Comments on k-hop access and connectivity probabilities in VANET
Yang Yang
15 July 2010
(1) Page 1, title  “Multi-hop Access Probability and Connectivity Probability in
Infrastructure-based Vehicular Networks”
(2) Page 1, authors  Wuxiong Zhang, Yang Yang, Xiangyang Wang, Xuemin Hong, and Guoqiang
Mao
(3) Page 1, Abstract 
Following the IEEE 802.11p and IEEE 1609 standards, infrastructure-based vehicular networks
(consisting of a group of Base Stations (BSs) along the road) will be widely deployed to
support Wireless Access in Vehicular Environment (WAVE) and a series of safety and
non-safety related applications and services for vehicles on the road. As an important
measure of user satisfaction level, access probability is defined as the probability that any
specific vehicle can access the infrastructure (i.e. BSs) through a multi-hop path. While on the
system side, connectivity probability is defined as the probability that all vehicles can be
reached from the infrastructure through a multi-hop path, which indicates service coverage
performance of a vehicular network. This paper proposes an analytical model to derive, in
closed-form equations, the multi-hop access probability and connectivity probability in
infrastructure-based vehicular networks. Our analytical results, validated by simulations,
reveal the tradeoff relationships between these key performance metrics and some
important system parameters, such as BS and vehicle densities, radio coverage (or
transmission power), and maximum number of hops. This insight knowledge enables
vehicular network engineers and operators to effectively achieve high user satisfaction and
good service coverage, with just necessary deployment of BSs along the road according to
traffic density, user requirements and service types.
(4) Page 1, Key words  Vehicular Ad Hoc Network (VANET), Wireless Access in Vehicular
Environment (WAVE), IEEE 802.11p, IEEE 1609, Access Probability, Connectivity Probability.
(5) Pages 1-2, Introduction 
Infrastructure-based vehicular networks consist of a group of fixed Base Stations
(BSs), or Access Points (APs), deployed along roads to support traffic monitoring and
management, safety and emergency information delivery, Internet access, and other data
communications applications. Specifically, drivers and passengers on the road can
access the Internet or communicate with each other through a direct (single-hop) or
multi-hop connection with the roadside infrastructure (i.e. BSs), depending on the
locations of their vehicles.
Multi-hop communications is inevitable when a vehicle cannot directly communicate
with any BS (e.g. it is located in a coverage gap between adjacent BSs) and has to relay
on its neighboring vehicles to forward/relay data packets to/from a nearby BS. In doing so,
both access probability (i.e. the probability that any specific vehicle can access the
infrastructure through a multi-hop path) and connectivity probability (i.e. the probability
that all vehicles can be reached from the infrastructure through a multi-hop path) can be
greatly improved. The former is, arguably, the most important service requirement and
directly affects user experience and satisfaction level in uplink (from vehicles to a BS) data
transmissions. The latter is related to service coverage of a vehicular network and
determines the efficiency/quality of downlink (from a BS to many vehicles) broadcasting
services, such as safety and emergency information dissemination from a traffic manager
or a network operator to all vehicles.
The paper aims to fully investigate the access probability and connectivity probability
in multi-hop vehicular networks, which are determined by the densities and radio
coverage of BSs and vehicles, as well as the maximum number of hops and wireless
channel models. By understanding the tradeoff relationships between these key system
parameters and performance metrics, we can finally answer the most important and
challenging question -- how many BSs (investment) need to be deployed along a road in
order to guarantee the predefined access probability and connectivity probability for a
group of vehicles (potential customers and return), which are randomly distributed on the
road.
A: Standardization Activities
Figure 1 Architecture of IEEE 1609 standards family
As shown in Fig. 1, the IEEE 1609 standards family is currently under development to
support Wireless Access in Vehicular Environment (WAVE) and to deliver safety and
infotainment applications to vehicles on the road [802.11p,1609, ITS]. Specifically, IEEE
802.11p belongs to the IEEE 802.11 family and it is a draft amendment to the IEEE 802.11
standard to add WAVE capability. According to the official IEEE 802.11 Work Plan, the
final version of 802.11p amendment will be approved and published in 2010. The goal of
802.11p protocol is to provide communications including Vehicle to Vehicle (V2V) and
Vehicle to Infrastructure (V2I) at a range up to 1,000 meters and offer 6 Mbps in average
use of transmission on the dedicated 5.9 GHz (5.85-5.925 GHz) licensed band for both
safe and non-safe applications.
IEEE 802.11p uses an amended 802.11a physical specification. Specifically, it divides
the total 75MHz bandwidth into seven 10MHz channels, i.e. one Control Channel (CCH)
and six Service Channels (SCH). In physical layer, IEEE 802.11p adopts Orthogonal
Frequency-Division Multiplexing (OFDM) technology and can provide the data payload up
to 27 Mbps in a 10 MHz channel for WAVE applications. In Medium Access Control (MAC)
layer, it follows the Enhanced Distributed Channel Access (EDCA) protocol from the
802.11e standard to support Quality of Service (QoS). EDCA is a stop-and-wait MAC
protocol, in which the sender awaits an acknowledgment (ACK) after transmitting a packet.
As a new concept, IEEE 802.11p defines the WAVE-mode Basic Service Set (WBSS) and
data packet transmissions are only allowed to occur within the same WBSS. A node that
initiates a WBSS is called a WBSS provider and other nodes that join a WBSS are called
WBSS users.
As seen in Fig. 1, IEEE 1609 standards sit in upper layers and specify the
architecture, communications model, management structure, security mechanisms and
physical access for WAVE. The primary architectural components defined by these
standards are On Board Unit (OBU), Road Side Unit (RSU) and WAVE interface. IEEE
P1609 standards consist of the following key specifications in different areas.
 IEEE P1609.0 (not shown in Fig. 1) describes the architecture of WAVE for
enabling multichannel WAVE devices to communicate with each other in a
mobile vehicular environment and the associated services.
 IEEE P1609.1 specifies the services and interfaces of the WAVE Resource
Manager application. It describes the key components of the WAVE architecture
and defines the data flows and resources at all points. Recently, P1609.1
standard has been redefined to focus on low-end devices.
 IEEE P1609.2 defines the circumstances for using secure message exchanges,
its formats, and how those messages should be processed.
 IEEE P1609.3 defines network and transport layer services, including addressing
and routing. It also defines WAVE Short Messages, which can be directly
supported by applications, and Management Information Base (MIB) for the
WAVE protocol stack, which provides Service Access Points (SAPs) for higher
layer entities.
 IEEE P1609.4 describes how to support multi-channel operation (or channel
coordination) with the 802.11 MAC and physical layer specifications, by using a
control channel (CCH) and multiple service channels (SCHs).
 Some new standards have recently been added to IEEE 1609 family, such as
1609.5 (Communications Management), 1609.6 (Facilities) and 1609.11
(Electronic Payment Service). Their functions and relationships with other 1609
standards are shown in Fig. 1.
B. Related Work
In literature, the connectivity probability between any two nodes/vehicles in a Mobile
Ad Hoc Network (MANET) is derived in [4] for uniformly distributed vehicles under a unit
disk communication model. Further, queueing theory is applied in [6] to address the
connectivity problem in ad hoc networks under a realistic wireless channel model with
shadowing and fading effects. Poisson distribution is used in [5] to model road traffic flows,
with an assumption of exponentially distributed space-headways between adjacent
vehicles. Under this condition, the V2V connectivity probability in VANETs is obtained
under a unit disk model of radio coverage. In addition, the same probability in closed-form
equations is calculated in [7] under a novel vehicle mobility model by using
multi-dimensional hypercube and hyper-plane methods. For infrastructure-based vehicle
networks, the connectivity probability between any two nodes/vehicles through a hybrid
network, and the connectivity probability (defined as access probability in this paper) from
a vehicle to a BS are derived in [8] under the same radio coverage assumption for a
vehicle and a BS.
In contrast to previous work that mainly concentrates on ad hoc communications and
connectivity between vehicles, this research first derives and analyzes the access
probability and connectivity probability\footnote{Different from previous work, this paper
studies strict connectivity probability with the roadside infrastructure (i.e. BSs), which is
the probability that 100\% access probability for all vehicles can be achieved.},
respectively, from end users’ and network operator/service provider’s perspectives in
infrastructure-based vehicular networks. Then, the tradeoff relationships between these
key performance metrics and some important system parameters, such as BS and vehicle
densities, radio coverage (or transmission power), and maximum number of hops, are
fully investigated under different wireless channel and traffic models. This insight
knowledge enables vehicular network engineers and operators to effectively achieve high
user satisfaction and good service coverage, with just necessary deployment of BSs
along the road according to traffic density, user requirements and service types.
The rest of this paper is organized as follows. Section II defines the system model of
infrastructure-based vehicular networks. Multi-hop access probability and connectivity
probability between vehicles and roadside infrastructure (BSs) are then derived in section
III. Analytical and simulation results are compared and discussed in section IV, followed by
conclusions in section V.