The Maximum Likelihood Estimation(MLE)method is an established statistical method to estimate unknown parameters of a distribution.A disadvantage of the MLE method is that it requires an analytically tractable density...The Maximum Likelihood Estimation(MLE)method is an established statistical method to estimate unknown parameters of a distribution.A disadvantage of the MLE method is that it requires an analytically tractable density,which is not available in many cases.This is the case,for example,with applications in service systems,since waiting models from queueing theory typically have no closed-form solution for the underlying density.This problem is addressed in this paper.MLE is used in combination with Stochastic Approximation(SA)to calibrate the arrival parameterθof a G/G/1 queue via waiting time data.Three different numerical examples illustrate the application of the proposed estimator.Data sets of an M/G/1 queue,G/M/1 queue and model mismatch are considered.In a model mismatch,a mismatch is present between the used data and the postulated queuing model.The results indicate that the estimator is versatile and can be applied in many different scenarios.展开更多
In this study,we consider the problem of node ranking in a random network.A Markov chain is defined for the network,and its transition probability matrix is unknown but can be learned by sampling random interactions a...In this study,we consider the problem of node ranking in a random network.A Markov chain is defined for the network,and its transition probability matrix is unknown but can be learned by sampling random interactions among nodes.Our objective is to decompose the Markov chain into several ergodic classes and select the best node in each ergodic class.We propose a dynamic sampling procedure,which gives a probability guarantee on correct decomposition and maximizes a weighted probability of correct selection of the best node in each ergodic class.Numerical experiment results demonstrate the efficiency of the proposed sampling procedure.展开更多
文摘The Maximum Likelihood Estimation(MLE)method is an established statistical method to estimate unknown parameters of a distribution.A disadvantage of the MLE method is that it requires an analytically tractable density,which is not available in many cases.This is the case,for example,with applications in service systems,since waiting models from queueing theory typically have no closed-form solution for the underlying density.This problem is addressed in this paper.MLE is used in combination with Stochastic Approximation(SA)to calibrate the arrival parameterθof a G/G/1 queue via waiting time data.Three different numerical examples illustrate the application of the proposed estimator.Data sets of an M/G/1 queue,G/M/1 queue and model mismatch are considered.In a model mismatch,a mismatch is present between the used data and the postulated queuing model.The results indicate that the estimator is versatile and can be applied in many different scenarios.
基金This work was supported in part by the National Natural Science Foundation of China(Grants No.72022001,92146003,71901003).
文摘In this study,we consider the problem of node ranking in a random network.A Markov chain is defined for the network,and its transition probability matrix is unknown but can be learned by sampling random interactions among nodes.Our objective is to decompose the Markov chain into several ergodic classes and select the best node in each ergodic class.We propose a dynamic sampling procedure,which gives a probability guarantee on correct decomposition and maximizes a weighted probability of correct selection of the best node in each ergodic class.Numerical experiment results demonstrate the efficiency of the proposed sampling procedure.
