The push-pull queueing network is a simple example in which servers either serve jobs or generate new arrivals. It was previously conjectured that there is no policy that makes the network positive recurrent (stable) in the critical case. We settle this conjecture and devise a general sufficient condition for non-stabilizability of queueing networks which is based on a linear martingale and further applies to generalizations of the push-pull network.

翻译：推拉队列网络是一个简单的例子,服务器要么为工作服务,要么产生新到者。以前曾推测,在关键案例中,没有政策使网络呈正常数(稳定 ) 。 我们解决这一猜测,为排队网络的不稳定性设计一个普遍的充分条件。 排队网络以线性马丁格尔为基础,进一步适用于推拉网的常规化。