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...

a single server queue with bernoulli vacation has been considered. in addition the admission to queue is based on a bernoulli process and the server gives two type of services. for this model the probability generating function for the number of customers in the queue at different server's state are obtained using supplementary variable technique. some performance measures are calculated. ...

this paper analyzes renewal input state dependent queue with $n$- policy wherein the server takes exactly one vacation. using the supplementary variable technique and recursive method, we derive the steady state system length distributions at various epochs. various performance measures has been presented. finally, some numerical  computations in the form of graphs are presented to show the par...

this paper presents a discrete-time single-server finite buffer n threshold policy queue with renewal input and discretemarkovian service process. the server terminates service whenever the system becomes empty, and recommencesservice as soon as the number of waiting customers in the queue is n. we obtain the system-length distributionsat pre-arrival and arbitrary epochs using the supplementary...

We present a paradigm for developing thermodynamical consistent numerical algorithms thermodynamically partial differential equation (TCPDE) systems, called the supplementary variable method (SVM). add proper number of variables to TCPDE system coupled with its energy and other deduced equations through perturbations arrive at consistent, well-determined, solvable structurally stable system. Th...

Keywords: Supplementary variable technique Chapman–Kolmogorov Variable failure and repair rates Lagrange's method Runge–Kutta fourth order a b s t r a c t The purpose of this paper is to compute reliability of Polytube manufacturing plant having four units using supplementary variable technique. The failure and repair rates of the subsystems are variable. The mathematical equations are derived ...

This paper presents a low-complexity variable step-size control for acoustic echo cancellation filters. The proposed control method is based on two supplementary adaptive filters with low memory length. The first supplementary filter is used to control the double-talk situations while the second supplementary filter is employed to detect variations of the echo-path impulse response. The variabl...