Discrete-time Queues With Correlated Arrivals And Negative Customers

Discrete-time queue with correlated arrivals is an important research area in queueing theory.In discrete-time queue with correlated arrivals,arrivals of customers are not independent,but correlated.There are two parametersαandβ,defined asα= Prob[ one arrival during a slot | one arrival during previous slot],β= Prob[no arrival during a slot | no arrival during previous slot].Discrete-time queueing models are widely used in the slot system such as Aloha and ATM(Asynchronous Transfer Mode )in B-ISDN(broadband integrated services digital network ),where events can only happen at regularly spaced epochs.One of the main reasons for analysing discrete-time queues is that these systems are more appropriate than their continuous-time counterparts for modelling computer and telecommunication systems.Negative arrives have been interpreted as inhibitor and synchronization signals. So the existence of negative customers provides a mechanism to control an excessive 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 two queueing systems.The first is discrete-time queues with correlated arrivals and negative arrivals and constant service times.Negative customers remove a customer who is being served.We focus on a discrete-time singleserver queueing system with constant service times of arbitrary length,a finite storage capacity and a simple non-independent arrival model.The second is discrete-time queues with correlated arrivals and negative arrivals and generally distributed service times.Negative customers remove a customer who is being served.We focus on a discrete-time single-server queueing system with generally distributed service times of arbitrary length,a infinite storage capacity and a simple non-independent arrival model. In each model,we analysis the Markov chain underling the queueing system and obtain its ergodicity.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.