具有两种不同服务的负顾客M^ξ／（G1／G2）／1可修排队系统

Repairable M^ξ/（G1/G2）/1 queueing system with negative customers and two-phase heterogeneous service

批量到达排队系统的基础上，考虑单服务台提供两种不同服务的负顾客M^ξ／（G1/G2）/1可修排队模型，每个正顾客接受第1种服务后以概率θ（0≤θ≤1）接受第2种服务，或以概率1-θ离开系统。服务规则是先到先服务．正顾客接受两种服务的过程中均可能有负顾客到达，负顾客不接受服务，只抵消正在接受服务的正顾客．通过补充变量法求得系统队长分布及一些可靠性指标。

Considering the situation that the server can provide two-phase heterogeneous service on the basis of batch arrival, a repairable M^ξ/（G1/G2）/1 queueing system with negative customers and two-phase heterogeneous service was established. Based on the ＇first come, first serve＇ discipline, a positive customer may receive the second phase service with probability 0（0 ≤ θ≤ 1） after the first one, or leave with probability 1 - θ directly. The negative customer was not served, and the positive customer of the head who had been served was removed. By the method of supplemental variable and the state transfer analysis, the distribution of the queue length and the reliability indexes were derived.