负顾客排队模型由于其灵活模拟各种复杂随机现象的广阔的应用前景,当前正越来越受到各类高性能通讯网络研究多方面的广泛关注.由于负顾客的抵消作用这类系统可以容许在顾客到达率大于服务率的情况下,进入平稳状态.本文用马尔可夫更新理论和Foster负偏移准则,研究了两类M/G1/1负顾客排队模型进入平稳状态的充要条件,首次得到了负顾客更新到达情况下,带负顾客抵消队列头部正顾客和队列尾部正顾客两种策略下的M/G1/1(FCFS)系统的统计平衡条件.当负顾客到达取更新过程的特例-泊松过程时,这一结果与Harrison&Pital(1996)中所得结果完全一致.%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 & necessary conditions for two types of M/GI/1 queue with negative arrivals entering into their steady states by means of the Markov renewal theory and Foster's negative drift crierien. The stability conditions for M/GI/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 in Harrison & pital (1996) when negative arrivals are poisson streams instead of the general renewal arrivals.
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