Cooperative Content Offloading Through WiFi and Mobile Device-to-Device Networks

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by  Guoqiang Mao

Cooperative Content Offloading Through WiFi and Mobile Device-to-Device
Networks
Guoqiang Mao1,2 and Xiaofeng Tao2
Abstract—ThispaperinvestigatestheuseofWiFiandmobile This paper proposes a novel cooperative content dissem-
device-to-devicenetworks,withvehicularadhocnetworksbeing ination and offloading strategy for a heterogeneous network
a typical example, as a complementary means to offload and consisting of different types of devices with different levels
reducethetrafficloadofcellularnetworks.Anovelcooperative
of mobility, ranging from static WiFi access points (APs) to
content disseminationstrategy isproposedfor a heterogeneous
7 network consisting of different types of devices with different mobiledevicessuch as vehicles,to reducethe traffic load of
1
levels of mobility, ranging from static WiFi access points to cellular networks while guaranteeingthe successful delivery
0
mobiledevicessuchasvehicles. Theproposedstrategy offloads ofcontent.Thestrategyisparticularlysuitedforthedelivery
2
asignificantproportionofdatatrafficfromcellularnetworksto
of delay tolerant content. More specifically, the following
n WiFiordevice-to-devicenetworks.Detailedanalysisisprovided
contributions are made in the paper:
a forthecontentdisseminationprocessinheterogeneousnetworks
J adopting the strategy. On that basis, the optimal parameter 1) a cooperative content dissemination strategy is pro-

3 settings for the content dissemination strategy are discussed. posed,whichexploitsallthreedatadisseminationmeth-
] Sstirmatuelgaytioenffeacntidvelnyurmeedruicceasl dstautadietsraffishcowforthcaetllutlhaer npertowpoorsekds ods,i.e.cellularnetworks,complementarynetworksand
I while guaranteeing successful content delivery. device mobility, to disseminate content;
N
2) erasure codes, to be introduced in Section III, are
. I. Introduction employed to further reduce the data traffic load;
s
c Recent years have seen an exponential annual increase 3) analytical results are presented to stochastically char-
[ in mobile data traffic [1], [2]. Content dissemination and acterise the content dissemination process, taking into

1 offloading, where a portion of data traffic is offloaded from account the heterogeneity in the devices, in terms of
v cellular networks to high-capacity and low-cost comple- mobility and transmission capability. In particular, the
7 mentary networks, including WiFi, vehicular and device-to- reduction in the amount of data traffic in cellular net-
3
device networks, to ease the burden of cellular networks, works is calculated;
8
0 becomesanincreasinglyimportantandchallengingtask[3]– 4) based on the above results, optimal parameter settings
0 [9]. of the content dissemination strategy are discussed,
1. In addition to complementary networks, the mobility of which minimise the data traffic load of the cellular
0 users can also be exploited to assist the content dissemi- network while guaranteeing the successful delivery of
7 nation. When users carry mobile devices physically while all content.
1
walkingarounduniversitycampus,shoppingcentresortrav- Therestofthispaperisorganisedasfollows:SectionIIre-
:
v elling by taxis, buses or privatevehicles,the contentin their viewsrelatedwork.SectionIIIintroducesthesystemmodel,
i mobiledevicesalsomovewith themwithoutconsumingany including the content dissemination strategy. Section IV
X
bandwidth. Together with device-to-device communication presents the analysis of the content dissemination process,
r
a technologiessuchasvehicle-to-vehiclecommunications,mo- whose optimal design is studied in Section V. Section VI
bility of users offers an alternative way to transport delay- validates the analysis using simulations. Finally Section VII
tolerant content efficiently and cost effectively [1]. concludes this paper and discusses possible future work.
A large proportion of the content delivered over mobile
networks is delay-tolerant content, like videos, newspapers, II. Relatedwork
weather reports and vehicular info-entertainment. For these
In this section, we give a brief review of the work most
types of content, content offloading reduces the traffic load
related to this paper.
of cellular networks (and boosts the capacity of cellular
Recent research [9] has shown that WiFi networks have
networks in the sense that more users can be served) and
already carried and offloaded a large amount of mobile data
also provides a higher data rate for the users. The expense
traffic. When a device enters into a WiFi covered area, it
is that content offloading will incur higher delay compared
can switch its data traffic from cellular networks to WiFi
with direct transmission using cellular networks.
networks[10]to reducethe traffic load of cellular networks.
AmajorissueinWiFioffloadingistheoptimumdeployment
This research is supported by Chinese National Science Foundation
project 61428102. of WiFi APs. Bulut et al. [10] compared different methods
1 School of Computing and Communications, The University of Tech- of deploying WiFi APs for efficient offloading of mobile
nologySydney
data traffic. They also proposed a greedy approach that can
2 National Engineering Lab. for Mobile Network Security, Beijing
University ofPostsandTelecommunications achieve a high offloading efficiency.
In additionto usingWiFi APs, recenttechnologyhasalso B. Wireless communication model
allowed mobile devices to become a virtual WiFi access
We consider two types of wireless networks: the cellular
points(a.k.a.WiFi Tethering),sothatdevicescancommuni-
network and the complementarynetwork. It is assumed that
catewithoneanotherviaadhocconnectionswithoutrelying
everynodeis directly connectedto at least one cellularbase
oninfrastructure.Inthisway,devicescancooperatewithone
station (BS) at anytime. Inthe complementarynetwork,de-
another to disseminate content.
vices communicatewith one anothervia ad hoc connections
Usingatypicalcooperativecontentdisseminationstrategy
using device-to-device communication technologies such as
[11], the service providersfirst deliver the content to only a
Bluetooth, WiFi or DSRC [18]. These ad hoc connections
smallgroupofusers,thentheseuserscanfurtherdisseminate
are usuallyof highcapacity,andcan be exploitedbymobile
the content to other subscribed users when their mobile
devices to cooperatively share content of common interest.
devices are in the proximity and can communicate using
Due to the limited communication range, the ad hoc
WiFi tethering or Bluetooth technology. It is obvious that
connection between two nodes only emerges opportunisti-
such opportunistic content dissemination cannot guarantee
cally when they move close to each other. Considering a
the delivery of content. This paper proposes a mechanism
commonlyusedmodel,calledtheunitdiskconnectionmodel
that can provide guarantee on the delivery of content.
(UDM),two nodesare directlyconnectediff their Euclidean
Furthermore, some work in cooperative mobile data of-
distance is not larger than the radio range r . Adopting this
0
floading(e.g.[1], [12])investigatedthe design and selection
commonly used connection model, we say that two nodes
of helpers,viz.some specialmobile devicesselected to help
meet each other when they move into the radio range of
the content provider to deliver messages to other mobile
eachother.Consequentlydefinetheinter-meetingtimeoftwo
devices using ad hoc connections.
nodesasthetimeintervalbetweentwoconsecutivemeetings
As vehicular networks form an important class of mobile
of two nodes (a more rigorous definition is given later in
networks, there is significant research on content dissemi-
Section IV-A).
nation in vehicular networks [8]. Wireless access through
Therehavebeenanumberofstudiesonthedistributionof
vehicle-to-roadside communications can be used in public
theinter-meetingtime.Inparticular,CaiandEun[19]analyt-
transportvehiclesforstreamingapplications,e.g.,videosand
icallyprovedthatfortwonodesmovinginafinitearea(with
interactiveadvertisements.As pointedout in [13],it is chal-
reflective or wrapping boundary)under randomwaypoint or
lenging to develop an efficient wireless access scheme that
random walk mobility models, their inter-meeting time has
minimises the cost of wireless connectivityfor downloading
an exponential distribution, whereas the inter-meeting time
data. There are also some empirical studies on content
of nodes moving in an infinite area follows a power-law
dissemination methods for vehicular networks [14].
distribution.
III. Systemmodelandcontentdisseminationstrategy This paper also considers that the inter-meeting time
follows an exponential distribution. The analysis presented
A. Network model
in this paper however is directly applicable to other inter-
We consider a network of N nodes. These N nodes can
meeting time distributions as shown in Section IV-A.
be classified into H types according to their mobility, e.g.
static WiFi APs, mobile devices carried by pedestrians and
C. Cooperative content dissemination strategy
vehicles, and social characteristics, e.g. students in the same
class. Let N be the number of nodes of the hth type: This subsection describes the cooperativecontent dissem-
h
H N = N. ination and offloading strategy.
h=1 h
PSuppose that at some initial time instant t = 0, the N ConsiderthatacontentproviderhasMmessagestodeliver
nodesareindependently,randomlyanduniformlydistributed to the N nodes. The contentdissemination processhas three
on a torus (0,L]2 [15]. It follows that the nodes’ density phases: initial phase, sharing phase and complement phase.
in this network is λ = N/L2. Then these nodes start to Phase 1 Initially at time t = 0, the cellular BSs transmit β
moveindependentlyaccordingtosomemobilitymodels[16]. packets to β different nodes via cellular networks.
We assume that the nodes’ mobility is such that the spatial Note that the content in these packets depends
distributionofnodesisstationaryandergodicwithstationary on the coding scheme to be described in Section
uniformdistributiononthetorus.Asshownin[17],anumber III-C.1.
of mobility models have this property. Phase 2 Then the network enters into the sharing phase,
Theuseofa toroidalratherthanplanarregionasatoolin wherethenodesbroadcasttheirreceivedpacketsvia
analysingnetworkpropertiesiswellknown.Theuseoftorus ad hoc connections using the Susceptible-Infected-
allows nodes located near the boundary to have the same Recovered(SIR) epidemic scheme, to be described
number of connections probabilistically as a node located in Section III-C.2.
nearthecentre.Thereforetheconsiderationofatorusimplies Phase 3 At time T (called deadline), the sharing phase
end
that there is no need to consider special cases occurring stops and then the network enters into the com-
near the boundary of the region. This often simplifies the plement phase, where every node requests the re-
analysis without obscuring the relationship between main mainingpacketsrequiredtodecodeall M messages
performance-impactingparameters. from BSs, where the remaining packets requiredto
decode the messages are determined by the coding disseminations and minimises the traffic load of the cellular
scheme. network by fully utilising the complementary networks to
The main objective of the content dissemination strategy share content.
is to minimise the total number of packets requiring to Notethatthispaperconsidersalargenetworkwhere N ≫
be transmitted through cellular networks, which include the M. Furthermore, in the next section, when we consider an
packetstransmittedintheinitialphaseandinthecomplement asymptotic network with N → ∞, we increase the network
phase, while guaranteeing the successful delivery of the areaL→∞whilekeepingthedensityofeverytypeofnodes
content. unchanged. That is, a well-known extended network model
1) Coding scheme: We consider the use of a simple is considered. The analytical results obtained are therefore
erasure coding scheme. Specifically, the M messages are applicable for a large network only.
encoded into β coded packets [20]. We assume that the IV. Analysisofthecontentdisseminationprocess
Galois field [20], [21] used in the encoding process is large
The main challenge in the analysis of the content dis-
enough so that the content provider can generate β linear-
semination process is the characterisation of the packet
independentlycodedpackets.Itfollowsthateachnodeneeds
propagation process in the sharing phase. This section first
to acquire M distinct coded packetsto reconstructall the M
analyses the propagation process of a single packet, say the
messages.
packet j, and then generalises to multiple packets.
Consequently, if a node receives B < M distinct coded
packets by the end of the sharing phase, then it needs to A. Characterising the ad hoc connections
request M−B coded packets in the complement phase via
DenotebyT theinter-meetingtimebetweenarandomly-
cellular networks in order to decode all M messages. h,k
chosen type-h nodeand a randomly-chosentype-k node,for
For benchmarking, we also consider the case that no
h,k∈{1,2,...,H}. Assume that T follows an exponential
codingtechniqueisemployed.In thiscase, the BSs transmit h,k
distributionwithmeanλ .Thepdfoftheinter-meetingtime
βˆ ∈{0,1,...,β} copesof the mth message in the first phase h,k
m isthengivenbyPr(T =t)=λ exp(−λ t).Itfollowsthat
for m = {1,2,...,M} and M βˆ = β. Then each node h,k h,k h,k
m=1 m the probability that the type-h node meets the type-k node
needs to receive at least onePcopy of each message. during the active period τ of the type-h node is
2) Epidemic sharing scheme: In the sharing phase, the h
β packets are shared among N nodes using a Susceptible- τh
γ = Pr(T =t)dt=1−exp(−λ τ ). (1)
h,k h,k h,k h
Infected-Recovered(SIR) epidemic sharing scheme. Z
0
Without loss of generality, consider the epidemic sharing Note that given other probability distribution of inter-
of an arbitrary packet, say packet j. Using a classic SIR meetingtime,onecanuseasimilarmethodtocalculateγ .
h,k
broadcastscheme,anodeinthenetworkcanbeinanyofthe Thus our analysis does not critically dependon the assump-
following three states: the node that has never received the tion of the exponential inter-meeting time distribution.
packet jisinthestateofsusceptible(S ).Asusceptiblenode
j
goesintothestateofinfectedandinfectious(I )immediately B. Extinct probability
j
after receiving the packet j. The node in state I keeps In this subsection, we construct a multi-type branching
j
transmittingthe packet j to everynodeit meetsfora certain process [22], [23] to study the number of informed nodes
timeperiod,whichisreferredtoastheactiveperiod.Denote of a typical packet, say packet j, where the 0th generation
by τ the length of the active period of a type-h node. Note of the branching process includes the nodes that receive the
h
that τ is a pre-determined value, which is the same for all packet jattime0(i.e.inthefirstphase).Further,thenumber
h
nodes of the same type. After the active period, the node of type-k children generated by a type-h node is denoted by
recovers and enters into state R . A recovered node stops a random variable Qˆ . Because nodes move independently
j h,k
transmitting and receivingthe packet j. The nodesthat have of one another, it is evident that Qˆ follows a Binomial
h,k
received the packet j are referred to as the informed nodes distributionBin(N ,γ ),whereγ isgiveninEq.1.Denote
k h,k h,k
of the packet j. byXh thenumberoftype-hnodesintheαth generation.The
α
Note that the value of τ may be different for different branching process modelling the number of informed nodes
h
types of nodes. For example, a pre-installed WiFi AP can foratypicalpacketbecomesextinct ifthereexistsaninteger
have a significantly larger value of τ compared with other value of α such that H Xh =0.
h h=1 α
mobiledevicesthatarepoweredbybattery.Further,thevalue The following resuPlt is required in the later analysis:
of τ for a mobile device can be tuned by introducingsome
h Lemma 1 (Threshold phenomenon). Define matrix Ξˆ ,
incentives(e.g.a lower subscriptionfee or some rewards)to
{E[Qˆ ] = N γ ;h,k = 1,2,...,H}. Let R be the largest
the mobileusers[12],so thatthemobileusersarewillingto h,k k h,k q
eigenvalue of Ξˆ. Then the branching process will become
share more packets with other users.
extinct with probability 1 if and only if R ≤1.
When the length of the sharing phase T is long, the q
end
epidemic sharing process stops naturally (i.e. reaches the This result can be readily obtained by applying Theorem
steady state) when,for all the packets, there is no infectious 2 in [22, Chapter V]. Hence the proof is omitted.
node. We are particularly interested in the case where the When R > 1, there is a positive probability that the
q
T is long because it is suitable for delay-tolerant content branching process does not become extinct, i.e. the packet
end
can be disseminated to a significant fraction of nodes as the are the solutions to the following system of equations:
network size becomes asymptotically large.
H
Note that in a heterogeneous network, the type of source w = exp N γ (w −1) , (5)
1 k 1,k k
nodes that a branching process is rooted at can have a ... Yk=1 (cid:0) (cid:1)
significant impact on the probability that the branching
H
processbecomesextinct.Denotebyw theextinctprobability
h w = exp N γ (w −1) ,
H k H,k k
of type-h source, which is defined as the probability that a
Yk=1 (cid:0) (cid:1)
branching process rooted at a type-h node becomes extinct.
where N is the number of type-k nodes in the network and
The following theorem characterises w . k
h γ is given by Eq. 1. (cid:3)
h,k
Theorem 1 (Extinct probability). Consider an asymptotic
network with L → ∞ while keeping nodes’ density un- Using Theorem 1, we can further obtain the extinct
changed and the node’s communication range varying with probability for several special-case of networks.
LsuchthatN γ isafiniteconstant1.Theextinctprobabil-
k h,k Corollary 2. [Extinct probability for homogeneous net-
ities w for h=1,2,...,H are the solutionsto the following
h works] Consider the special case of a network with only
system of equations:
H = 1 type of nodes, the extinct probability is w =
1
−W(−Nγ1,1exp(−Nγ1,1)), where W(.) is the Lambert-W function.
H Nγ1,1
w =exp N γ (w −1) , for h=1,2,...,H. (2)
h  k h,k k  Corollary 3. [Extinct probability with multiple source
Proof. Firstly,Xkn=1ote that in the constructionof the branching nβo=des]hH=S1uβphpsoosuerctehantodaespaatctkheet bisegiinnintiinagllyofbprhoaasdeca2s,twfhreorme
process, we consider that every node that a type-h node βh isPthe number of type-h source nodes. Then the extinct
meets is a susceptible node. As the packet propagates, the probability for this packet is hH=1wβhh.
probability that a type-h node meets an informed node Q
The proof of the above two corollaries is straightforward
increases. This may reduce the expected number of newly
and hence omitted.
informed nodes generated by an infectious node. However,
Note that when the branching process does not become
there is no need to consider the impact of this effect in the
extinct, the packet is disseminated to a significant number
analysis of the extinct probability because when analysing
of nodes and we say that the packet spreads out. The next
theextinctprobability,weareonlyinterestedinthecasethat
sub-section quantifies the number of recipients of a packet
the fraction of recipients is vanishingly small (i.e. becomes
when it spreads out.
extinct)as L→∞ and N →∞. Accordingly,the probability
that a type-h node meets an informed node is vanishingly C. Expected fraction of recipients
small and hence negligible.
Denote by zˆ the expectedfraction of type-hnodeswhich
Because N γ is a finite constant as the network size h
k h,k receive the packet j in the steady state, where the packet
increases, the distribution of Qˆ , i.e. a Binomial distribu-
h,k propagationstarts from a randomly-chosensource node and
tion Bin(N ,γ ), approaches a Poisson distribution with an
k h,k the packet spreads out. Now we further investigate zˆ .
expected value N γ [24]. The difference between the Qˆ h
k h,k h,k
and its Poisson distribution counterpart (denoted by Q ) Theorem 2 (Fraction of recipients when a packet spreads
h,k
diminishesas N →∞ and γ →0, where the convergence out). In a large network with N → ∞, suppose that the
k h,k
rate is given in [24]. packet j is broadcast from a randomly chosen source node,
Denote by G (s) the probability generating function of nomatterwhich typethe sourcenodebelongsto.Given that
h,k
Q : the packet is spread out, the expected fractions of recipients
h,k
Gh,k(s)=E[sQh,k]=exp Nkγh,k(s−1) . (3) zˆh for h = 1,2,...,H are the solutions to the following
system of equations
(cid:0) (cid:1)
Further, define the multi-variate probability generat- H
ing function Gˆ (s) , E[sQh1sQh2...sQhH], where s , 1−zˆ =exp − N γ zˆ , for h=1,2,...,H. (6)
h 1 2 H h  k k,h k
{s1,s2,...,sH} is a row vector. It can be shown that  Xk=1 
Thistheoremcan be readilyobtainedfromthe analysisof
Gˆ (s)=G (s )G (s )...G (s ). (4)
h h,1 1 h,2 2 h,H H epidemics [25], [26] and the proof is omitted.
Next we consider the case that there are more than one
Denote the extinct probabilities by a row vector w ,
source node of the packet j.
[w ,w ,...,w ].ThenaccordingtoTheorem2in[22,Chap-
1 2 H
terV],theextinctprobabilitiessatisfyw=Gˆ(w),whereGˆ(s) Corollary 4 (Fraction of recipients with multiple source
is a row vector Gˆ (s),Gˆ (s),...,Gˆ (s) . The conclusion nodes). Supposethatinitiallyattime0,thereare H β =β
1 2 H h=1 h
follows that the exhtinct probabilitieswh foir h={1,2,...,H} nodesthathavereceivedthepacket j,whereβhisPthenumber
oftype-hsourcenodes.Denotebyz(β ,...,β )theexpected
1 H
1Thiscondition isrequiredtoavoidtriviality intheanalysis fractionofnodes,outofthetotalN nodes,whichreceivethe
packet in the steady state. In a large network with N →∞, intheinitialphase.Thentheoptimalstrategythatminimises
there holds the cellular traffic load is to push β different packets to the
H H first β nodes in the above order.
N zˆ
z(β ,...,β )= h h 1− wβh . (7)
1 H  N  h  Proof. First, it can be readily shown that the strategy that
Proof. From CorollaryXh3=,1 the probabYhil=i1ty that the packet minimisesthecellulartrafficloadistopushβdifferentcoded
packets in the initial phase rather than pushing multiple
spreads out is 1− H wβh . Note that if the packet is not
h=1 h copies of any coded packet.
spread out, the(cid:16)fracQtion of re(cid:17)cipients goes to 0 as N → ∞.
Because different encoded packets are shared indepen-
If the packet spreads out, the expected number of type-h
dently of one another, we next consider a randomly-chosen
recipients is N zˆ , where zˆ is given by Theorem 2. The
h h h
conclusion follows. (cid:3) packet, say packet j. It is obvious that to minimise the
cellular traffic load, one needs to maximise the number of
For the special case that there is only H =1 type of node recipientsofpacket j.AccordingtoCorollary4,theexpected
in a network, a closed form expression can be obtained. fraction of nodes, out of the total N nodes, which receive
packet j in the steady state is
Corollary 5 (Fraction of recipients for homogeneous net-
works). Suppose that there is only H = 1 type of node in
H H
a network and a packet is sent to β different nodes in the z(β ,...,β )= Nhzˆh 1− wβh , (10)
first phase. Then in the steady state, the expected fractionof 1 H  N  h 
recipients of this packet is Xh=1  Yh=1 
z(β) = 1+ W(−Nγ1,1exp(−Nγ1,1)) wthheepreroβp1a+gaβt2io+n·o··f+siβnHgl=e 1pabcekceatu-sepawcekeatrej.nIonwocthoenrsiwdeorridnsg,
Nγ !
1,1
only one value among β ,β ,...,β is equal to one and the
W(−Nγ exp(−Nγ )) β 1 2 H
× 1− − 1,1 1,1 . (8) othervaluesareallequalto0.Itisobviousthattomaximise
V. Minimisingthetr afficloadoNfγc1e,1llularnetw! orks zin(βa1,w..a.y,βthHa)t, monienismhiosuesld ashHs=i1gwnβhthh,ei.ev.alluetesthoefoβn1l,yβ2n,o.n.-.z,eβrHo
Basedontheabovecharacterisationofthecontentdissem- value βk =1 for the kth tyQpe of nodes that have the smallest
value of the extinct probability w among all w for h ∈
ination process, this section investigates the optimal content k h
{1,2,...,H}.
disseminationstrategythatminimisesthetotaltrafficloadof
Itcanbeshownthattomaximisethesharingperformance,
cellular networks.
the β coded packets need to be pushed to β different nodes.
Recallthatin the initialphase,the BSs transmitβ packets
Therefore,when the numberof type-k nodes N is less than
to β differentnodesthroughthe cellular network.Denote by k
the total number of packets β, some packets need to be
Y the expected numberof packets that BSs need to transmit
pushed to the nodes that have the second (and if needed,
in the complement phase.
thethird,forth,etc.)smallestvalueoftheextinctprobability
Definition 1 (Cellular traffic load). The cellular traffic w among all w for h∈{1,2,...,H}. (cid:3)
i h
load is the expected number of packets transmitted by BSs
through the cellular network, which consist of the packets
Next we focus on determining the optimum value of β
transmitted in the first and the third phases, i.e. β+Y, in
for the special case of a homogeneous network with H =
order to transmit M messages to N nodes.
1. The optimum value of β for the more general case of
Note that the value of β determines the value of Y, a heterogeneous network with H > 1 can be determined
which is calculated later in this section. Then the problem analogously albeit with greater complexity.
of minimising the cellular traffic load can be formulated as
Denote by random variable B the number of packets
follows:
received by a randomly-chosen node at the end of the
Minimise β+Y
β (9) sharing phase. Then B follows a Binomial distribution, i.e.
Subject to β∈{1,2,...,N}. the probability that a node receives B=b packets is Pr(B=
b)= β (z(1))b(1−z(1))β−b, where β = β! .
Using the erasure coding technique introduced in Section b b b!(β−b)!
Th(cid:16)en(cid:17) in the complement phase(cid:16), (cid:17)the number of packets
III-C.1,theBSspushβcodedpacketstoβdifferentnodesin
that need to be transmitted to a randomly-chosen node is
the initial phase. The following lemma gives the optimum
(M−B)+, where (x)+ =max{0,x}.
strategy to choose the source nodes to disseminate the
packets. Finally,theexpectednumberofpacketsthatthe BSsneed
to transmit in the complement phases is
Lemma 6 (Sharing maximisation strategy). Label all nodes
in the networkin the descendingorderoftheirvaluesofwh, Y = NE[(M−B)+] (11)
which is given by Theorem 1. If more than one node have
M
β
thesamevalueofwh,theirordercanbearbitrarilyassigned. = N (M−b) (z(1))b(1−z(1))β−b. (12)
SupposethatBSspushβencodedpacketstoβdifferentnodes Xb=0 b!
Then the optimisation problem in Eq. 9 becomes Fig. 2 shows the results of another interesting case where
thecomplementarynetworkconsistsofasetoffixed-location
M
β base stations (e.g. WiFi APs). In the second phase, the
Minimise β+N (M−b) zb(1−z )β−b
β Xb=0 b! 1 1 (13) message is disseminated from these WiFi APs to mobile
users (i.e. type-1 nodes). Specifically, we consider that a
Subject to β∈{1,2,...,N}.
small number of WiFi APs are randomly and uniformly
deployed in a given area, which is a widely-used setting
This optimisation problem can be readily solved numer-
for AP deployment [2]. Because the WiFi APs are usually
ically using Matlab, where the results are presented in the
connected to the Internet via wired connections, we set
next section.
γ = 1. Other parameters are the same as those in the
2,2
previous sub-section. A message is transmitted to all the
VI. Simulationanddiscussion
WiFi APs at time 0. Then the WiFi APs keep transmitting
This section reports on simulations to verify the accuracy the message for a given time period τ2. In Fig. 2, we let
of the analysis presented in the previous sections. The the active period of type-2 nodes be τ2 = 500,1500 while
simulationsare conductedusing a mobile networksimulator varying the active period of type-1 nodes. Note that τ1 = 0
written in C++. Specifically, N = 960 nodes are uniformly correspondsto the traditional case [9], [10] where nodes do
deployed on a square (0,8000]2. Consequently the nodes’ notcooperativelysharereceivedpacketsandtheysolelyrely
densityequalsto15nodes/km2,whichisequaltothedensity on WiFi APs to offload data traffic from cellular networks.
of cabs in New York metropolitan area [27]. After initial Itcan be seenin Fig. 2 thata longeractiveperiodofmobile
deployment of the nodes, they start to move according to nodes τ1 leads to a larger expected fraction of recipients.
the random direction mobility model. When the nodes hit It is obvious that packet sharing using ad hoc connections
the boundary of the square, they may appear from the other between mobile nodes can significantly increase the number
sideoftheboundary.Itcanbeshownthatwhennodesmove of recipients of a packet, hence reducing the number of
accordingto the randomdirectionmobility model,the inter- transmissions required by BSs.
meetingtimefollowsanexponentialdistribution.Thenode’s
H=2, V=10, V=0, λ=0.000015, r=20, τ=0~500, N=10 WiFi APs
speed is V = 10m/s (typical vehicle moving speed). The nts 1 1 2 0 1 2
e
radio range r = 20m or 250m (typical radio ranges using pi
Wsimi-uFliatTioenthereris0nugltoisr tDheSRavCer[a1g8e])v.aEluveerfyropmoi5n0t0shsoimwunlaitniotnhse. action of reci000...468 ASAninmaa τττ22===5510050000
Consider two types of nodes moving according to the ed fr0.2 Sim τ2=1500
ir.aen.dmomobdiliereacntidonstmatoicdenlowdeitsh,sapnededthseVre1 =are10emqu/aslannudmVb2e=r o0f, Expect 00 100 200 300 400 2 500
Active period of mobile nodes τ
1
nodesineachtype.Fig.1showstheprobabilitythatapacket
spreadsoutandtheexpectedfractionofrecipientsofasingle Fig.2. Theexpected fraction ofrecipients ofapacket inanetwork with
10fixedWiFiAPsandsomemobilenodes.
packet. The analytical result of the probability that a packet
spreads out when the source node is of type-1 (resp. type- The following results further evaluate the cellular traffic
2) is givenby w (resp.w ) from Theorem1. The analytical loads.
1 2
resultoftheexpectedfractionofrecipientsofapacketwhen Fig. 3 shows the expected cellular data traffic load β+Y
thesourcenodeisoftype-1(resp.type-2)isgivenbyz(1,0) with different values of β, viz. the number of packets sent
(resp. z(0,1)) from Corollary 4. It is interesting to note that in the first phase, using different content dissemination
the probability that a packet spreads out and the expected strategies.Tostudytheimpactofcodingonthecellulartraffic
fractionofrecipientscanbesignificantlyaffectedbythetype load,weconsidertwonetworkswiththesamesettingexcept
ofsourcenode.Morespecifically,otherthingsbeingequal,it that one network employs the erasure coding technique
can beseen thata mobilesourcenodecanspreadthe packet (c.f. Section III-C) but the other network does not. The
to more recipients than a static source node. performance of the network without employing network
coding can be readily obtained using the same technique
H=2, V=10, V=0, λ=0.000015, τ=τ=τ=1~50, β=1, Source Node Type (ST)=1 or 2 adoptedforanalysingnetworkemployingtheerasurecoding
Probability of spreading out0000....0124680 110 220 30 SASA4ininmm0aa SSSS1TTTT====521212 0 Expected fraction of recipients0000....0124680 10SASAininmmaa 2 SSSS0TTTT====1212 30 40 5 0 rtFlcteireoimaclrmSanhsittestnpilemvvyildqeee,irumltwaytneeleu.hdhnmeiittnngaobtrheeytβhrrceeniesostelufiltsnuswemnglaroosarrdtlkvrlete,,risaanthffidwcreeseocncllceculneioalveanaetmrdw.nbtooheeTsrettkwhsoipposbaahrskcciaeskksvr.eeevbAtteessadscataβshuriirnemsioneuicdFlgraoiierrhngeal.csaytetnhl3sdyae.,
(a) Length of active period τ (b) Length of active period τ the cellular traffic load first decreasesrapidly,due to a rapid
increase in the expected fraction of recipients in the sharing
Fig.1. Simulationandanalyticalresultsof(a)Theprobabilitythatapacket
phase.Thenafteracertainpoint,thecellulartrafficloadstarts
spreadsoutand(b)theexpected fraction ofrecipients ofapacket.
to graduallyincreasesas βfurtherincreases.Thisis because numberof recipientsof a packetatan arbitrarytime instant.
theexpectedfractionofrecipientshaslimitedincreasewhen Furthermore, it is an interesting extension of our work
βincreasesfurther;ontheotherhandtheincreaseinβcauses to consider different probability distributions for the inter-
morecellulardatatraffic.Itisinterestingtonotethatsending meeting time of nodes, which can be affected by the nodes’
outmorepacketsintheinitialphaseisnotalwaysbeneficial. mobility and network area as described in Section III.
Furthermore, it is interesting to note that above a certain
valueofβ,e.g.β=17inFig.3(a),thetrafficloadofcellular References
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