Bottlenecks and stability in networks with contending nodes

This paper considers a class of queueing network models where nodes have to contend with each other to serve their customers. In each time slot, a node with a non-empty queue either serves a customer or is blocked by a node in its vicinity. The focus of our study is on analyzing the throughput and identifying bottleneck nodes in such networks. Our modeling and analysis approach consists roughly of two steps. First, considering the slotted model on a longer timescale, the behaviour is described by a continuous time Markov chain with state dependent service rates. In the second step, the state dependent service rates are replaced by their long run averages resulting in an approximate product formnetwork. This enables us to determine the bottleneck nodes and the stability condition of the system. Numerical results show that our approximation approach provides very accurate results with respect to the maximum throughput a network can support. It also reveals a surprising effect regarding the location of bottlenecks in the network when the offered load is further increased.