Analysis on stability conditions for M/G/1 queueing models with negative arrivals

Recently queueing models with negative customers have been more and more brought to a widespread notice in the research field for various communication networks of high performance, due to their broad applying prospect to simulate many complicated stochastic phenomena with flexibility. Rely on the removal function of the negative customers such queueing system may enter its equilibrium state even when the ordinary arriving rate is great than its service rate. In this paper we study some sufficient and necessary conditions for two types of M/G/1 queue with negative arrivals entering into their steady states by means of the Markov renewal theory and Foster's negative drift criterion. The stability conditions for M/G/1 FCFS (First Come First Serve) system with negative renewal arrivals and killing strategy: RCH (Removal of Customer at the Head) and RCE (Removal of Customer at the End) are derived at the first time respectively. It is interesting that the results are evidently coincided with the known results of Harrison and Pital when negative arrivals are Poisson streams instead of the general renewal arrivals.