In this paper ,we discuss the Geom/G/1 queue with Bernoulli feedback and server setup/closedown times.We derive the probability generating function (PGF) of the steady-state queue length immediately after a service completion by the embedded Markov chain and the PGF of the queue length immediately after an arbitrary slot boundary .We also get the PGF of the stationary waiting times under first ...

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...

This manuscript deals with a parameter estimation of non-negative integer-valued (NNIV) time series based on the so-called probability generating function (PGF) method. The theoretical background PGF technique for very general, stationary class NNIV is described, as well asymptotic properties obtained estimates. After that, particular emphasis given to estimators independent identical distribut...

A unified treatment is presented here of compounding with the bivariate Poisson distribution. Exploiting the exponential nature of its probability generating function, it is shown that the pgf of the compound distribution is the moment generating function of the compounding random variable. This relationship leads to rather interesting general results. Particularly, the development of the condi...

We associate with a Bienaymé-Galton-Watson branching process a family tree rooted at the ancestor. For a positive integer N , define a complete N -ary tree to be the family tree of a deterministic branching process with offspring generating function s . We study the random variables VN,n and VN counting the number of disjoint complete N -ary subtrees, rooted at the ancestor, and having height n...

Abstract This paper is concerned with the analysis of an infinite-capacity batch arrival multi-server queueing system Bernoulli feedback, synchronous multiple and single working vacation policies, waiting servers, reneging retention reneged customers. The steady-state solution obtained by using probability generating function (PGF). In addition, important performance measures are derived. Then,...

We study a batch arrival M/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtain...

The principle of the procedure to go from (4) to (5) is explained in the paper. The function S(z) given by (4) is a probability generating function (of the system contents of an output buffer during an arbitrary slot). Probability generating functions (pgf’s) have the property that they are analytic inside the unit disc, i.e. for {z : |z|6 1}. Among other things, this means that a pgf cannot ha...

To accurately estimate the service delay behavior of IEEE 802.11 networks, this paper comprehensively considers four main factors that affect performance networks and establishes a model with statistical characteristics. We analyzed operation mechanism DCF, using backoff stage counter to portray dynamic change characteristics system regarding data frame transmission states. Afterward, we calcul...