Multi-channel Wireless Networks with Infrastructure Support: Capacity and Delay

In this paper, we propose a novel multi-channel network with infrastructure support, called an \textit{MC-IS} network, which has not been studied in the literature. To the best of our knowledge, we are the first to study such an \textit{MC-IS} network. Our \textit{MC-IS} network is equipped with a number of infrastructure nodes which can communicate with common nodes using a number of channels where a communication between a common node and an infrastructure node is called an infrastructure communication and a communication between two common nodes is called an ad-hoc communication. Our proposed \textit{MC-IS} network has a number of advantages over three existing conventional networks, namely a single-channel wireless ad hoc network (called an \textit{SC-AH} network), a multi-channel wireless ad hoc network (called an \textit{MC-AH} network) and a single-channel network with infrastructure support (called an \textit{SC-IS} network). In particular, the \textit{network capacity} of our proposed \textit{MC-IS} network is $\sqrt{n \log n}$ times higher than that of an \textit{SC-AH} network and an \textit{MC-AH} network and the same as that of an \textit{SC-IS} network, where $n$ is the number of nodes in the network. The \textit{average delay} of our \textit{MC-IS} network is $\sqrt{\log n/n}$ times lower than that of an \textit{SC-AH} network and an \textit{MC-AH} network, and $\min(C_I,m)$ times lower than the average delay of an \textit{SC-IS} network, where $C_I$ and $m$ denote the number of channels dedicated for infrastructure communications and the number of interfaces mounted at each infrastructure node, respectively.Comment: 12 pages, 6 figures, 3 table

On Capacity and Delay of Multi-channel Wireless Networks with Infrastructure Support

In this paper, we propose a novel multi-channel network with infrastructure support, called an MC-IS network, which has not been studied in the literature. To the best of our knowledge, we are the first to study such an MC-IS network. Our proposed MC-IS network has a number of advantages over three existing conventional networks, namely a single-channel wireless ad hoc network (called an SC-AH network), a multi-channel wireless ad hoc network (called an MC-AH network) and a single-channel network with infrastructure support (called an SC-IS network). In particular, the network capacity of our proposed MC-IS network is $\sqrt{n \log n}$ times higher than that of an SC-AH network and an MC-AH network and the same as that of an SC-IS network, where $n$ is the number of nodes in the network. The average delay of our MC-IS network is $\sqrt{\log n/n}$ times lower than that of an SC-AH network and an MC-AH network, and $\min\{C_I,m\}$ times lower than the average delay of an SC-IS network, where $C_I$ and $m$ denote the number of channels dedicated for infrastructure communications and the number of interfaces mounted at each infrastructure node, respectively. Our analysis on an MC-IS network equipped with omni-directional antennas only has been extended to an MC-IS network equipped with directional antennas only, which are named as an MC-IS-DA network. We show that an MC-IS-DA network has an even lower delay of $\frac{c}{\lfloor \frac{2\pi}{\theta}\rfloor \cdot C_I}$ compared with an SC-IS network and our MC-IS network. For example, when $C_I=12$ and $\theta=\frac{\pi}{12}$, an MC-IS-DA network can further reduce the delay by 24 times lower that of an MC-IS network and reduce the delay by 288 times lower than that of an SC-IS network.Comment: accepted, IEEE Transactions on Vehicular Technology, 201

Profit Maximization with Sufficient Customer Satisfactions

In many commercial campaigns, we observe that there exists a tradeoff between the number of customers satisfied by the company and the profit gained. Merely satisfying as many customers as possible or maximizing the profit is not desirable. To this end, in this article, we propose a new problem called k - &lt;underline&gt;S&lt;/underline&gt;atisfiability &lt;underline&gt;A&lt;/underline&gt;ssignment for &lt;underline&gt;M&lt;/underline&gt;aximizing the &lt;underline&gt;P&lt;/underline&gt;rofit ( k -SAMP), where k is a user parameter and a non-negative integer. Given a set P of products and a set O of customers, k -SAMP is to find an assignment between P and O such that at least k customers are satisfied in the assignment and the profit incurred by this assignment is maximized. Although we find that this problem is closely related to two classic computer science problems, namely maximum weight matching and maximum matching, the techniques developed for these classic problems cannot be adapted to our k -SAMP problem. In this work, we design a novel algorithm called Adjust for the k -SAMP problem. Given an assignment A , Adjust iteratively increases the profit of A by adjusting some appropriate matches in A while keeping at least k customers satisfied in A . We prove that Adjust returns a global optimum. Extensive experiments were conducted that verified the efficiency of Adjust . </jats:p