Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other ...Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.展开更多
A method is proposed to calculate the railway transport capacity in an emergency to support the dispatching work of control centers.The effect of an emergency on section transport capacity is analyzed and the basic me...A method is proposed to calculate the railway transport capacity in an emergency to support the dispatching work of control centers.The effect of an emergency on section transport capacity is analyzed and the basic method to calculate the transport capacity is presented.The results show that the situation-changing process in emergency is actually a Markov process.The calculation rule is presented based on division of the time segment during which the emergency lasts.The algorithm is designed to calculate the transport capacity of each time segment.The pessimistic strategy and the fuzzy strategy are proposed to determine the computing value of the transport capacity of each time segment,to satisfy the calculating requirements in different occasions.Our study shows that the method is reasonable and practical and the method can be embedded in the train dispatching system to support the operation work in an emergency.展开更多
We provide the derivation of a new formula for the approximation of an integral Markov process arising in the approximation of stochastic differential equations. This formula extends an existing formula derived in <...We provide the derivation of a new formula for the approximation of an integral Markov process arising in the approximation of stochastic differential equations. This formula extends an existing formula derived in <a href="#ref1">[1]</a>. We have shown numerically that the leading order approximation of the differential equation with noise by solving an associated averaged problem and estimating the difference between them and the result is illustrated through some examples.展开更多
The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process ...The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained: the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent incre- ments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given.展开更多
In order to solve the problem the existing vertical handoff algorithms of vehicle heterogeneous wireless network do not consider the diversification of network's status, an optimized vertical handoff algorithm bas...In order to solve the problem the existing vertical handoff algorithms of vehicle heterogeneous wireless network do not consider the diversification of network's status, an optimized vertical handoff algorithm based on markov process is proposed and discussed in this paper. This algorithm takes into account that the status transformation of available network will affect the quality of service(Qo S) of vehicle terminal's communication service. Firstly, Markov process is used to predict the transformation of wireless network's status after the decision via transition probability. Then the weights of evaluating parameters will be determined by fuzzy logic method. Finally, by comparing the total incomes of each wireless network, including handoff decision incomes, handoff execution incomes and communication service incomes after handoff, the optimal network to handoff will be selected. Simulation results show that: the algorithm proposed, compared to the existing algorithm, is able to receive a higher level of load balancing and effectively improves the average blocking rate, packet loss rate and ping-pang effect.展开更多
The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average d...The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems, assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.展开更多
Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augme...Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.展开更多
The authors investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, ∞) and increasing path.
By using Lamperti's bijection between self-similar Markov processes and Levy processes,we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in...By using Lamperti's bijection between self-similar Markov processes and Levy processes,we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in(0,∞).We also investigate the behavior of the process when it crosses a level.A limit theorem concerning the distribution of the process immediately before it crosses some level is proved.Some useful examples are given.展开更多
This article concerns a class of Ornstein-Uhlenbeck type Markov processes and for which the level sets will be approached. By constructing a new class f processes,we shall obtain an inequality on the Hausdorff dimensi...This article concerns a class of Ornstein-Uhlenbeck type Markov processes and for which the level sets will be approached. By constructing a new class f processes,we shall obtain an inequality on the Hausdorff dimensions of the level sets for the Ornstein-Uhlenbeck type Markov processes. Based on this result, we finally verify that any two independent O-U.M.P with α-stable processes could collide with probability one.展开更多
Water distribution and gas supply systems are among the infrastructure systems that have many buried steel pipelines. Corrosion gradually appears inside and outside of the pipe walls over the service life of these pip...Water distribution and gas supply systems are among the infrastructure systems that have many buried steel pipelines. Corrosion gradually appears inside and outside of the pipe walls over the service life of these pipelines, the corrosion is primarily caused by the surrounding soil and the materials that flow through the pipelines. However, due to the uncertainty of the characteristics of the soil and materials, the size of the corrosion region is a stochastic variable. In this paper, using a homogeneous Markov process, a model is presented to simulate the occurrence of corrosion. Then, in combinations with a linear corrosion development model, the probability density function of the pipeline area corrosion percentage is derived. Based on the corrosion model, the pipeline seismic displacements and stresses are predicted. Furthermore, using the random perturbation approach, the mean and variance of the pipeline seismic response are given. To illustrate the validity of the proposed approach, a 200-meter long pipeline is numerically investigated and its random seismic response is obtained.展开更多
This paper investigates the feedback control of hidden Markov process(HMP) in the face of loss of some observation processes.The control action facilitates or impedes some particular transitions from an inferred curre...This paper investigates the feedback control of hidden Markov process(HMP) in the face of loss of some observation processes.The control action facilitates or impedes some particular transitions from an inferred current state in the attempt to maximize the probability that the HMP is driven to a desirable absorbing state.This control problem is motivated by the need for judicious resource allocation to win an air operation involving two opposing forces.The effectiveness of a receding horizon control scheme based on the inferred discrete state is examined.Tolerance to loss of sensors that help determine the state of the air operation is achieved through a decentralized scheme that estimates a continuous state from measurements of linear models with additive noise.The discrete state of the HMP is identified using three well-known detection schemes.The sub-optimal control policy based on the detected state is implemented on-line in a closed-loop,where the air operation is simulated as a stochastic process with SimEvents,and the measurement process is simulated for a range of single sensor loss rates.展开更多
In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/...In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/G/1 queue again. Through establishing and solving the density evolution equa tions, the busy-period distribution, and the stationary distributions of waitin g time and queue length were obtained. In addition, the stability condition of th is queue system was given by means of an imbedded renewal process.展开更多
To ensure the correctness of train control system design and development,the ways of simulation,test and formalization were compared.According to the safe critical attribute of train control system,the characters rela...To ensure the correctness of train control system design and development,the ways of simulation,test and formalization were compared.According to the safe critical attribute of train control system,the characters related to system safety were propounded such as real time,hybrid,distribution(concurrence)and reactivity,and the specific formal methods associated with every character were introduced in details.The analysis and classification of the methods were done based on their mathematical basis and applications,and their advantages and disadvantages were given.Analysis result indicates that every method has determinate limitations,which is determined by the essences of model checking and theory proving.It is pointed out that the presentation of new method,the expansion of existing methods and the integration of many methods will be the development trend of formalization in train control system.展开更多
A variational formula for the asymptotic variance of general Markov processes is obtained.As application,we get an upper bound of the mean exit time of reversible Markov processes,and some comparison theorems between ...A variational formula for the asymptotic variance of general Markov processes is obtained.As application,we get an upper bound of the mean exit time of reversible Markov processes,and some comparison theorems between the reversible and non-reversible diffusion processes.展开更多
In this paper,we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting.We first describe a more ...In this paper,we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting.We first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive mechanism.Then we establish a pyramid Markov process and show that it is irreducible and positive recurrent,and its stationary probability vector is matrix-geometric with an explicitly representable rate matrix.Also,we use the stationary probability vector to study the influence of orphan blocks on the waste of computing resource.Next,we set up a pyramid Markov reward process to investigate the long-run average mining profits of the honest and dishonest mining pools,respectively.As a by-product,we build one-dimensional Markov reward processes and provide some new interesting interpretation on the Markov chain and the revenue analysis reported in the seminal work by Eyal and Sirer(2014).Note that the pyramid Markov(reward)processes can open up a new avenue in the study of blockchain selfish mining.Thus we hope that the methodology and results developed in this paper shed light on the blockchain selfish mining such that a series of promising research can be developed potentially.展开更多
We investigate Hoeffding's inequality for both discrete-time Markov chains and continuous-time Markov processes on a general state space. Our results relax the usual aperiodicity restriction in the literature, and...We investigate Hoeffding's inequality for both discrete-time Markov chains and continuous-time Markov processes on a general state space. Our results relax the usual aperiodicity restriction in the literature, and the explicit upper bounds in the inequalities are obtained via the solution of Poisson's equation. The results are further illustrated with applications to queueing theory and reective diffusion processes.展开更多
The goal of this paper is threefold. First, we survey the existing results on Hunt’s hypothesis(H) for Markov processes and Getoor’s conjecture for Lévy processes. Second, we investigate(H)for multidimensional ...The goal of this paper is threefold. First, we survey the existing results on Hunt’s hypothesis(H) for Markov processes and Getoor’s conjecture for Lévy processes. Second, we investigate(H)for multidimensional Lévy processes from the viewpoint of projections. Third, we present a few open questions for further study.展开更多
In Wireless Sensor Network(WSN),energy and packet forwarding tendencies of sensor nodes plays a potential role in ensuring a maximum degree of co-operation under data delivery.This quantified level of co-operation sig...In Wireless Sensor Network(WSN),energy and packet forwarding tendencies of sensor nodes plays a potential role in ensuring a maximum degree of co-operation under data delivery.This quantified level of co-operation signifies the performance of the network in terms of increased throughput,packet delivery rate and decreased delay depending on the data being aggregated and level of control overhead.The performance of a sensor network is highly inclined by the selfish behaving nature of sensor nodes that gets revealed when the residual energy ranges below a bearable level of activeness in packet forwarding.The selfish sensor node needs to be identified in future through reliable forecasting mechanism for improving the lifetime and packet delivery rate.Semi Markov Process Inspired Selfish aware Co-operative Scheme(SMPISCS)is propounded for making an attempt to mitigate selfish nodes for prolonging the lifetime of the network and balancing energy consumptions of the network.SMPISCS model provides a kind of sensor node’s behavior for quantifying and future forecasting the probability with which the node could turn into selfish.Simulation experiments are carried out through Network Simulator 2 and the performance are analyzed based on varying the number of selfish sensor nodes,number of sensor nodes and range of detection threshold.展开更多
文摘Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.
基金Supported by the State Key Laboratory of Rail Traffic Control and Safety (RCS2011K004)Beijing Jiaotong University,Fundamental Research Funds of Gansu Province (620030)+1 种基金the National Natural Science Foundation of China(61074151)Project of Research and Development on Train Control Center Operation Expressing System of TubeRail(306086)
文摘A method is proposed to calculate the railway transport capacity in an emergency to support the dispatching work of control centers.The effect of an emergency on section transport capacity is analyzed and the basic method to calculate the transport capacity is presented.The results show that the situation-changing process in emergency is actually a Markov process.The calculation rule is presented based on division of the time segment during which the emergency lasts.The algorithm is designed to calculate the transport capacity of each time segment.The pessimistic strategy and the fuzzy strategy are proposed to determine the computing value of the transport capacity of each time segment,to satisfy the calculating requirements in different occasions.Our study shows that the method is reasonable and practical and the method can be embedded in the train dispatching system to support the operation work in an emergency.
文摘We provide the derivation of a new formula for the approximation of an integral Markov process arising in the approximation of stochastic differential equations. This formula extends an existing formula derived in <a href="#ref1">[1]</a>. We have shown numerically that the leading order approximation of the differential equation with noise by solving an associated averaged problem and estimating the difference between them and the result is illustrated through some examples.
基金Supported by the National Natural Science Foundation of China (10671197)
文摘The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained: the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent incre- ments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given.
基金supported in part by the National Natural Science Foundation of China under grant No. 61271259, No. 61301123, No. 61471076Scientific and Technological Research Program of Chongqing Municipal Education Commission of Chongqing of China under Grant No.KJ130536
文摘In order to solve the problem the existing vertical handoff algorithms of vehicle heterogeneous wireless network do not consider the diversification of network's status, an optimized vertical handoff algorithm based on markov process is proposed and discussed in this paper. This algorithm takes into account that the status transformation of available network will affect the quality of service(Qo S) of vehicle terminal's communication service. Firstly, Markov process is used to predict the transformation of wireless network's status after the decision via transition probability. Then the weights of evaluating parameters will be determined by fuzzy logic method. Finally, by comparing the total incomes of each wireless network, including handoff decision incomes, handoff execution incomes and communication service incomes after handoff, the optimal network to handoff will be selected. Simulation results show that: the algorithm proposed, compared to the existing algorithm, is able to receive a higher level of load balancing and effectively improves the average blocking rate, packet loss rate and ping-pang effect.
基金the National Natural Science Foundation of China (60674027, 60574007)Doctoral Foundation of Education Ministry of China (20050446001).
文摘The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems, assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.
文摘Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.
基金the National Natural Science Foundation of China and the StateEducation of Commission Ph.D. Station Foundation
文摘The authors investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, ∞) and increasing path.
基金supported in part by the National Natural Science Foundation of China(1117126211171263)
文摘By using Lamperti's bijection between self-similar Markov processes and Levy processes,we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in(0,∞).We also investigate the behavior of the process when it crosses a level.A limit theorem concerning the distribution of the process immediately before it crosses some level is proved.Some useful examples are given.
文摘This article concerns a class of Ornstein-Uhlenbeck type Markov processes and for which the level sets will be approached. By constructing a new class f processes,we shall obtain an inequality on the Hausdorff dimensions of the level sets for the Ornstein-Uhlenbeck type Markov processes. Based on this result, we finally verify that any two independent O-U.M.P with α-stable processes could collide with probability one.
基金Natural Science Funds for the Innovative Research Group of China Under Grant No. 50621062
文摘Water distribution and gas supply systems are among the infrastructure systems that have many buried steel pipelines. Corrosion gradually appears inside and outside of the pipe walls over the service life of these pipelines, the corrosion is primarily caused by the surrounding soil and the materials that flow through the pipelines. However, due to the uncertainty of the characteristics of the soil and materials, the size of the corrosion region is a stochastic variable. In this paper, using a homogeneous Markov process, a model is presented to simulate the occurrence of corrosion. Then, in combinations with a linear corrosion development model, the probability density function of the pipeline area corrosion percentage is derived. Based on the corrosion model, the pipeline seismic displacements and stresses are predicted. Furthermore, using the random perturbation approach, the mean and variance of the pipeline seismic response are given. To illustrate the validity of the proposed approach, a 200-meter long pipeline is numerically investigated and its random seismic response is obtained.
文摘This paper investigates the feedback control of hidden Markov process(HMP) in the face of loss of some observation processes.The control action facilitates or impedes some particular transitions from an inferred current state in the attempt to maximize the probability that the HMP is driven to a desirable absorbing state.This control problem is motivated by the need for judicious resource allocation to win an air operation involving two opposing forces.The effectiveness of a receding horizon control scheme based on the inferred discrete state is examined.Tolerance to loss of sensors that help determine the state of the air operation is achieved through a decentralized scheme that estimates a continuous state from measurements of linear models with additive noise.The discrete state of the HMP is identified using three well-known detection schemes.The sub-optimal control policy based on the detected state is implemented on-line in a closed-loop,where the air operation is simulated as a stochastic process with SimEvents,and the measurement process is simulated for a range of single sensor loss rates.
基金Project supported by the National Natural Science Foundation of China(Grant No.70171059)
文摘In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/G/1 queue again. Through establishing and solving the density evolution equa tions, the busy-period distribution, and the stationary distributions of waitin g time and queue length were obtained. In addition, the stability condition of th is queue system was given by means of an imbedded renewal process.
基金This work is supported by Research projects of Beijing National Railway Research and Design Institute of Signal and Communication Co Ltd(No.2300-K1220007)。
文摘To ensure the correctness of train control system design and development,the ways of simulation,test and formalization were compared.According to the safe critical attribute of train control system,the characters related to system safety were propounded such as real time,hybrid,distribution(concurrence)and reactivity,and the specific formal methods associated with every character were introduced in details.The analysis and classification of the methods were done based on their mathematical basis and applications,and their advantages and disadvantages were given.Analysis result indicates that every method has determinate limitations,which is determined by the essences of model checking and theory proving.It is pointed out that the presentation of new method,the expansion of existing methods and the integration of many methods will be the development trend of formalization in train control system.
基金Supported by NSFC(Grant No.11901096)NSF-Fujian(Grant No.2020J05036)+3 种基金the Program for Probability and Statistics:Theory and Application(Grant No.IRTL1704)the Program for Innovative Research Team in Science and Technology in Fujian Province University(IRTSTFJ)the National Key R&D Program of China(2020YFA0712900,2020YFA0712901)the National Natural Science Foundation of China(Grant No.11771047)。
文摘A variational formula for the asymptotic variance of general Markov processes is obtained.As application,we get an upper bound of the mean exit time of reversible Markov processes,and some comparison theorems between the reversible and non-reversible diffusion processes.
基金This work is supported by the National Key R&D Program of China under Grant No.2020AAA0103801Quanlin Li is supported by the National Natural Science Foundation of China under Grant Nos.71671158 and 71932002+1 种基金the Beijing Social Science Foundation Research Base Project under Grant No.19JDGLA004Xiaole Wu is supported by the National Natural Science Foundation of China under Grant No.72025102.
文摘In this paper,we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting.We first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive mechanism.Then we establish a pyramid Markov process and show that it is irreducible and positive recurrent,and its stationary probability vector is matrix-geometric with an explicitly representable rate matrix.Also,we use the stationary probability vector to study the influence of orphan blocks on the waste of computing resource.Next,we set up a pyramid Markov reward process to investigate the long-run average mining profits of the honest and dishonest mining pools,respectively.As a by-product,we build one-dimensional Markov reward processes and provide some new interesting interpretation on the Markov chain and the revenue analysis reported in the seminal work by Eyal and Sirer(2014).Note that the pyramid Markov(reward)processes can open up a new avenue in the study of blockchain selfish mining.Thus we hope that the methodology and results developed in this paper shed light on the blockchain selfish mining such that a series of promising research can be developed potentially.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11971486,11771452)the Natural Science Foundation of Hunan Province(Grant Nos.2019JJ40357,2020JJ4674)the Innovation Program of Central South University(Grant No.2020zzts039).
文摘We investigate Hoeffding's inequality for both discrete-time Markov chains and continuous-time Markov processes on a general state space. Our results relax the usual aperiodicity restriction in the literature, and the explicit upper bounds in the inequalities are obtained via the solution of Poisson's equation. The results are further illustrated with applications to queueing theory and reective diffusion processes.
基金Supported by National Natural Science Foundation of China(Grant Nos.11771309 and 11871184)Natural Sciences and Engineering Research Council of Canada(Grant No.4394-2018)。
文摘The goal of this paper is threefold. First, we survey the existing results on Hunt’s hypothesis(H) for Markov processes and Getoor’s conjecture for Lévy processes. Second, we investigate(H)for multidimensional Lévy processes from the viewpoint of projections. Third, we present a few open questions for further study.
文摘In Wireless Sensor Network(WSN),energy and packet forwarding tendencies of sensor nodes plays a potential role in ensuring a maximum degree of co-operation under data delivery.This quantified level of co-operation signifies the performance of the network in terms of increased throughput,packet delivery rate and decreased delay depending on the data being aggregated and level of control overhead.The performance of a sensor network is highly inclined by the selfish behaving nature of sensor nodes that gets revealed when the residual energy ranges below a bearable level of activeness in packet forwarding.The selfish sensor node needs to be identified in future through reliable forecasting mechanism for improving the lifetime and packet delivery rate.Semi Markov Process Inspired Selfish aware Co-operative Scheme(SMPISCS)is propounded for making an attempt to mitigate selfish nodes for prolonging the lifetime of the network and balancing energy consumptions of the network.SMPISCS model provides a kind of sensor node’s behavior for quantifying and future forecasting the probability with which the node could turn into selfish.Simulation experiments are carried out through Network Simulator 2 and the performance are analyzed based on varying the number of selfish sensor nodes,number of sensor nodes and range of detection threshold.
