Optimal throughput-delay scaling in wireless networks: Part I: the fluid model

A El Gamal, J. Mammen, B. Prabhakar, D. Shah
IEEE/ACM Transaction on Networking, Volume 52, No. 6, pp. 2568- 2592, 2006
Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per source-destination pair is Theta(1/radic(nlogn)). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant throughput scaling per source-destination pair. In most applications, delay is also a key metric of network performance. It is expected that high throughput is achieved at the cost of high delay and that one can be improved at the cost of the other. The focus of this paper is on studying this tradeoff for wireless networks in a general framework. Optimal throughput-delay scaling laws for static and mobile wireless networks are established. For static networks, it is shown that the optimal throughput-delay tradeoff is given by D(n)=Theta(nT(n)), where T(n) and D(n) are the throughput and delay scaling, respectively. For mobile networks, a simple proof of the throughput scaling of Theta(1) for the Grossglauser-Tse scheme is given and the associated delay scaling is shown to be Theta(nlogn). The optimal throughput-delay tradeoff for mobile networks is also established. To capture physical movement in the real world, a random-walk (RW) model for node mobility is assumed. It is shown that for throughput of Oscr(1/radic(nlogn)), which can also be achieved in static networks, the throughput-delay tradeoff is the same as in static networks, i.e., D(n)=Theta(nT(n)). Surprisingly, for almost any throughput of a higher order, the delay is shown to be Theta(nlogn), which is the delay for throughput of Theta(1). Our result, thus, suggests that the use of mobility to increase throughput, even slightly, in real-world networks would necessitate an abrupt and very large increase in delay.