Instability of LIFO queueing networks

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