Throughput and Delay Scaling in Supportive Two-Tier Networks

Consider a wireless network that has two tiers with different priorities: a primary tier vs. a secondary tier, which is an emerging network scenario with the advancement of cognitive radio technologies. The primary tier consists of randomly distributed legacy nodes of density $n$, which have an absolute priority to access the spectrum. The secondary tier consists of randomly distributed cognitive nodes of density $m=n^\beta$ with $\beta\geq 2$, which can only access the spectrum opportunistically to limit the interference to the primary tier. Based on the assumption that the secondary tier is allowed to route the packets for the primary tier, we investigate the throughput and delay scaling laws of the two tiers in the following two scenarios: i) the primary and secondary nodes are all static; ii) the primary nodes are static while the secondary nodes are mobile. With the proposed protocols for the two tiers, we show that the primary tier can achieve a per-node throughput scaling of $\lambda_p(n)=\Theta(1/\log n)$ in the above two scenarios. In the associated delay analysis for the first scenario, we show that the primary tier can achieve a delay scaling of $D_p(n)=\Theta(\sqrt{n^\beta\log n}\lambda_p(n))$ with $\lambda_p(n)=O(1/\log n)$. In the second scenario, with two mobility models considered for the secondary nodes: an i.i.d. mobility model and a random walk model, we show that the primary tier can achieve delay scaling laws of $\Theta(1)$ and $\Theta(1/S)$, respectively, where $S$ is the random walk step size. The throughput and delay scaling laws for the secondary tier are also established, which are the same as those for a stand-alone network.Comment: 13 pages, double-column, 6 figures, accepted for publication in JSAC 201

On the Delay-Throughput Tradeoff in Distributed Wireless Networks

This paper deals with the delay-throughput analysis of a single-hop wireless network with $n$ transmitter/receiver pairs. All channels are assumed to be block Rayleigh fading with shadowing, described by parameters $(\alpha,\varpi)$, where $\alpha$ denotes the probability of shadowing and $\varpi$ represents the average cross-link gains. The analysis relies on the distributed on-off power allocation strategy (i.e., links with a direct channel gain above a certain threshold transmit at full power and the rest remain silent) for the deterministic and stochastic packet arrival processes. It is also assumed that each transmitter has a buffer size of one packet and dropping occurs once a packet arrives in the buffer while the previous packet has not been served. In the first part of the paper, we define a new notion of performance in the network, called effective throughput, which captures the effect of arrival process in the network throughput, and maximize it for different cases of packet arrival process. It is proved that the effective throughput of the network asymptotically scales as $\frac{\log n}{\hat{\alpha}}$, with $\hat{\alpha} \triangleq \alpha \varpi$, regardless of the packet arrival process. In the second part of the paper, we present the delay characteristics of the underlying network in terms of the packet dropping probability. We derive the sufficient conditions in the asymptotic case of $n \to \infty$ such that the packet dropping probability tend to zero, while achieving the maximum effective throughput of the network. Finally, we study the trade-off between the effective throughput, delay, and packet dropping probability of the network for different packet arrival processes.Comment: Submitted to IEEE Transactions on Information Theory (34 pages