We study the Multiserver-Job Queuing Model (MJQM) with general independent arrivals and service times under FCFS scheduling, using stochastic recurrence equations (SREs) and ergodic theory. We prove the monotonicity and separability properties of the MJQM SRE, enabling the application of the monotone-separable extension of Loynes' theorem and the formal definition of the MJQM stability condition. Based on these results, we introduce and implement two algorithms: one for drawing sub-perfect samples (SPS) of the system's workload and the second one to estimate the system's stability condition given the statistics of the jobs' input stream. The SPS algorithm allows for a massive GPU parallelization, greatly improving the efficiency of performance metrics evaluation. We also show that this approach extends to more complex systems, including MJQMs with typed resources.

翻译：本文研究了采用先到先服务调度的多服务器作业排队模型，该模型具有一般独立到达和服务时间特性，我们运用随机递归方程和遍历理论进行分析。我们证明了多服务器作业排队模型随机递归方程的单调性和可分离性，从而能够应用Loynes定理的单调可分离扩展，并正式定义了多服务器作业排队模型的稳定性条件。基于这些结果，我们提出并实现了两种算法：第一种用于生成系统工作负载的次完美样本，第二种用于根据作业输入流的统计特性估计系统稳定性条件。次完美样本算法支持大规模GPU并行化，显著提升了性能指标评估的效率。我们还证明了该方法可扩展至更复杂的系统，包括具有类型化资源的多服务器作业排队模型。