We study the queue length performance in non-exhaustive asymmetric polling systems with Bernoulli feedback. We obtain the PGF (Probability Generating Functions) and the mean values of the queue lengths, For the gated polling model, we define two new service policies: departure-gated policy and service-gated policy, and we demonstrate their difference in queueing performance. In an asymmetric sy...

This paper treats a discrete-time batch arrival queue with single working vacation. The main purpose of this paper is to present a performance analysis of this system by using the supplementary variable technique. For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. Next, we present the stationary distributions of the system len...

We study Polling Systems (POLS) with both positive and negative customers, a direction not yet pursued in the literature on POLS. We analyze the Gated, Exhaustive and Globally-Gated service regimes and derive expressions for the Probability Generating Functions (PGFs) of the system’s states and for the Laplace-Stieltjes Transforms of the waiting times. Since the transforms depend on an unknown ...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

Asymptotic residue expansions are proposed for inverting probability generating functions (PGFs) and approximating their associated mass survival functions. The useful in the wide range of stochastic model applications which a PGF admits poles its analytic continuation. error such an expansion is contour integral continuation saddlepoint approximations developed errors using method steepest des...

every digital transmission system requires frame alignment. it is necessary to identify the varius signal componets and to bring receiver into phase with respect to the transmission format so that the digits can be properly assembled for demultiplexing. fast and reliable frame alignmant is important, and therefore has been a subject for study. this paper a comprehensive analysis of frame alignm...

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. Some ...