Delay and Capacity Trade-offs in Mobile Wireless Networks with Infrastructure Support

Abstract

In this paper, we investigate the trade-offs between delay and capacity in mobile wireless networks with infrastructure support. We consider three different mobility models, independent and identically distributed (i.i.d) mobility model, random walk mobility model with constant speed and Lévy flight mobility model. For i.i.d mobility model and random walk mobility model with the speed $\Theta \left( {\frac{1}{{\sqrt {n} }}} \right)$, we get the theoretical results of the average packet delay when capacity is Θ(1), $\Theta \left( {\frac{1}{{\sqrt {n} }}} \right)$ individually, where n is the number of nodes. We find that the optimal average packet delay is achieved when capacity $\lambda (n) < \frac{1}{{2 \cdot n \cdot \log \left( {\frac{1}{{1 - {e^{ - \frac{K}{n}}}}} + 1} \right)}}$, where K is the number of gateways. It is proved that average packet delay D(n) divided by capacity λ(n) is bounded below by $\frac{n}{{K \cdot W}}$. When $\omega \left( {\sqrt {n} } \right) \leqslant K < n$, the critical average delay for capacity compared with static hybrid wireless networks is $\Theta \left( {\frac{{{K^2}}}{n}} \right)$. Lévy flight mobility model is based on human mobility and is more sophisticated. For the model with parameter α, it is found that $\frac{{D(n)}}{{\lambda (n)}} > O\left( {{n^{\frac{{\left( {1 - n} \right) \cdot \left( {\alpha + 1} \right)}}{2}}}\ln n} \right)$ when K = O(n ⁿ) (0 ≤ η < 1). We also prove that when $\omega \left( {\sqrt {n} } \right) \leqslant K < n$, the critical average delay is $\Theta \left( {{n^{\frac{{\alpha - 1}}{2}}} \cdot K} \right)$.