On Capacity and Delay of Multichannel Wireless Networks With Infrastructure Support

In this paper, we propose a novel multichannel network with infrastructure support, which is called an <bold><italic>MC-IS</italic></bold> network, that has not been studied in the literature. To the best of our knowledge, we are the first to study such an <bold><italic>MC-IS</italic></bold> network. Our proposed <bold><italic>MC-IS</italic></bold> network has a number of advantages over three existing conventional networks: a single-channel wireless ad hoc network (called an <bold><italic>SC-AH</italic></bold> network), a multichannel wireless ad hoc network (called an <bold><italic>MC-AH</italic></bold> network), and a single-channel network with infrastructure support (called an <bold><italic>SC-IS</italic></bold> network). In particular, the <bold><italic>network capacity</italic></bold> of our proposed <bold><italic>MC-IS</italic></bold> network is <inline-formula><tex-math notation="LaTeX">$\sqrt{n\log n}$</tex-math></inline-formula> times higher than that of an <bold><italic>SC-AH</italic></bold> network and an <bold><italic>MC-AH</italic></bold> network and the same as that of an <bold><italic>SC-IS</italic></bold> network, where <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of nodes in the network. The <bold><italic>average delay</italic></bold> of our <bold><italic>MC-IS</italic></bold> network is <inline-formula><tex-math notation="LaTeX">$\sqrt{\log n/n}$</tex-math></inline-formula> times lower than that of an <bold><italic>SC-AH</italic></bold> network and an <bold><italic>MC-AH</italic></bold> network and <inline-formula><tex-math notation="LaTeX">$\min\{C_{I},m\}$</tex-math></inline-formula> times lower than the average delay of an <bold><italic>SC-IS</italic></bold> network, where <inline-formula><tex-math notation="LaTeX">$C_{I}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> denote the number of channels dedicated for infrastructure communications and the number of interfaces mounted at each infrastructure node, respectively. Our analysis on an <bold><italic>MC-IS</italic></bold> network equipped with <bold><italic>omnidirectional antennas</italic></bold> has been extended to an <bold><italic>MC-IS</italic></bold> network equipped with <bold><italic>directional antennas</italic></bold> only, which are named as an <bold><italic>MC-IS-DA</italic></bold> network. We show that an <bold><italic>MC-IS-DA</italic></bold> network has an even lower delay of <inline-formula><tex-math notation="LaTeX">$c/(\lfloor \text{2}\pi/\theta\rfloor\cdot C_{I})$</tex-math></inline-formula> compared with an <bold><italic>SC-IS</italic></bold> network and our <bold><italic>MC-IS</italic></bold> network. For example, when <inline-formula><tex-math notation="LaTeX">$C_{I}=\text{12}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\theta=\pi/\text{12}$</tex-math></inline-formula>, an <bold><italic>MC-IS-DA</italic></bold> can further reduce the delay by 24 times lower than that of an <bold><italic>MC-IS</italic></bold> network and by 288 times lower than that of an <bold><italic>SC-IS</italic></bold> network.