带负顾客和非空竭服务随机休假的M^([x])/G/1可修排队系统

AN M^([X])/G/1 REPAIRABLE QUEUEING SYSTEM WITH NEGATIVE CUSTOMERS AND RANDOM VACATION ON NON-EXHAUSTIVE SERVICE

研究了带负顾客和非空竭服务随机休假的M^([X])/G/1可修排队系统.负顾客不仅仅移除一个正在接受服务的正顾客,而且还使得服务器损坏而立即进行修理.通过构造一个具有吸收态的马尔可夫链求得了系统稳态存在的充分必要条件.利用补充变量法求得了系统的排队指标和可靠性指标.最后我们还给出了一个数值实例.

This paper considers an M^[X]/G/1 queue with negative customers and random vacation on non-exhaustive service subject to the server breakdowns and repairs. Negative customers not only remove the customer being in service, but also make the server under repair. The necessary and sufficient condition for the system stability is obtained by constructing a Markov chain with a absorb state. The queue and the main reliability indices of server are derived with the method of supplementary variables. At last a numerical example is given.