Under the last-in, first-out (LIFO) discipline, jobs arriving later at a class always receive priority of service over earlier arrivals at any class belonging to the same station. Subcritical LIFO queueing networks with Poisson external arrivals are known to be stable, but an open problem has been whether this is also the case when external arrivals are given by renewal processes. Here, we show that this weaker assumption is not sufficient for stability by constructing a family of examples where the number of jobs in the network increases to infinity over time. This behavior contrasts with that for the other classical disciplines: processor sharing (PS), infinite server (IS) and first-in, first-out (FIFO), which are stable under general conditions on the renewals of external arrivals. Together with LIFO, PS and IS constitute the classical symmetric disciplines; with the inclusion of FIFO, these disciplines constitute the classical homogeneous disciplines. Our examples show that a general theory for stability of either family is doubtful.

在后进先出 (LIFO) 原则下，较晚到达一个班级的作业总是比早到属于同一站的任何班级获得服务优先。已知具有泊松外部到达的亚临界 LIFO 排队网络是稳定的，但一个开放的问题是，当外部到达由更新过程给出时，是否也是这种情况。在这里，我们通过构建网络中的工作数量随时间增加到无穷大的一系列示例来表明这种较弱的假设不足以保证稳定性。这种行为与其他经典学科的行为形成对比：处理器共享 (PS)、无限服务器 (IS) 和先进先出 (FIFO)，它们在外部到达更新的一般条件下是稳定的。与 LIFO 一起，PS和IS构成经典的对称学科；加入先进先出后，这些学科就构成了经典的同质学科。我们的例子表明，任何一个家庭稳定性的一般理论都是值得怀疑的。