Wireless networks: An instance of tandem discrete-time queues

We model end-to-end flows in an ad-hoc wireless network using a tandem of finite-size, discrete-time queues, located at the nodes along the routes used by the flows, with appropriate restrictions that capture the first- and second-order interference constraints. In addition, we assume there are no capture effects, that is, there is at most one arrival into a queue at any discrete-time instant. The half-duplex nature of communication also supposes there cannot be a simultaneous arrival and departure from a discrete-time queue. These queues are characterized by the channel access probabilities of the node. If the objective is to bound the buffer overflow probability at each queue along a flow, we show that is not necessary to maintain separate queues for each flow that is routed through a node. We present simulation results to support our conclusions. This observation significantly eases the implementation of the distributed algorithm that enforces end-to-end proportional fairness subject to constraints on the buffer overflow probabilities (Singh N, Sreenivas R, Shanbhag U (2008) Enforcing end-to-end proportional fairness with bounded buffer overflow probabilities. Technical Report UILU-ENG-08-2211, Aug 2008, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana).