Cross-Layer Design for Scheduling in CooperativeVANETs

Liang Zhou�, Benoit Geller�, Baoyu Zheng‡, and Jingwu Cui‡�UEI, ENSTA-ParisTech, Paris, France

‡Institute of SP&T, Nanjing University of Posts and Telecommunications, Nanjing, China

Abstract— In this paper, we jointly address the schedulingproblem such as rate control, medium access control (MAC) androuting for cooperative vehicular ad-hoc networks (VANETs) inthe framework of cross-layer design. Compared to its counterpartin a wired network where link capacities are assumed to befixed, congestion control in a multi-hop cooperative VANETs ismuch more complex and requires joint optimization at both thetransport layer and the MAC layer. This is due to the fact thatthe attainable function value on each path in the network is“elastic” which results in typically non-convex (non-concave) ornon-separable function of the transmission attempt rates. A newcross-layer algorithm is proposed to solve the system problemwith constraints that arise from the cooperation among the usersand contention for the wireless channel access. The algorithmworks at the MAC layer to adjust link persistence probabilityand at the transport layer to adjust flow rates joitly, and itis designed in distributed manner that is amenable to on-lineimplementation for VANETs. Experimental results show that theproposed opportunistic cooperation strategy combined with ajoint control algorithm achieves the desired performance overVANETs.

I. INTRODUCTION

VANETs are emerging wireless networks in which vehicles

constitute the mobile nodes of the network. This kind of

networks supports vehicle-to-vehicle and vehicle-to-gateway

communications by providing a self-organized and multi-hop

network. The main technical challenges for communication

in VANETs are the strong mobility of the nodes, the high

dynamic change of the topology, the high variability in node

density, and the very short duration of communications [1].

In recent years, several research efforts have been proposed

to target scheduling in vehicle systems. Among these, the

FleetNet project investigates the integration of the Internet

and vehicular networks, in which it contains stationary Internet

gateways (IGW) along the road with two interfaces connecting

vehicular networks to the Internet, and vehicles communicate

with distant IGW via multi-hopping [1]. However, there are

no specific solutions describing how to solve the data flow

movement problem over multiple hops in this architecture.

In fact, one of most challenge issues in VANETs is rate or

congestion control: the Internet is based on an end-to-end

paradigm, where the transport protocol (e.g. TCP) instances

at the endpoints detect overload conditions at intermediate

nodes. When congestion occurs, the source reduces its data

rate [2],[4]. However, in VANETs the topology changes within

seconds and a congested node used for forwarding a few

seconds might not be used at all at the point in time when

the source reacts to the congestion [6].

Nowadays, a new paradigm of content delivery on the ad-

hoc network using cooperative communication (CC) schemes

to increase the throughput of the total system is emerging [9].

In CC system, the wireless agents, which also called users,

increase their effective quality of service via cooperation, in

which each wireless user is assumed to transmit data as well

as act as a cooperative agent for another user. That is to say, it

may be possible for one user to receive the other, in which case

it can forward some version of “overheard” information along

with its own data. Because the fading paths from two users are

statistically independent, this generates spatial diversity [3].

In this paper, we formulate the rate control, MAC and

routing problem for cooperative VANETs in the framework

of utility function optimization by proposing an Opportunistic

Cooperation (OC) strategy. The fundamental purpose is to

decompose the utility function into a flow control problem

which determines the total source rate, and a division problem

which describes how to split the total rate among a set of least

congested paths according to the link persistence probability.

We develop cross-layer control algorithm by joint working

at the medium access control (MAC) layer to adjust link

persistence probability and at the transport layer to adjust flow

rates to solve the utility maximization problem with constraints

that arise from the cooperation among the users and contention

for the wireless channel access.

II. SYSTEM MODEL

Here, we begin with an overview the cooperative VANETs

system in which each vehicle acts as node or user, followed

by the problem formulation from the perspective of utility

function maximization based on the described system.

A. System Description

The VANETs system consists of a set of N nodes with

same computation and transmission capabilities, communicat-

ing through bidirectional wireless links between each other,

which is the infrastructure-less ad-hoc mode of operation.

There are wireless gateways at regular intervals providing

access to the rest of the Internet. A unicast routing proto-

col is available to support packet transmissions between the

network nodes, we assume each node is running AODV [8].

The vehicular wireless architecture is composed of such two

kinds of communications as Vehicle-to-Gateway and Vehicle-

to-Vehicle. The characteristics of the cooperative VANETs

978-1-4244-5347-4/09/$26.00 ©2009 IEEE 505

architecture and its differences with the traditional ad-hoc

always-connected model motivate the need to revisit the design

of swarming protocols which are designed for wired infras-

tructure. In this paper, we employ the OC protocol [9], which

builds on the fundamental mechanisms of partial downloading

and sharing of content in BitTorrent but adapts to the wireless

scenario by using different mechanisms for peer discovery,

selection and content delivery.

The basic operation of the OC as follows: when a new

user enters the vehicular network (such as entering a freeway

or a section of freeway with access points), it requests the

gateway for the particular file. If the gateway has the file in

its cache, it starts uploading a piece to the node. In addition,

OC does some intelligent peer selection based on the distance

of the peer possessing a certain piece it intends to download.

And then, when two peers become neighbors, they exchange

bit-fields that describe which pieces they possess. When a

peer fully receives a piece, it immediately notifies all of

its neighbors. Thus, every peer always knows exactly which

pieces its neighbors’ possesses.

B. Problem Formulation

Consider this VANETs whose links are denoted by L ={1, 2...L}. Let cl be the capacity of link l ∈ L and c =[c1, c2, ..., cL]T . Let S = {1, 2...S} be the set of sources. Each

source s has ns available paths or routers from the source to

the destination. Let the L × 1 vector Rs,i denotes the set of

links used by source s ∈ S on its path i ∈ {1, 2, ..., ns}, whose

lth element equals to 1 if path contains link l and 0 otherwise,

and Ns,i denotes the number of links on the path i. The set

of all the available paths of user s is defined by

Rs = [Rs,1, Rs,2, ..., Rs,ns] (1)

and the total paths in the network are defined by a L × Rrouting matrix R,

R = [R1, R2, ..., RS ] (2)

For each source s, let xs,i be the rate of source s on path Rs,i,

and xs =ns∑i=1

xs,i be the total source rate. Let ms ≥ 0 and

Ms ≤ ∞ be the minimum and maximum rates, respectively,

i.e., ms ≤ xs ≤ Ms. When each source s transmits at a total

rate of xs, it attains a utility Us(xs). We assume that Us:

R+ → R is continuous, increasing and strictly concave. Let

x = [x1,1, . . . , x1,n1 , . . . , xn,1, . . . , xn,nS]T ∈ RR

+ (3)

be the vector of all path rates of all sources. Our objective is to

choose rates x so as to maximize the total utility∑s∈S

Us(xs):

maxxs≥0

∑s∈S

Us(xs) (4)

subject to xs ≤ns∑i=1

xs,i,

Rx ≤ c

xs,i ≥ 0, ms ≤ xs ≤ Ms

However, in the cooperative VANETs system, each node

and each link has a contention resolution protocol based on the

transmission persistence probability [5]. Let Lout(s) denotes

the set of outgoing links from node s ∈ S, N Ito(l) as the set of

nodes whose transmissions cause interference to the receiver

of link l, excluding the transmitter node of link, and LIfrom(s)

as the set of links whose transmissions get interfered from the

transmission of node s, excluding the outgoing links from node

s. Therefore, if the transmitter of link l and a node in N Ito(l)

transmit data simultaneously, the transmission of link l fails. If

node s and the transmitter of a link l in LIfrom(s) transmit data

simultaneously, the transmission of link l also fails. Assuming

each node s transmits data with a probability p′s. When it

determines to transit data, it chooses one of its outgoing paths

with a probability ql, l ∈ Lout(s). Consequently, link l ∈Lout(s) transmits data with a probability pl = p′sql, which

is called persistence probability of link l. Therefore, the data

rate on path i, xs,i, is obtained as minimum rate of link in the

path:

xs,i(Ps) = minl∈[1,Ns,i]

clpl

∏k∈NI

to(l)

(1 −∑

m∈Lout(k)

pm) (5)

where Ps = [p1, ..., pNs,i], P = [P1, P2, ..., PS ].

With the above analysis, we can specify the cooperative

VANETs utility maximization with “contention” link:

maxxs≥0

∑s∈S

Us(xs) (6)

subject to xs ≤ns∑i=1

xs,i(Ps)

Rx ≤ c

xs,i ≥ 0, ms ≤ xs ≤ Ms, 0 � P � 1

III. JOINT OPTIMAL CONTROL ALGORITHM

In this section, we present a joint Optimal Congestion

and Medium Access Control (OC-MAC) algorithm based on

subgradient method in the framework of cooperative wireless

system and later prove that it converges to the joint and globe

optimum of (6) and give an upper bound of convergence rate.

A. OC-MAC Algorithm

The fundamental purpose is to decompose the source prob-

lem into a flow control problem which determines the total

source rate, and a division problem which describes how

to split the total rate among a set of least congested paths

according to the link persistence probability.

As stated previously, the cooperative wireless system is

a typical multi-source-multi-path problem. In the case of

multi-path flow control problem, many literatures have been

proposed by introducing the variable of path price to maximum

the total utility function of the system [10-12]. In [11], the

author solves the optimal congestion control problem by taking

the path price into consideration, and the optimal source rate

x∗s is given by

x∗s =

∑R∗

s,i∈R∗s

x∗s,i =

[U ′

s(pr∗s )

]Ms

ms

, and xs,i = 0 if prs,i > pr∗

s

506

where [z]Msms

= max(ms, min(Ms, z)

), pr∗

s is the minimum

path price among Rs, path R∗s,i has the minimum path price

pr∗s,i = pr∗

s , and R∗s defines the set of all minimum price

paths R∗s,i of source s. The above equation suggests a way

to adapt the total source to congestion, but it does not specify

how to distribute the total rate among the available paths. A

naive approach is to simply split it evenly along paths that

have the least current price. This algorithm, however, does not

converge, e.g. when multiple paths have different path prices.

In the cooperative wireless system, we can view the persistence

probability as a special path price, the distributed optimal xs

at each source can be adjusted according to the persistence

probability of each link. Similarly, the persistence probability

is adjusted according to current xs. Intuitively, the expected

result will allocate the “right” amount persistence probability

to the “right” links to alleviate the congestion, which may then

induce an increase in end-to-end throughput of the total system

[12]. Therefore, we need to find an algorithm that distributively

and adaptively control the flow rate and persistence probability

of each link from the aspects of link and source respectively.

OC-MAC Algorithm: during each time slot t, the following

five updates are carried out simultaneously until convergence.

(1) Each link l receives flow rates xs,i(t) for all paths Rs,i

that contain link l, and compute a new persistence probability

pl(t + 1) =[pl(t) + κ

cl −∑s

Rs,ix

pl(t)− κ

∑k∈LI

from(tl)

εk

1 − ∑m∈Lout(tl)

pm

]1

0

(7)

tl is the transmitter user whose path contains link l, κ > 0,

and

εl =

⎧⎨⎩

0, if∑s

xs,i(t) ≤ clpl

∏k∈NI

to(l)

(1 − ∑m∈Lout(k)

pm)

1, otherwise

(2) Communicates new probability pl(t + 1) to all sources

s whose path Rs,i contains link l; and each source receives

from the network prs,i = PT

s Rs,i, for all its paths Rs,i, i =1, 2, . . . , ns and decides the maximum persistence probability

pr∗s = maxi=1,2,...,ns pr

s,i(t).(3) Updates the source rate xs(t + 1):

xs(t + 1) =[U ′

s(pr∗s (t))

]Ms

ms(8)

(4) To these paths which do not have the maximum persistence

probability, path rate xs,i(t + 1) on path Rs,i:

xs,i(t + 1) =[xs,i(t) − γ(pr∗

s (t) − prs,i(t))

]+, γ > 0 (9)

(5) To the path Rs,j that has the maximum persistence prob-

ability and set its rate to:

xs,j(t + 1) =[xs(t + 1) −

∑i∈[1,ns],i �=j

xs,i(t + 1)]+

(10)

and then communicates all the new flow rate xs,j(t + 1) to

links l contained in path Rs,i.

At the step t+1, the persistence probability of link l depends

on two aspects: the first one is the current flow rate relative

to link capacity, while the other one is the other users affects

current link. In the case of path rate, the rates on all paths

that have less than the maximum persistence probability are

reduced by an amount proportional to the absent probability,

and the rate on the maximum probability path is increased, so

that the new rates on all paths sum to the new total source

rate determined in the flow control decision.

B. Characteristics of OC-MAC

As to optimum problem, we first associate Lagrange multi-

plier for each of the constraints, and use the KKT optimality

conditions for optimization [7], [13], solving this problem is

equivalent to satisfying the complementary slackness condition

and finding the stationary points of the Lagrange.

Lsys = L(x, P, λ̄, λ)

=∑s∈S

Us(xs) − λ̄s(xs −ns∑i=1

xs,i(Ps)) − λTl (c-Rx)

= (∑s∈S

Us(xs) − λ̄sxs) + λ̄s

ns∑i=1

xs,i(Ps)

− λTl (c-Rx) (11)

where λ̄ = [λ̄1, λ̄2, . . . , λ̄S ], λ = [λ1, λ2, . . . , λL]T . By lin-

earity of the differentiation operator, this can be decomposed

into two separate maximization problems

maxx�0

Lx(x, λ̄) =∑s∈S

Us(xs) − λ̄sxs

maxP�0

LP (λ̄, λ, P ) = λ̄s

ns∑i=1

xs,i(P ) − λTl (c-Rx)

= λ̄s

ns∑i=1

( minl∈[1,Ns,i]

clpl

∏k∈NI

to(l)

(1 − ∑m∈Lout(k)

pm))

−λTl pl(cl − xl)

The first maximization is already implicitly solved by the

congestion control mechanism for different Us [11], [15],

[16], while the second maximization also need to solve which

aims at allocating exactly the right persistence probability of

each link to reduce the congestion at the network bottlenecks.

Here, we focus on proving the convergence of the persistence

probability problem.

Because max LP (P ) is a typical non-concave (non-convex)

problem, it is difficult to take the derivative of LP (P ) with

respect to pl directly. To get around the difficulty, we take

logarithm operator on LP (P ) to get LP (P̃ ), that is LP (P̃ ) =

minl∈[1,Ns,i]

ns∑i=1

log(clpl

∏k∈NI

to(l)

(1− ∑m∈Lout(k)

pm))+ log pl(cl −xl), where p̃l = log pl. According to [7], it is easy to show

that the partial Lagrange is a strictly concave function of

a logarithmically transformed probability vector. So we can

507

decompose that

LP (P̃ ) =ns∑i=1

log[clpl

∏k∈NI

to(l)

(1 −

∑m∈Lout(k)

pm

)

−∑

n∈LIfrom(tl)

cnpn

∏k∈NI

to(n),k �=tl

(1 −

∑m∈Lout(k)

pm

)]

+ log pl

(cl −

∑s

Rs,ix)

Taking the derivative of LP (P̃ ) with respect to P̃ , we have

∇lLP (P̃ ) =(cl −

∑s

Rs,ix) − pl

∑k∈LI

from(tl)

εk

1 − ∑m∈Lout(tl)

pm

Coming back to the P solution space instead of p̃l, it is easy

to verify that the derivate of LP (P ) with respect to pl is

∇lLP (P ) =cl −

∑s

Rs,ix

pl−

∑k∈LI

from(tl)

εk

1 − ∑m∈Lout(tl)

pm(12)

Therefore, the logarithmic change of variables simply scales

each entry of the gradient by pl: ∇lLP (P ) = ∇lLP (P̃ )/pl.

We now use the subgradient method [14], with a constant step

size κ, to maximize LP (P )

pl(t + 1) = pl(t) + κ∇lLP (P )

=[pl(t) + κ

cl −∑s

Rs,ix

pl(t)− κ

∑k∈LI

from(tl)

εk

1 − ∑m∈Lout(tl)

pm

]1

0

This is the exact step (1) in the OC-MAC algorithm. Substi-

tuting the known equation into xs(t + 1) =[U ′

s

(pr∗

s (t))]Ms

ms

to compute the total rate of s at t + 1, the following is the

same as the proof in [10]. Since xs,i can be turned into

a concave function in P , each constraint xs ≤ns∑i=1

xs,i(P )

is upper bound constraint on a convex function in (x, P ),problem (6) can be turned into maximizing a strictly concave

objective function over a convex constraint set. Therefore, the

established convergence is towards the global optimum.

IV. SIMULATION RESULTS

First, we compare the proposed OC strategy with respec-

tively a “conventional” client-server scheme (using IEEE

802.11 at the MAC layer, and for which the gateway is the only

source), a “no-relay” cooperation approach (it does not use any

relay, but uses our VDP) and an “always-relay” cooperation

approach (it uses our VDP with as much relays as possible at

any time losing energy unwisely). For notational convenience,

we note the above three competing schemes as conventional,

no-relay and always-relay scheme, respectively. Fig. 1 shows

the throughput variation as the number of nodes increases

(PPS: number of Packets successfully received Per Second).

The proposed OC method can be seen to achieve a much

Fig. 1. Throughput comparisons for various nodes (the speed is 100km/h).

higher performance in terms of throughput compared to the

conventional client-server method. Obviously, this is due to the

introduction of the cooperation. For the cooperative system,

there are many possible sources to provide the information

that other nodes may be interested in. It should also be noted

from this figure that the performance achieved by the proposed

OC method is also superior to the no-relay and always-relay

cooperation methods.

Fig. 2 shows the influence of the speed of nodes on

the throughput performance. With the increase of speed, the

link quality deteriorates. Our proposed OC can achieve a

satisfactory performance because a relay node keeps a copy

of the data frame which increases the possibility of a correct

reception if it is necessary to employ the relay. One can deduce

from this figure that a relay is useful when the velocity is large

and channel conditions are not good.

Finally, to demonstrate the effectiveness of our proposed

OC-MAC algorithm for the cooperative VANETs system, we

plot the throughput curves in Fig. 3 when the nodes speed

is equal to 130km/h. The proposed OC-MAC scheme is

benchmarked against the scheme with only OC, for which no

control method is employed. The proposed OC-MAC method

can be seen to achieve a much higher performance in terms

of throughput.

V. CONCLUDING REMARKS

Based on the selected objective simulation results described

above, there are three main observations:

• Opportunistic cooperation strategy can improve the

throughput of the VANETs.

• The joint optimal control algorithm actually adjusts flow

rates at Transport layer according to the link persistence

probability adjusted at the MAC layer.

• The proposed OC-MAC scheme outperforms the compet-

ing schemes and can provide a good service for practical

VANETs system.

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Fig. 2. Throughput comparisons for various speeds (the number of nodes is20).

Fig. 3. Performance comparisons when speed is 130km/h.

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