International Journal of Aerospace Engineering

Volume 2015 (2015), Article ID 380714, 7 pages

http://dx.doi.org/10.1155/2015/380714

## Degree Distribution of Arbitrary AANET

^{1}College of Communication Engineering, Chongqing University, Chongqing 400044, China^{2}Chongqing Communication Institute, Chongqing 400035, China

Received 26 October 2014; Revised 15 February 2015; Accepted 16 February 2015

Academic Editor: Ronald M. Barrett

Copyright © 2015 Xue Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Taking the safe distance between two adjacent planes in the same airline into account, we give a model for the multiairline aeronautical ad hoc network (AANET). Based on our model, we analyze the plane’s degree distribution of any arbitrary AANET. Then, the expressions of the degree distributions of one single plane and the whole networks are both worked out and verified by the simulations, in which we generate several random AANETs. Since our model is a reasonable abstraction of the real situation, the theoretical result we get is very close to the result of the real networks, which is also shown in the simulations.

#### 1. Introduction

With the rapid development of civil aviation, the demands of accessing Internet on board have become stronger than ever before. However, in polar, desert, marine, and other areas where base stations cannot be built, aircrafts have to use satellite links or large span multihop links within AANET to reach base stations. Due to the large delay, high cost, and limited bandwidth of satellite links, AANET is preferred for internet accessing in these regions [1, 2].

For AANET, the Newsky project has proposed networking strategies with mobile IPv6 technology [3]. ATENAA project (advanced technologies for networking in aeronautical applications) has studied Ka-band array antennas and optical communications between aircrafts [4]. Rohrer et al. have presented cross-layer networking solutions among physical, mac, network, and transport layers [5]. Vey et al. have proposed the use of direct sequence CDMA (DS-CDMA) at the access layer [2] while Yan et al. have studied the capacity of single flight path AANET [6].

In an ad hoc network, the number of a node’s neighbors is called “degree” of that node. Thus, the degree distribution of an ad hoc network tells the probability that the degree is an exact number by choosing a node randomly. Based on the degree distribution of the network, a lot of work can be done: the analysis of connectivity and robustness of the network by using the method of generating function formalism [7]; the design of routing and mac protocols; for example, we can choose planes with high degree expectation to relay messages, since usually we cannot know where all the planes are; the site selection of base stations; for example, base station can be set at a place to make sure that the average of the degree expectations of planes in coverage region of that base station is high, which makes it reach more planes through multihop links.

The degree distribution of mobile ad hoc networks has been widely discussed, but most of them are based on the scenarios that nodes in the networks move randomly. However, for AANET and vehicle ad hoc networks (VANET), the nodes are moving along specified lines, which is different from the old scenarios. In VANET, which is also studied a lot in recent years, the speed of vehicles can be affected by plenty of factors (such as pedestrian crosswalks, traffic jams, and traffic lights) and the degree distribution which a vehicle is hard to calculate or even to assume. Thus, the problem about calculating the degree distribution of the networks where nodes move along specified lines has not been solved yet.

In this work, we give a model for the AANET, from which we can approximately calculate the degree distribution of any arbitrary AANET.

#### 2. The Model

Since AANET is not deployed currently and none of the achievements mentioned previously is taken as standard or in real use, we do not consider the physical or access layer of AANET and use a fixed value, (between 50 nmi and 300 nmi as used in [8]), as the communication range for all planes.

According to the specifications of the International Civil Aviation Organization (ICAO) [9], a safe distance, call it (it is around 20 nmi according to ICAO), should be kept between two adjacent planes in the same airline. As the length of an airline is far greater than , we take as the smallest unit of length. Thus, we assume that the distance between two adjacent planes in the same airline can only be . Since the distance of two airlines at different height level is usually several hundred of meters, which is much less than the assumed planes’ communication range , we ignore the distance of two airlines.

In Figure 1, there are several random lines crossing each other with points uniformly spaced on them. The lines stand for airlines while points denote the possible locations of planes. The distance between two adjacent points in the same line is . Furthermore, we assume that the spatial distribution of planes on each airline obeys discrete uniform distribution.