# Capacity and Delay Analysis for Large Social-Aware Mobile Ad Hoc Wireless Networks
## 2 Related Works  
[PERSON] and [PERSON] [5; 6] analyzed large wireless networks capacity from the perspective of the network layer for the first time. The wireless network is modeled as an interference network in their work. In other words, whether data is received depending on the interference between nodes. Based on this assumption, they derived the upper bound throughput of each node in random ad hoc networks with asymptotic method. However, the throughput of each node cannot reach the upper bound.  
The seminal work has inspired researchers to study performances of large wireless networks. In particular, [PERSON] and [PERSON] [7; 8] showed that throughput capacity changes dramatically allowing the nodes to move. A 2-hop relay algorithm was proposed with random Independent Identically Distributed Mobility Model. Using 2-hop relay algorithm, they show that the per-node throughput in large wireless networks can keep constant. But, 2-hop relay algorithm comes at the expense of latency and requires higher node speed.  
Subsequently, a great deal of research has emerged on exploring performance for large wireless networks under various physical technologies and various traffic model. These include directional antennas [9], cognitive radios [10], Multiple Input Multiple Output techniques [11], etc. Multicast is a more common pattern of unicast. [PERSON] et al. [12; 13] studied multicast scenario with \(k(k<n)\) destinations in large static wireless ad hoc networks. The results demonstrate that the upper bound throughput of each node is \(\Theta(\frac{1}{\sqrt{nk\log n}})\).  
Performance of large wireless networks with more mobility models are extensively studied, such as the Brownian Mobility Model [14], Correlated Mobility Model [15], Levy Mobility Model [16], Reference Point Group Mobility Model [17], and Human Mobility Model [18].  
However, high throughput and low latency cannot be obtained simultaneously. Delay can be reduced at the cost of a lower per-node throughput capacity, and vice versa. [PERSON] and [PERSON] [19] analyzed this issue under different scheduling policies. The corresponding delay is \(O(n)\), \(O(\sqrt{n})\) and \(O(\log n)\) respectively when per-node throughput is \(O(1)\), \(O(\frac{1}{\sqrt{n}})\) and \(O(\frac{1}{n\log n})\). They showed the necessary delay and capacity tradeoffs in large wireless ad hoc network. The redundancy (flooding scheme) can decrease delay because of more transmission opportunities.  
Newly added backbone nodes are beneficial for capacity and delay in mobile ad hoc networks. Data can be delivered by high-bandwidth links between backbone nodes. In Reference [20], [PERSON] and [PERSON] studied the asymptotic scaling for hybrid ad hoc networks. They analyzed the throughput capacity by dividing the number of backbone nodes into three regions. [PERSON] et al. [21] studied multicast traffic model impacts on capacity of hybrid networks.  
Social characteristics have also become an important indicator for mobile communication network. Geographic location has a significant impact on their social relations in online social networks [22; 23]. However, existing social models have not captured small world phenomenon that arbitrary nodes are likely connected through shorter friends chain. The probability of contacts decreases with the increase of distance, which obeys the power law distribution. Literature initiated the research on capacity scaling of networks with social attributes [24; 25].  
As the number of devices increases in large mobile ad hoc wireless networks, new challenges have to be faced in order to maintain their performance. It is of great importance how to improve the performance of such networks with social attributes. To the best of our knowledge, there are a few researches about the interaction between social networks and mobile communication networks. We are among the first attempt to study the interaction between social networks and mobile communication networks.