Logarithmic expected packet delivery delay in mobile ad hoc wireless networks

Abstract

It has been shown that in a mobile ad hoc wireless network per node throughput remains constant as the number of nodes approaches infinity, when the nodes lie in a disk of unit area. However, this requires that some packets are delivered indirectly by a relay node. In this paper, we prove, in the same setup, that D(k) 2 Â(log k), where D(k) is the expected delay time of a mobile ad hoc wireless network with k nodes. As consequence, we have concluded that mobile ad hoc wireless networks are not scalable for real-time applications. z Observe that the rôle played by the unitary disk in Reference [6] is not of importance for their results. For example, the estimate lim z!0 FðzÞ=z 2= ¼ , obtained in Reference [6], does not depend on the fact that the nodes lie on the unitary disk. This estimate only depends on the fact that the measure used on the unitary disk is the restriction of the Lebesgue measure. The same estimate can be obtained for the unitary square, see Reference [11].