The present investigation deals with the bulk arrival M/G/1 retrial queue with impatient customers and modified vacation policy. The incoming customers join the virtual pool of customers called orbit if they find the server being busy, on vacation or in broken down state otherwise the service of the customer at the head of the batch is started by the server. The service is provided in k</em...

The purpose of this study is to analyze the behavior some industrial systems in light cost-free warranty policy. According policy, we assume that repairman not always present system. When active unit fails, will be called visit system; however, administrative procedures may delay for time. Once on system, first inspects whether fault caused by user or and it repairable not. product laws, carrie...

This paper presents the analysis of a renewal input  finite buffer queue wherein the customers can decide either to  join the queue with a probability or balk. The service process is Markovian service process ($MSP$) governed  by an underlying $m$-state Markov chain. Employing the supplementary  variable and imbedded Markov chain techniques,   the steady-state system length distributions at pre...

We revisit the ladder operators for orthogonal polynomials and re-interpret two supplementary conditions as compatibility conditions of two linear over-determined systems; one involves the variation of the polynomials with respect to the variable z (spectral parameter) and the other a recurrence relation in n (the lattice variable). For the Jacobi weight w(x) = (1− x)(1 + x) , x ∈ [−1, 1], we s...

‎in this article‎, we use a finite difference technique‎ ‎to solve variable-order fractional integro-differential equations‎ ‎(vofides‎, ‎for short)‎. ‎in these equations‎, ‎the variable-order fractional integration(vofi) and‎ ‎variable-order fractional derivative (vofd) are described in the‎ ‎riemann-liouville's and caputo's sense,respectively‎. ‎numerical experiments‎, ‎consisting of two exam...

The present investigation deals with performance analysis of single server preemptive priority retrial queue with immediate Bernoulli feedback. There are two types of customers are considered, which are priority customers and ordinary customers. The priority customers do not form any queue and have an exclusive preemptive priority to receive their services over ordinary customers. After complet...

In this paper, we discuss a deteriorating system with one repairman. In this system, it is assumed that the component cannot be repaired ”as good as new” after failures and the repairman takes a delayed vacation, the repair time is taken into account. Under these assumptions, we derive a model of partial differential equations by using the geometric process and supplementary variable technique....

Two different system configurations with warm standby components, standby switching failures, two types of failures "common cause failure and hardware failure" and general repair are compared based on the availability. The time-tofailure for each of the primary and warm standby components are assumed to follow the exponential distribution. Laplace transforms of state probability equations are d...