arXiv subjects
Publications and source records attributed to Tewfik Kernane.
We consider a single server retrial queue with the server subject to interruptions and classical retrial policy for the access from the orbit to the server. We analyze the equilibrium distribution of the system and obtain the generating functions of the limiting distribution.
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which requires differentiation unlike the fixed point iteration which is also easier to implement. Graphical approaches are also usually proposed in the literature. We prove that these reduce in fact to the fixed point solution proposed in this paper.
We propose a new approach for estimating the parameters of a probability distribution. It consists on combining two new methods of estimation. The first is based on the definition of a new distance measuring the difference between variations of two distributions on a finite number of points from their support and on using this measure for estimation purposes by the method of minimum distance. For the second method, given an empirical discrete distribution, we build up an auxiliary discrete theoretical distribution having the same support of the first and depending on the same parameters of the parent distribution of the data from which the empirical distribution emanated. We estimate then the parameters from the empirical distribution by the usual statistical methods. In practice, we propose to compute the two estimations, the second based on maximum likelihood principle of known theoretical properties, and the first being as a control of the effectiveness of the obtained estimation, and for which we prove the convergence in probability, so we have also a criterion on the quality of the information contained in the observations. We apply the approach to truncated or grouped and censored data situations to give the flavour on the effectiveness of the approach. We give also some interesting perspectives of the approach including model selection from truncated data, estimation of the initial trial value in the celebrate EM algorithm in the case of truncation and merged normal populations, a test of goodness of fit based on the new distance, quality of estimations and data.
We introduce a new distance and we use it to parameter estimation purposes. We observe how it operates and we use in its place the usual methods of estimation which we call the methods of the new approach. We realize that we obtain a discretization of the continuous case. Moreover, when it is necessary to consider truncated data nothing is changed in computations.
We study the stability of single server retrial queues under general distribution for retrial times and stationary ergodic service times, for three main retrial policies studied in the literature: classical linear, constant and control policies. The approach used is the renovating events approach to obtain sufficient stability conditions by strong coupling convergence of the process modeling the dynamics of the system to a unique stationary ergodic regime. We also obtain instability conditions by convergence in distribution to improper limiting sequences.