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

Abstract

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 P {S > x} 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 Part of the research was conducted while R. Bekker was affiliated to CWI. Hans van den Berg (Telecom ICT) is acknowledged for bringing this model under our attention.

Asymptotic analysis of Lévy-driven tandem queues

“…This idea has been used in several papers before, see e.g. [24,44], or, in a more complex model, [7]. The proof consists of a lower bound that focuses on the probability of the single most likely event, in conjunction with an upper bound that shows that all other scenarios (for instance those with multiple big jumps) yield negligible contributions.…”

“…The proof consists of a lower bound that identifies a most likely scenario, and an upper bound that shows that all other scenarios lead to asymptotically negligible contributions; the line of reasoning resembles that of earlier papers, e.g. [7,44].…”

Performance analysis of differentiated resource-sharing in a wireless ad-hoc network

“…The focus of [20] was on the validation of the fluid model for m ≥ 1; by system simulations incorporating all details of the  802.11e ireless  technology (see, e.g., [11]) it was demonstrated that the fluid model accurately captures the resource sharing amongst source nodes and a common relay node. In [2] the fluid model for m = 1 is analyzed in the special case of regularly varying (that is, heavy-tailed) flows. The tail asymptotics of the overall flow transfer time are derived by sample-path arguments; it is proven that the tail behaves roughly as the residual flow size.…”

Stationary analysis of a fluid queue driven by a two processor computer system

“…Fluid queues has became a fascinating area of research, in recent years due to its wide spread applicability in computer and communication systems [1,3], manufacturing systems [6] etc. A stochastic fluid flow model is an input-output system where the input is modelled as a continuous fluid that enters and leaves the storage devices called a buffer according to randomly varying rates.…”