Pathwise stability of multiclass queueing networks

It has been shown that, under some service policies, a queueing network can be unstable even if the load of every station is less than one. Although the stability of queueing systems in some special cases (e.g. under First-Buffer-First-Served policy) has been well addressed, there are still difficulties in coping with more general networks. In this paper, we study the stability problem through depicting the mutual blocking effect among different classes and generalize the concept of servers in the context of queueing networks based on the sample path analysis. We show that the general servers have similar impacts on the system stability as physical stations and a queueing network is pathwise stable if and only if the effective traffic intensity of every general server does not exceed one. Through case studies, we show that the stability of queueing networks and the structure of general servers are sensitive and depend on various factors, including the service policies. Furthermore, we prove that queueing systems operating under the Work-in-Progress-Dependent service policies are always stable if every physical station has sufficient capacity.