A fluid model for a relay node in an ad hoc network: the case of heavy-tailed input

Relay nodes in an ad hoc network can be modelled as fluid queues, in which the available service capacity is shared by the input and output. In this paper such a relay node is considered; jobs arrive according to a Poisson process and bring along a random amount of work. The total transmission capacity is fairly shared, meaning that, when n jobs are present, each job transmits traffic into the queue at rate 1/(n + 1) while the queue is drained at the same rate of 1/(n + 1). Where previous studies mainly concentrated on the case of exponentially distributed job sizes, the present paper addresses regularly varying jobs. The focus lies on the tail asymptotics of the sojourn time S. Using sample-path arguments, it is proven that $${\mathbb{P}\left\{ S > x \right\}}$$ behaves roughly as the residual job size, i.e., if the job sizes are regularly varying of index − ν, the tail of S is regularly varying of index 1 − ν In addition, we address the tail asymptotics of other performance metrics, such as the workload in the queue, the flow transfer time and the queueing delay. Copyright The Author(s) 2009