We study the maximum remaining service time in M⁽²⁾∣G₂∣∞ fork -join queueing systems where an incoming task forks on arrival for service into two subtasks, each of them being served in one of two infinite-sever subsystems. The following cases for the arrival rate are considered: (1) time-independent, (2) given by a function of time, (3) given by a stochastic process. As examples of service time distributions, we consider exponential, hyperexponential, Pareto, and uniform distributions. In a number of cases we find copula functions and the Blomqvist coefficient. We prove asymptotic independence of maximum remaining service times under high load conditions.

中文翻译：

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叉加入无限服务器队列中最大剩余服务时间的双变量分布

我们研究的最大剩余使用时间中号^（2） | g ^ ₂ |∞叉-join其中在抵达服务传入任务叉成两个子任务，他们每个人的两种无限服务器子系统一个被服务的排队系统。考虑以下到达率的情况：（1）与时间无关，（2）由时间函数给出，（3）由随机过程给出。作为服务时间分布的示例，我们考虑指数分布，超指数分布，帕累托分布和均匀分布。在许多情况下，我们找到了copula函数和Blomqvist系数。我们证明了在高负载条件下最大剩余服务时间的渐近独立性。