
Performance analysis on network connectivity for vehicular ad hoc networks 69
percolation theory. Some investments focused on the k-
connectivity (Wan et al., 2010), partial connectivity (Haiyan
et al., 2010) or asymptotic connectivity (Honghai et al.,
2005). The measurements of the connectivity performance
includes the critical communication range, the distribution of
the connectivity distance and node population, as well as the
connectivity probability.
Fundamental characteristics of the connectivity in
VANETs were studied in Shioda et al. (2008) with extensive
simulations, and the authors addressed how the road and
vehicle positions would affect the connectivity characteristic.
A new mobility model was presented in Hafeez et al.
(2010) to derive the number of vehicles on the road
and connectivity probability. Two probabilities, the access
probability that a vehicle can access the infrastructure and the
connectivity probability that all the vehicles can connect to
the infrastructure, were derived for vehicular relay networks
in Seh et al. (2011). Reference Yousefi et al. (2008) studied
the statistical properties of connectivity in VANETs with the
queuing theory.
The authors in Cheng et al. (2012) discussed the impacts
of the intervehicle spacing distribution on the connectivity of a
vehicular ad hoc network in a highway traffic scenario based on
a new empirical analysis. Reference Zhongjiang et al. (2012)
studied the connectivity in VANETs based on the uniform
stationary distribution without considering the mobility. A
new mobility model was proposed in Hafeez et al. (2013) and
the authors considered how the vehicles speeds would affect
the connectivity and the packet reception rates. In Pitsiladis
et al. (2012), spanning tree theory was adopted to present the
connectivity calculation in finite wireless multi-hop networks.
A general close form expression for the probability of the
existence of at least one connected spanning tree inside the
network’s graph was derived. Literature (Ren et al., 2011)
evaluated the percolation-based connectivity performance for
the secondary network in a large-scale ad hoc heterogeneous
network, based on the theory of continuum percolation.
Through analysing the existing research results, it is clear
that most of the previous literatures studied connectivity in
VANETs mainly from the macroscopic view, such as node
population and cluster size in the road. The effect of individual
vehicle’s movement on connectivity, which can be regarded
as the microscopic view, is still not clear. Macroscopic view
can be considered as the viewpoint of the entire network and
it mainly focuses on the global properties of the network,
while microscopic view can be regarded as the viewpoint
of a single vehicle or a communication pair of individual
vehicles. In the viewpoint of the macroscopic, connectivity
means the whole network is fully connected. In the viewpoint
of microscopic, connectivity means that there exist some
available paths between the communication pair of vehicles.
Since a great many safety-related services could be
broadcasted only within a small-range zone rather than the
whole network (for instance, the safety messages containing
the lane-changing information or collision avoidance warning
could be delivered to the surrounding vehicles only), the
microscopic properties are of great significance to ensure
the reliable safety-related communication in these cases.
Moreover, the inter-vehicle distance is one of the key factors
that affect the microscopic connectivity properties, which is
impacted by the relative movements of the individual vehicles.
Nonetheless, the distributions of the relative movement and
inter-vehicle distance have been paid less attention in most
of the previous works. The previous works analyse the
connectivity properties considering either the vehicle mobility
or the spatial distribution, while in this paper we take both the
relative speed and inter-vehicle distance into account.
1.2 Contribution
The objective of this paper is to study the network connectivity
in a highway mobility model from both the microscopic and
macroscopic view. We focus on the distributions of the relative
speed and inter-vehicle distance, and study how the individual
vehicle’s relative movements affect the microscopic and
the macroscopic connectivity performance. We then employ
three parameters: conditional connectivity probability, global
network connectivity probability, and the vehicle isolation
probability, to investigate the impact of the different system
parameters on the network connectivity.
The conditional connectivity is the probability that a
communication pair can stay connected during a whole data
transmission conditioned on the connection is successfully
built up when the transmission is initialised. In the VANETs
scenario, various types of data are transmitted in the network.
Some small sized data can be transmitted by packaging
into a few or even one packet (for example, the emergency
broadcast), while some other data may need much longer
transmission duration (for example, the video-on-demand
data stream). It is clear that the small sized data has better
adaptivity to the not guaranteed network connectivity, but
the transmission of data for entertainment services may face
frequent link interruptions. Therefore, we will focus on the
effect of conditional connectivity on the data transmission
service like entertainment or other large-data-based ones. In
particular, we will study how the conditional connectivity
would be influenced by vehicles’ relative mobility and inter-
vehicle initial distance.
Moreover, different from the previous work (Chen
et al., 2012) which only focuses on a communication pair
of individual vehicles, this paper also studies the global
properties of the whole network. Global network connectivity
is the probability that the whole network is fully connected
and an arbitrary vehicle can directly communicate with its
neighbourhood; while vehicle isolation probability means
the probability that a randomly chosen vehicle has no
neighbour and cannot directly communicate with others.
Considering a highly dynamic network topology and the
stringent delay requirements for some of the VANETs
safety-related applications, the delay-critical messages like
collision avoidance warning are supposed to be disseminated
immediately through direct one-hop communication. There
should exist the fully connected paths for the safety-
related message dissemination through the entire network to
guarantee the successful reception of the whole network. In
order to ensure the reliable broadcast for the one-hop safety-
critical services, it is essential that there exists no isolated
vehicle in the network and any arbitrary vehicle can establish