstract":"Abstract Let $(X_{1},ldots,X_{n})$ be a random vector distributed according to a time-transformed exponential model . This is a special class of exchangeable models, which, in particular, includes multivariate distributions with Schur-constant survival functions. Let for $1leq ileq n$ , $X_{i:n}$ denote the corresponding i th-order statistic. We consider the problem of comparing the strength of dependence between any pair of X i ’s with that of the corresponding order statistics. It is in particular proved that for $m=2,ldots,n$ , the dependence of $X_{2:m}$ on $X_{1:m}$ is more than that of X 2 on X 1 according to more stochastic increasingness (positive monotone regression) order, which in turn implies that $(X_{1:m},X_{2:m})$ is more concordant than $(X_{1},X_{2})$ . It will be interesting to examine whether these results can be extended to other exchangeable models.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135481884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Structured Replacement Policies for Offshore Wind Turbines 海上风力涡轮机的结构性更换政策
3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2023-10-02 DOI: 10.1017/s0269964823000165
Morteza Soltani, Jeffrey P. Kharoufeh, Amin Khademi
{"title":"Structured Replacement Policies for Offshore Wind Turbines","authors":"Morteza Soltani, Jeffrey P. Kharoufeh, Amin Khademi","doi":"10.1017/s0269964823000165","DOIUrl":"https://doi.org/10.1017/s0269964823000165","url":null,"abstract":"Abstract We consider the problem of optimally maintaining an offshore wind farm in which major components progressively degrade over time due to normal usage and exposure to a randomly varying environment. The turbines exhibit both economic and stochastic dependence due to shared maintenance setup costs and their common environment. Our aim is to identify optimal replacement policies that minimize the expected total discounted setup, replacement, and lost power production costs over an infinite horizon. The problem is formulated using a Markov decision process (MDP) model from which we establish monotonicity of the cost function jointly in the degradation level and environment state and characterize the structure of the optimal replacement policy. For the special case of a two-turbine farm, we prove that the replacement threshold of one turbine depends not only on its own state of degradation but also on the state of degradation of the other turbine in the farm. This result yields a complete characterization of the replacement policy of both turbines by a monotone curve. The policies characterized herein can be used to optimally prescribe timely replacements of major components and suggest when it is most beneficial to share costly maintenance resources.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135895606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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