Discrete-Time Queueing System With Negative Customers

Discrete-Time Queueing System with Negative customers,G-Queues has been a repaid increase in the literature. Discrete-Time Queueing models was widely used in the slot system such as slotted Aloha and ATM in B-ISDN.Negative customers are used as a control mechanism in many telecommunication and computer networks.Negative arrivals have been interpreted as inhibitor and synchronization signals .so the existence of negative customers provides a mechanism to control an excessive congestion congestion at the system.Typical killing strategies are RCH:removal of customer at the head;RCE:removal of customer at the end;DST:removal all customers in the system;In this paper we consider three Queueing systems.that is:[1]A Discrete-Time Geo/Geo/1/∞G-queue with unreliable server. This model we analysis a discrete-time single-server ,we consider both the cases where negative customers remove positive customers from the head of the queue and ,the end of the queue.[2]On the Geo/Geo/1 Retrial G-Queue with Late and Early Arrivals .This model we consider EAS and LAS ,and we give the compare of the two models.[3]A Discrete-Time Retrial Queue with Negative Arrivals and Server Failures .In this model,it is shown that,in the limiting case,the relations developed here tend to the continuous-time counterpart.In each model,we analysis the Markov chain underling the queueing system and obtain its ergodicity condition .we present some performance measures of the system in steady-steady,the effect of negative customers on the system.Finally,some numerical examples show the influence of the parameters on several performance characteristics.In the retrial queueing system,we give the stochastic decomposition laws and an application we give bounds for the proximity between the system size distributions of our model and the corresponding model without retrial.