we consider an m/g/1 queue with regular and optional phase vacation and withstate dependent arrival rate. the vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of k -phases, each phase is generally distributed. here the first phase is compulsory where as the other phases are optional. for this model the supplementary var...

The notion of generating functions of Poisson structures was first studied in [2]. They are special functions which induce, on open subsets of R, a Poisson structure together with the local symplectic groupoid integrating it. A universal generating function was provided in terms of a formal power series coming from Kontsevich star product. The present article proves that this universal generati...

As an important tool for performance assessment in multi-state systems, the universal generating function approach is introduced and developed aiming at strength reliability analysis of structural systems. Static reliability models of statically determinate and statically indeterminate systems are built by constructing special generating functions, which are used to describe probability distrib...

Abstract: In this paper a non-repairable multi-state system with imprecise probabilities and performance rates are taken, representing imprecise probabilities by interval valued probabilities. These intervals are evaluated by computing bound of interval valued ordinary differential equation of the system. For imprecise performance rates random fuzzy variables are introduced. The proposed method...

in this paper, we propose and study exp-kumaraswamy distribution. some of its properties  are derived, including the density function, hazard rate function, quantile function, moments,  skewness  and kurtosis.   adata set isused to illustrate an application of the proposed distribution. also, we obtain a new distribution by transformation onexp-kumaraswamy distribution.   new distribution is an...