Computer Communications 35 (2012) 1819–1827

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Computer Communications

journal homepage: www.elsevier .com/locate /comcom

Distributed media-aware flow scheduling in cloud computing environment

Joel J.P.C. Rodrigues a,⇑, Liang Zhou b, Lucas D.P. Mendes a, Kai Lin c, Jaime Lloret d

a Instituto de Telecomunicações, University of Beira Interior, Portugalb Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Chinac Dalian University of Technology, Chinad Polytechnic University of Valencia, Spain

a r t i c l e i n f o a b s t r a c t

Article history:Available online 15 March 2012

Keywords:Body area networkCloud computingMedia-aware schedulingMultimedia application

0140-3664/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.comcom.2012.03.004

⇑ Corresponding author. Tel.: +351 275 319 891.E-mail addresses: joeljr@ieee.org (J.J.P.C. Rod

(L. Zhou), lucas.mendes@it.ubi.pt (L.D.P. Mendes)jlloret@dcom.upv.es (J. Lloret).

Media-aware flow scheduling in cloud computing environment has attracted much attention nowadaysbecause of the new possibilities they bring to many research and industry fields. Particularly, body areanetworks, as a typical computing environment application in healthcare, allow ubiquitous monitoring ofpatients, and more thorough patient diagnoses can be done with the help of multimedia service. In thiswork, we propose a novel media-aware flow scheduling architecture with the aims of improving the mul-timedia quality and increasing the network’s lifetime. In order to avoid interfering with the multimediaapplications’ delay requirements, this work also proposes to analyze frames delay and jitter. The proposalhas proven to improve the multimedia quality and decrease the transmission delay in a controllable man-ner, and thus the tradeoffs between QoS, lifetime, and delay requirements can be achieved according tothe considered scenario. In addition, extensive simulation results validates the efficiency of the proposedmethod.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Cloud computing environment (CCE) has received much atten-tion recently since it viewed as an alternative to conventionaloffice-based computing [1]. As CCE becomes more widespread,the demand of the multimedia service in CCE has increaseddramatically [2]. Typically, the architecture of CCE is comprisedby restrained devices called sensor nodes, which can sense envi-ronmental conditions, perform local processing, and send theacquired data to a base station through wireless links. It is fore-seen that these devices can be used in several fields, such as inmedicine [3], security [4], industry [5], and others.

Currently, body area network (BAN) is developed as a typicalapplication scenario in CCE [6]. Despite the advantages that theuse of BAN can bring to multimedia applications, there are someproblems that limit their dissemination. The main concern is thatsensor nodes are small and have limited battery as power source.Hence, the lifetime of the BAN is dependent of the used routingprotocol, modulation, frames scheduling, security mechanisms,and the application requirements. With regard to a specific videoapplication, quality of service (QoS) is also a problem, since videopackets cannot experience long delays, or the goal of the network

ll rights reserved.

rigues), liang.zhou@ieee.org, link@dlut.edu.cn (K. Lin),

may be compromised [14]. Therefore, all solutions for the afore-mentioned problems need to be energy efficient.

One of the techniques that has proven to use sensors resourcesmore efficiently in BAN is cross-layer design [7]. Cross-layer designstates that parameters of two or more layers can be retrieved and/or changed in order to achieve an optimization objective. This con-cept has been first proposed for TCP/IP networks, when wirelesslinks were deployed [8], and it has been used not only to overcomeenergy limitations, but also increase network throughput and toimprove quality of service.

It can be seen in the literature on cross-layer design that twomedium access methods are generally considered – carrier sensemultiple access (CSMA) and time division multiple access (TDMA).The first is frequently considered in wireless sensor networks witha large number of nodes [9]. However, the scenarios considered inthis work are comprised of at most 20 sensor nodes, and thus theuse of CSMA would incur in unacceptable medium contentionoverheads. The second provides a simpler analysis, but at the costof synchronization overhead. Achieving nodes synchronization isnot an easy task, and it is a research field by itself [10]. Thus, inorder to avoid the disadvantages of these medium access methods,slotted ALOHA is considered in this work.

In this work, a cross-layer proposal for energy consumptionreduction through sleep periods is proposed. In particular, amedia-aware low scheduling scheme is presented by joint consid-ering the characteristics of network and applications. Also, analyt-ical expressions are derived in order to analyze frame delay and

1820 J.J.P.C. Rodrigues et al. / Computer Communications 35 (2012) 1819–1827

jitter, and they are validated through simulations. Slotted ALOHAmedium access method is considered for the reasons given previ-ously, using body area networks and multimedia sensor networksas scenarios for performance assessment.

The remainder of the paper is organized as follows. Preliminar-ies related to this work is presented in Section 2. In Section 3, thesystem model, the considered characteristics of IEEE 802.15.4 andIEEE 802.15.3 protocols are shown, and the problem is formulated.The distributed media-aware flow scheduling scheme is proposedin Section 4. The analytical expressions and delay and jitter analy-sis methodology are presented in Section 5. Extensive simulationresults of frame delay and jitter analysis, and also the analyticalexpressions validation, are shown in Section 6. Finally, the conclu-sions and possible future work are pointed out in Section 7.

2. Related works

2.1. Multimedia applications in CCE

In order to provide multimedia services, CCE as to face the chal-lenges imposed by these applications. Some of the challenges iden-tified by Akyildiz et al. [7, 11] are resource constraints, quality ofservice (QoS) requirements, high data transmission rates, variablewireless channel capacity, parameters interdependence acrossthe layers, and data coding and processing. As also pointed bythe aforementioned authors, multimedia applications in CCE areused for many different applications, including surveillance andhealth-care. An example of these applications is given next section.

Luo et al. [24] have proposed a new mannerless human gaittracking system that simplifies the expensive and lengthy processused in clinics. Their cross-layer transmission process determinesthe video quantization step and the adaptive modulation andcoding (AMC) scheme according to the channel bit error rate.Thus, the delay and video distortion bounds are respected whiletransmission is adapted according to the channel state. In theirexperiments, video playback deadlines of 20, 30, and 40 [ms]have been defined, and they have proven to achieve gains of3–5 [dB] in the peak signal-to-noise ratio of the video transmittedframes.

A scenario with 18 video sensor nodes with a central processingunit has been defined by Wang et al. [18] in order to assess the vi-sual recognition efficiency of their proposed algorithm. The videosensor nodes are trained by using raw data in order to recognizehuman targets and objects. Then, when acquiring data for classifi-cation, the irrelevant set of data for target recognition is detectedand discarded, and the relevant part is compressed. A decision ismade by each sensor node and transmitted to the central process-ing unit, which is responsible for combining the observations toachieve a final result. Their new algorithm has proved to greatly re-duce the training and classifying time, and thus sensors spend lessenergy on data processing. In another paper by the same authors[19], the effects of the adopted computing paradigm on the recog-nition accuracy and delay is assessed. The comparison has beencarried out considering centralized client/server (C-CS), distributedclient/server (D-CS), mobile agent (MA), and peer-to-peer (P2P)paradigms. Then, it has been pointed out that the P2P paradigmcould yield the best accuracy and delay on the target recognitionprocess. However, these authors have not addressed the issueson the transmission between the sensors and the central unit,focusing only on the target tracking process.

2.2. An example: BAN for healthcare

Body area networks (BAN) are generally characterized by theuse of a few sensors and a coordinator that receives data from

the sensors and have some degree of control over them. Thiscommon topology for BSNs has been used to define the behaviorof the wireless channel near the human body. Chen et al. [20] haveconsidered only one sensor communicating with a gateway nodethrough the ultrawideband (UWB) technology. Also, they have pro-posed the use of cooperative nodes to relay data from the sensor tothe gateway, increasing the diversity gain and improving the qual-ity of the signal received at the gateway. Furthermore, Reusens etal. [21] have characterized the channel model considering differentparts of the body – legs, arms, torso, and back. They have also con-sidered the impact of the sensors topology on the sensors energyconsumption, arguing that multihop communication is needed.However, for multihop communication, a larger number of sensorsis needed, and in their work they have even considered 6 node lev-els, which is generally not the scenario seen in BSNs. Thus, in thiswork single-hop transmission will be considered.

Su and Zhang [17] have proposed a cross-layer time divisionmultiple access (TDMA) method considering the battery dischargedynamics, the healthcare applications quality of service (QoS)requirements, and the channel quality to control the used modula-tion. They have proven that their proposal outperforms IEEE802.15.4 [22] and Bluetooth in terms of delay and packet loss rate.In order to carry out the performance assessment, the authors haveconsidered a case with Poisson packet arrival and an electrocardio-gram (ECG) application, with constant packet arrival. These scenar-ios will be revisited in this work considering the cross-layersolution explained in a later section. Furthermore, some scenariosfor multimedia applications will be considered, and some of theseapplications considered in the literature are discussed next.

3. System model and problem formulation

3.1. Network model

Since body area networks (BAN) and some multimedia applica-tions need only a few sensors to work [16], e.g. in ECG [17](Fig. 1(a)), human recognition [18] (Fig. 1(b)), and surveillance ofsmall areas, the network topology can be generalized as a centralsink node with surrounding sensor nodes, as shown in Fig. 1(c).

The transmitted frames will follow either the IEEE 802.15.4 dataframe format [22] or the IEEE 802.15.3 data frame format [23],with their respective maximum payload sizes, as depicted in Figs.2a and 2b. Since IEEE 802.15.4 [22] allows either the source or des-tination part of the addressing fields to be omitted and for the cho-sen topology there is only one destination, it can be seen in Fig. 2athat the destination part has 0 octets.

The adopted medium access method is slotted ALOHA and someconsiderations have been made in order to analyze it. First, theframe size cannot change during the network operation. Thus, ifthe size for IEEE 802.15.4 is considered, it keeps this size untilthe end of the analysis. In another analysis, the same scenariocan be investigated with the use of IEEE 802.15.3, as long as it doesnot change during the network operation. Second, sensors cannotgenerate frames while transmitting. This also implies that noqueues are considered at the link layer level, and that all data arriv-ing at this layer must fit one single frame.

Moreover, in order to calculate the sensors power consumption,the transmission power had to be calculated. In order to performthis calculation, a free space attenuation channel model has beenselected. Thus, considering a R = 30 [m] range for the sensors trans-mission (suiting all the scenarios explained later), the transmissionpower Pt can be calculated by Friss’ transmission equation [25],given by

Pt ¼Pr � ð4pRÞ2

Gt � Gr � k2 ; ð1Þ

Fig. 1. Examples of body area networks.

Fig. 2b. IEEE 802.15.3 data frame format [23].

Fig. 2a. IEEE 802.15.4 data frame format [22].

J.J.P.C. Rodrigues et al. / Computer Communications 35 (2012) 1819–1827 1821

where Pr is the required received power, Gt is the transmissionantenna gain, Gr is the reception antenna gain, and k is the transmit-ted signal wavelength.

3.2. Application requirements

According to Su and Zhang [17], the delay of ECG signals in amyoelectric prosthesis control application should be less than300 [ms], considering a constant packet arrival. Also, they haveconsidered a number of sensors varying from 2 to 16, and packetarrival rates of 10 and 20 [arrivals/s]. The packets are encapsulatedin frames without packet fragmentation. Although they have con-sidered shorter packets, in this work it is considered that the pack-et will occupy the whole IEEE 802.15.4 frame payload. Thesementioned parameters will be designated by Scenario 1. In thesame paper [17], a Poisson arrival process has been considered,which is also studied in this proposal, but focusing on optimalframe generation rates instead of varying these rates within arange of values. This will be called Scenario 2.

In the work by Luo et al. [24], the gait tracking application dis-cussed before has been discussed. Three video playback deadlineshave been defined – 20, 30, and 40 [ms], resulting in delivery ratesof 100, 33.333, and 25 [video frames/s]. Here, it is considered thateach video frame will occupy the whole IEEE 802.15.3 frame pay-load, even if a very efficient video compression is needed to realizethat. Furthermore, video frames are considered to arrive at the linklayer at a constant rate, defining Scenario 3, and according to aPoisson process, defining Scenario 4.

3.3. Problem formulation

We model a general BAN as a graph G ¼ fV; E;Ag, whereV ¼ f1; . . . ; i; . . . ;Ng is the set of network nodes, E is the set of linksand A ¼ ½aij� 2 RN�N is the weighted adjacency matrix of G. A linkdenoted by the pair (i, j) represents a channel from i to j and

ðj; iÞ 2 E if and only if ði; jÞ 2 E. Each node i 2 V interferes with aset of other nodes in V, which we denote as Ni. degi ¼

PNj¼1aij is

called the degree of i, and d = maxidegi is called the degree of G.The Laplacian matrix of G is ! corresponding to the network con-nection. In particular, ! ¼ D�A, where D ¼ diagðdeg1; . . . ; degNÞ.

In BAN, there are S ¼ f1; . . . ; s; . . . ; Sg sources andZ ¼ f1; . . . ; z; . . . ; Zg hybrid flows. Each flow z is assumed to beclassified into one of K classes (i.e., C ¼ fC1; . . . ;CKg). A class Ck

can be modeled as (Dk,Rk,kk): Dk represents the delay deadline ofCk; Rk is the average source rate of Ck; kk denotes the quality impactfactor of Ck. We employ kkRk as the average quality gain when theflows of Ck with source rate Rk are received by the receiver. LetNsk denote the number of flows in class Ck streaming from s, andCs denotes the subset of classes for s (e.g., Cs � C). T(i,j),k is themaximum transmission rate supported by the modulation andcoding scheme for Ck, so the effective transmission rate for a flowz over a link (i, j) can be calculated as T(i,j),kt(i,j),z, where t(i,j),z

represents the time sharing fraction for z to transmit over link (i, j).We define the allocation of a flow z as qz ¼ ftði;jÞ;z; ði; jÞ 2 Eg.

q = [q1,q2, . . . ,qZ] is the joint allocation for all Z flows. dz(qz) isthe end-to-end delay for transmitting the flow z based on qz. Wedefine ETT(i,j),z as the effective transmission time (ETT) [12] of thelink (i, j) for the flow z

ETTði;jÞ;z ¼Lk

tði;jÞ;z � Tði;jÞ;k; for z 2 Ck; ð2Þ

where Lk is average packet length of Ck. Then, the end-to-end delaydz(qz) can be computed by

dzðqzÞ ¼P

ði;jÞ;tði;jÞ;z>0ETT ði;jÞ;zðqzÞ: ð3Þ

Therefore, the received flow quality Qs from s can be expressed as:

Qs ¼P

Ck2Cs

PNsk

z¼1kk � Rk � IðdzðqzÞ 6 DkÞ; ð4Þ

1822 J.J.P.C. Rodrigues et al. / Computer Communications 35 (2012) 1819–1827

where I(�) is the indicator function [13]. Based on the joint alloca-tion q, the proposed scheduling paradigm can be formulated as ageneralized optimization problem:

qopt ¼ arg maxq

PSs¼1

QsðqÞ� �

;

s:t:PZz¼1

tði;jÞ;z 6 1; 8ði; jÞ 2 E; dzðqzÞ 6 Dk; 8z 2 Ck; z ¼ 1; . . . ; Z:ð5Þ

Specifically, the first constraint is the resource constraint for eachnetwork link, and the second constraint is the delay constraint foreach flow. To get the solution of (5), two types of information areneeded, namely network and source information. Roughly speaking,network information includes the transmission rate T(i,j),k over eachlink ði; jÞ 2 E to calculate the delay dz. On its side, the source infor-mation contains the flow priority kk, source rate requirement Rk

and the delay deadline Dk.

4. Distributed media-aware flow scheduling

Many kinds of distributed scheduling algorithms have been pre-sented to seek for the optimal solution of (5). Generally speaking,no matter what kind of method, the core idea aims at allocatingappropriate resource to appropriate flow. Let xi,k(t) denote thepacket number of class Ck in the node i’s queue at time t. Theweighted queue length of node i at time t, xi(t), can be given by [12]

xiðtÞ ¼PKk¼1

kkRk

Dkxi;kðtÞ: ð6Þ

Therefore, the optimal scheduling measures how to achieve a bal-ance value of xi(t) for all i 2 V.

Definition 1. Optimal scheduling solution [14]The solution of (5)satisfies:

limt!1

xiðtÞ ¼1jNij

Pj2Ni ;j–i

xjð0Þ; 8i 2 V: ð7Þ

As stated previously, the flow scheduling over CPE is character-ized by constrained communication link. In particular, we employthe scaling factor function (SFF) g(t) to capture the characteristicsof constrained communication link [15]. From the perspective ofcontrolling, xi(t + 1) can be written as:

xiðt þ 1Þ ¼ xiðtÞ þ hðtÞ � uiðtÞ; ð8Þ

where ui(t) is node i’s control input, and h(t) is the control gain func-tion (CGF). Obviously, ui(t) depends on the SFF g(t) and the state ofits j neighbor node xj(t). Specifically,

uiðtÞ ¼ g�1ðtÞPj2Ni

xjðtÞ: ð9Þ

Therefore, our goal is that: how to design h(t) based on observed g(t)to satisfy (7).

4.1. Optimal scheduling strategy

According to [13], we can make the following assumption:

Assumption 1. The queue of each node i 2 V follows:

maxijxiðtÞj 6 Cx;max

ijliðtÞj 6 Cd; t ¼ 0;1; . . . ;

where Cx and Cd are known nonnegative constraints.To design a distributed algorithm to achieve the optimal sched-

uling scheme as described in Definition 1, the core points are toshape a reasonable CGF h(t) and a scaling function g(t). Accordingto [13], an exponential model can be achieved by

hðtÞ ¼ hð0Þ/t ; gðtÞ ¼ gð0Þut; ð10Þ

where h(0) and g(0) are the inial values at t = 0, while / and u arethe gain factor and scaling factor, respectively.

Lemma 1. Suppose that Assumption 1 holds and the system is stable,let the stable factor qh ¼max26i6N j 1� hðtÞNi j. We can get

(1) If hðtÞ > 2D, then qh < 1;

(2) If hðtÞ < 2AþD, then qh < 1/2;

(3) If 2AþD 6 hðtÞ 6 2

D, then qh <jCx�Cd j

Cx.

Lemma 2. When the system is stable, no matter the initial value ofh(0) and g(0), / and u satisfy:

Zð/;uÞ ¼ bMð/;uÞ þ /dc; ð11Þ

Mð/;uÞ ¼ffiffiffiffiNp

/2!2uju� /j þ

1þ 2/d2u

: ð12Þ

In this case, the minimum bit number of information exchange betweeneach node to achieve Definition 1 is dlog2jZ(/,u)je.

Proof 1. The proof process is similar to that of in [15, Theorem3.1], so we omit it here. h

Lemma 3. Suppose Assumption 1 holds. When

gð0Þ > maxCx

jZð/;uÞj ;2ðCduþ Cx/ÞDjMð/;uÞj

� �; ð13Þ

hð0Þ > maxCd

jMð/;uÞj ;2ðCduþ Cx/ÞAjZð/;uÞj

� �; ð14Þ

there exists h(t) and g(t) to achieve the optimal scheduling as de-scribed in (7).

Outline of the proof: The idea of optimal scheduling is to decou-ple the coupled objective function (7) by introducing auxiliaryvariables and additional constraints, and then use Lagrange dualdecomposition to decouple all of the constraints. There are two ex-act steps: (1) introducing new variables to enable decoupling; (2)employing dual decomposition and gradient descent method toderive (7). h

Theorem 1. Suppose Assumption 1, Lemmas 1, 2 and Lemma 3hold. For any given E½gðtÞ� ¼WðW > 0Þ, let

XW ¼ ð/;uÞj/ 2 2AþD ;

2D

� �;u 2 ðqh;1Þ; Zð/;uÞ < W þ 1

2

� �:

ð15Þ

Then (1) XW is nonempty. (2) For (/,u) 2XW, there exists a distributedscheduling algorithm which satisfies the optimal scheduling as de-scribed in Definition 1.

Proof 2. (1) Noting that

lim/!1

ffiffiffiffiNp

/A2N

þ 1þ /D2

!¼ 1

2;

we know that for any given W P 1, there exists /� 2 2AþD ;

2D

h isuch

thatffiffiffiffiNp

/�A2N

þ 1þ /�D2

< W þ 12: ð16Þ

By Lemma 1, it is known that qh < 1. So with Lemma 2, we get

J.J.P.C. Rodrigues et al. / Computer Communications 35 (2012) 1819–1827 1823

limu!1

Zð/�;uÞ ¼ffiffiffiffiNp

/�A2N

þ 1þ /�D2

:

Then by (16), we know that there exists u⁄ 2 [qh,1], such that

Zð/�;u�Þ < W þ 12:

Therefore (/⁄,u⁄) 2XW, that is, XW is nonempty.(2) For any (/,u) 2XW, by (15), we know that / 2 2

AþD ;2D

h i, and

u 2 [qh,1], and

12< Zð/;uÞ < W þ 1

2;

together with Lemma 3, we can get the conclusion. h

4.2. Performance analysis

In this section, we first define the asymptotical convergencerate, then we provide the main result on that.

Definition 2. Asymptotical convergence rate [15]The asymptoticalconvergence rate r of the scheduling scheme can be defined as:

r ¼ supXð0Þ–JN Xð0Þ

limt!1

kXðtÞ � JNXð0Þk2

kXð0Þ � JNXð0Þk2

� �1=t

: ð17Þ

Theorem 2. Suppose Assumption 1 holds. Then for any given W P 1,we have

limN!1

inf ð/;uÞ2XWr

expf� WA2ffiffiffiNpDg¼ 1: ð18Þ

The proof of Theorem 2 needs the following lemmas which can beobtained from [15,13].

Lemma 4. For any given W P 1, and � 2 [0,1], let

XW;� ¼ ð/;uÞj/ 2 ½ 2�AþD ;

2�D �; u ¼ 1� ð1� �Þ/A

� �:

Then we have

XW ¼S

�2½0;1�XW ;�: ð19Þ

Lemma 5. Format of the asymptotical convergence rateSupposeAssumption 1 and Lemma 4 hold, the convergence rate of the methodin Lemma 3 satisfies

r / jZð/;uÞjjMð/;uÞj þ jZð/;uÞj : ð20Þ

Lemma 6. Suppose Assumption 1 holds. For any given W P 1 and� 2 [0,1], one can achieve

inf�2½0;1�;/2½0;2�D�

½1� ð1� �Þ/A�P 1� WA2ffiffiffiffiNpD: ð21Þ

Proof 3. From Lemma 1, we have

/ <2W�Affiffiffiffi

NpD; 8/ 2 ½0;2�D�:

Then for any � 2 [0,1] and / 2 ½0; 2�D�, noting that �(1 � �) 6 1/4, we

get

1� ð1� �Þ/A > 1� 2Wð1� �Þ�AffiffiffiffiNpD

P 1� WA2ffiffiffiffiNpD:

This leads to the conclusion of this lemma. h

Lemma 7. Suppose Assumption 1 holds. For any given W P 1, onecan achieve

inf�2½0;1�;/2½0;2�D�

½1� ð1� �Þ/A� 6 1� WA2ð

ffiffiffiffiNpþ 2WÞD

: ð22Þ

Proof 4. From Lemma 1, we have

2�D P min

1D ;

2W�AffiffiffiffiNpDþ 2WD

� �¼min

1D ;

2W�AðffiffiffiffiNpþ 2WÞD

( )

¼ 2W�AðffiffiffiffiNpþ 2WÞD

:

Together with Lemma 4, we have

inf/2 0;2�D½ �

½1� ð1� �Þ/A� 6 1� 2ð1� �Þ�WAðffiffiffiffiNpþ 2WÞD

:

From this, it follows that

1� 2ð1� �Þ�WAðffiffiffiffiNpþ 2WÞD

6 1�max�2½0;1�

2ð1� �Þ�WAðffiffiffiffiNpþ 2WÞD

¼ 1� WA2ð

ffiffiffiffiNpþ 2WÞD

:

Thus, the lemma holds. h

Proof 5. Now, we can prove Theorem 2.Proof of Theorem 2: By Lemma 6, we have

inf�2½0;1�;/2½0;2�D�½1� ð1� �Þ/A�

exp � WA2ffiffiffiNpD

n o P1� WA

2ffiffiffiNpD

exp � WA2ffiffiffiNpD

n o ; 8N P 1;

together with limN!1WA

2ffiffiffiNpD ! 0, one can then get

lim infN!1

inf�2½0;1�;/2 0;2�D½ �½1� ð1� �Þ/A�

exp � WA2ffiffiffiNpD

n o P 1:

Similarly, by Lemma 7, we have

inf�2½0;1�;/2 0;2�D½ �½1� ð1� �Þ/A�

exp � WA2ffiffiffiNpD

n o 6

1� WA2ffiffiffiNpD

ffiffiffiNpffiffiffiffiffiffiffiffiffiffi

Nþ2Wp

exp � WA2ffiffiffiNpD

n o ; 8N P 1;

which together with Wk2ðLÞ2ffiffiffiNpD ! 0, when N ?1 gives

lim supN!1

inf�2½0;1�;/2 0;2�D½ �½1� ð1� �Þ/A�

exp � WA2ffiffiffiNpD

n o 6 1:

By Lemmas 4 and 5, we get that

infð/;uÞ2XW

r ¼ inf�2½0;1�

infð/;uÞ2XW ;�

r ¼ inf�2½0;1�;/2½0;2�D�

½1� ð1� �Þ/A�:

Therefore, we get the result of Theorem 2. h

4.3. Cross-layer adaptation mechanism

According to [26], the throughput of a slotted ALOHA networkcan be calculated by

thpslotted ¼ G � e�G; ð23Þ

Fig. 4. Optimal mean time between frames generation.

1824 J.J.P.C. Rodrigues et al. / Computer Communications 35 (2012) 1819–1827

where G is the number of transmission attempts per slot time. Thecurve that represents the throughput as a function of the offeredload (G) can be seen in Fig. 3.

It is clear that there is an optimal offered load for the networkthroughput, which is proportional to the sensors frame generationrate (l). Nonetheless, finding the function that relates the framegeneration rate to the offered load is out of the scope of this work.Thus, the approximated optimal mean frame generation time(tgen = 1/l) have been found through simulation. The resultsaccording to the number of nodes in the network are shown inFig. 4, with the previously considered parameters regarding IEEE802.15.4. Details of the simulation are given in Section 6.

The mean increase rate of the curve in Fig. 4 is 3.6489 [ms],which is approximately the slot time defined for slotted ALOHAwith IEEE 802.15.4. Thus, it can be inferred that the optimal meanframe inter-arrival rate can be achieved by using the lowest opti-mal mean frame inter-arrival time and spending slots in sleepmode to result in the other inter-arrival time according to thenumber of nodes. Thus, when a frame is generated at the link layer,it waits until the boundary of the next time slot, then the sensorsleeps for j = [number of nodes in the network minus the mini-mum number of nodes] time slots, and finally it is transmittedthrough the medium.

Moreover, j can be adjusted to save more energy according tothe application delay requirements instead of according to thenumber of nodes. This approach will be considered in the simula-tion of the previously proposed scenarios since the number ofnodes is not supposed to change during the use of the application.

5. Delay and jitter theoretical analysis

5.1. Constant data generation

Considering that a new frame will be generated every 1/l sec-onds after the last frame has been transmitted, the transmissionprocess can be represented as shown in Fig. 5, in which the framewait time is represented by w and it can be calculated by

w ¼ tgen � sgb

tslot

� �� tslot � ðtgen � sgbÞ þ n � tslot; ð24Þ

where sgb is the guard bit duration, dxe represents the least integerthat exceeds x, and the other variables have already been definedpreviously. If the frame generation rate does not change directlyand if the number of nodes does not change regularly, thus varyingthe frame generation rate indirectly, w is constant and there is nojitter.

Fig. 3. Slotted ALOHA throughput as a function of the offered load (G).

5.2. Poisson data generation

In this case, frames will be generated according to a Poisson dis-tribution, resulting in exponential time between frames genera-tion. Thus, the number of time slots since the last transmissionand the frame waiting time will be random. Hence, the time sincethe last transmission will be represented by the random variable X,the number of time slots since last transmission will be repre-sented by the random variable N, and the waiting time by the ran-dom variable W, as shown in Fig. 6.

More precisely, the probability density function of X is given by

fXðxÞ ¼l � e�l�x; if x P 0;0; otherwise:

�ð25Þ

The probability mass function of N is developed inAppendix A, andit is given in Eq. 27. The random variable that defines the frame waittime (W) is given by

W ¼ N � tslot � X þ k � tslot; ð26Þ

pNðnÞ ¼1� e�l�sgb ; if n ¼ 0;e�l�½sgbþðn�1Þ�tslot � � e�l�ðsgbþn�tslot Þ; if n > 0;0; otherwise:

8><>: ð27Þ

Then, the mean frame wait time E[W], derived in Appendix B, is gi-ven by Eq. 28.

E½W� ¼P1n¼1

n � e�l�½sgbþðn�1Þ�tslot � � e�l�ðsgbþn�tslot Þ

� tslot �1lþ k � tslot:

ð28Þ

Finally, the jitter can be inferred from the standard deviation of themean frame wait time, which is given by

rW ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffit2

slot � r2N þ

1l2 � 2 � tslot � CovðN;XÞ

s: ð29Þ

In particular, rW depends on the variance of Nðr2NÞ and on the

covariance of N and X, which are given in Eqs. (30) and (31), bothdeveloped in Appendix C.

r2N ¼

P1n¼1

n2 � e�l�½sgbþðn�1Þ�tslot � � e�l�ðsgbþn�tslot Þ

�P1n¼1

n � e�l�½sgbþðn�1Þ�tslot � � e�l�ðsgbþn�tslot Þ � �2

; ð30Þ

CovðN;XÞ ¼P1n¼1

n �Z sgbþðnÞtslot

sgbþðn�1Þtslot

x � l � e�l�xdx� 1l� E½N�: ð31Þ

Fig. 8. Standard deviation of the frame wait time.

Fig. 5. Representation of constant frame generation.

Fig. 6. Representation of exponential time between frames generation.

J.J.P.C. Rodrigues et al. / Computer Communications 35 (2012) 1819–1827 1825

6. Simulation results

Simulations have been run using the OMNeT++ simulator [27].The considered scenario consists of a wireless sensor networkusing the IEEE 802.15.4 with the slotted ALOHA medium accessmethod with exponential time frame generation. The networkcomprises a sink node and from 7 to 20 sensors. The mean framewait time for this scenario is shown in Fig. 7.

It can be seen from Fig. 7 that the delay boundary of 20 [ms] isrespected up to 12 sensors, the boundary of 30 [ms] is respected upto 14 sensors, and the boundary of 40 [ms] is respected up to 17sensors in the network. Also, it can be seen that the analytical mod-el matches the results achieved by simulation. Moreover, the jittercan be inferred from the wait time standard deviation, shown inFig. 8.

From Fig. 8, it is possible to see that the increase in the numberof slots spent on sleep mode does not affect the standard deviationof the wait time, and thus does not affect jitter. Furthermore, theanalytical model could predict the results with good approxi-mation.

Finally, we test the proposed scheduling in BAN, which is a clas-sic CCE. There are multiple media flows in this BAN, and each flowbelongs to one of four classes (their parameters are listed in Table1). To demonstrate the effectiveness of our algorithm, we use theAdditive-Increase-Multiplicative-Decrease (AIMD)-based rate allo-cation method [28], which is used by TCP congestion control forcomparison. There are 10 nodes with 0–1 weights, which means

Fig. 7. Mean frame wait time.

that aij = 1 if ði; jÞ 2 E, otherwise, aij = 0. The initial states are chosenas xi(0) = i, i = 1, . . . ,10, and ! = 1.5683. The control gain is h = 0.75and the mean of scaling function is W = 0.5. To give a reasonableevaluation for hybrid media flows, we evaluate a concrete qualitymetric based on MOS (Mean Opinion Score) value. MOS reflectsthe average user satisfaction on a scale from 1 to 4.5 [13]. Fig. 9presents the average MOS for the 4 flows of different classes ob-tained by the AIMD method and the proposed method, respec-tively. It is observed that the proposed method outperforms theAIMD method on the aspect of constant performance. That is be-cause our proposed method manages to keep a rather constantapplication quality for all active flows by constantly adapting andredistributing the control gain h to all the media flows.

7. Conclusions and future work

Given the fast growth of cloud computing environment and itsdifferent applications, particularly for healthcare and multimedia,this work has proposed a media-aware flow scheduling scheme

Table 1Video sequence’s parameters.

Ck C1 C2 C3 C4

kk(dB/Kbps) 0.0170 0.0105 0.0064 0.0060Rk(Kbps) 550 500 400 400Dk(ms) 350 370 400 420

Fig. 9. Average performance comparison based on MOS.

1826 J.J.P.C. Rodrigues et al. / Computer Communications 35 (2012) 1819–1827

and an analysis of the frame delay and jitter in body area networkusing slotted ALOHA as the medium access method. Analyticalexpressions to calculate these two metrics when the cross-layersolution is used have been derived. Moreover, according to the re-sults shown, it can be seen that the cross-layer solution creates atradeoff between the frame delay and energy consumption. Also,the analytical expressions have proven to predict the resultsachieved by simulations correctly. Finally, it has been shown thatthe frame wait time jitter is kept at a low and constant level.

Future work might consider the use of other medium accessmethods like TDMA and CSMA. Thus, new analytical expressions willhave to be derived, including cross-layer dependencies on the anal-ysis. Moreover, multi-hop communication, routing protocols, andcross-layer solutions involving the network layer could be proposed.

Acknowledgments

This work has been partially supported by Instituto de Telecomu-nicações, Next Generation Networks and Applications Group (NetG-NA), Portugal, and by National Funding from the FCT – Fundaçãopara a Ciência e Tecnologia through the pest-OE/EEI/LA0008/2011.

Appendix A. Probability mass function of random variable N

According to the transmission process explained in Section 4.3,after a frame generation the sensor waits until the boundary of thenext time slot, resulting in n time slots since the last frame trans-mission. If the random variable X randomly selects the next framegeneration to be within the guard bit duration of the current trans-mission, the next frame will be transmitted after n = 0 time slots,considering the sensor does not sleep before transmitting. Thus,

P½N ¼ 0� ¼ P½0 6 X < sgb� ¼Z sgb

0l � e�l�xdx ¼ 1� e�l�sgb : ð32Þ

If the time selected is inside the time slot after the transmissionslot, shown as s0 in Fig. 6, the transmission will be done at the endof that slot, and n = 1. This probability is given by

P½N ¼ 1� ¼ P½sgb 6 X < sgb þ tslot� ¼Z sgbþtslot

sgb

l � e�l�xdx

¼ e�l�sgb � e�l�ðsgbþtslot Þ: ð33Þ

Analogue to the previous case, the boundaries of the randomgeneration of X will vary in multiples of tslot. Thus, ifsgb + tslot 6 X < sgb + 2 � tslot, then n = 2. If sgb + 2 � tslot 6 X < sgb +3 � tslot, then n = 3, and so on. Thus, since X never yields a negativeresult, n will never be negative, and since the n = 0 case does notfollow the progression for n > 0, the probability mass functioncan be generalized by the three cases of Eq. (27) shown previously.

Appendix B. Calculation of the mean of random variable W

The random variable W has been related to the other randomvariables in Eq. (26). Using the mean operator on both sides ofthe equation results in

E½W� ¼ E½N � tslot � X þ k � tslot�: ð34Þ

Since the mean of the sum is the sum of each mean [29], and themean of constants are equal to the constants, E[W] can be written as

E½W� ¼ E½N� � tslot � E½X� þ k � tslot: ð35Þ

Taking the definition of expected value [29], E[N] is given by

E½N� ¼Pþ1

n¼�1n � pNðnÞ ð36Þ

and since pN(n) has no negative part, and for n = 0 the multiplicationnullifies the term of the sum, the first term of E[W] given in Eq. (28)is proven. Since the mean of exponential random variables is well-known to be 1/l, and the mean of the constant part is the value ofthe constant, the remainder of Eq. 28 is proven.

Appendix C. Calculation of the standard deviation of randomvariable W

Before calculating the standard deviation, the variance is calcu-lated, and it is represented by

r2W ¼ VarðWÞ ¼ VarðN � tslot � X þ k � tslotÞ; ð37Þ

where the function Var(A), represents the variance of the randomvariable A. According to the following variance property [29], wecan have

Varða � Aþ b � Bþ cÞ ¼ Varða � Aþ b � BÞ ¼ a2 � VarðAÞþ b2 � VarðBÞ þ 2 � a � b � CovðA;BÞ; ð38Þ

where capital letters denote random variables, small letters denoteconstants, and Cov(A,B) represents the covariance of random vari-ables A and B. Thus, applying to random variable W, it yields

VarðWÞ ¼ t2slot � VarðNÞ þ VarðXÞ � 2 � tslot � CovðN;XÞ: ð39Þ

The variance of N can be calculated by [29], so we can have

VarðNÞ ¼ E½N2� � E½N�2 ¼Pþ1

n¼�1n2 � pNðnÞ � E½N�2; ð40Þ

where E[N] has been defined in Appendix B. From the discussion inAppendix B on the sum limits, it can be inferred that r2

N ¼ VarðNÞreduces to Eq. (30). The variance of the exponential random variableX is well-known to be 1/l2. Finally, Cov(N,X) can be calculated by

CovðN;XÞ ¼ E½N � X� � E½N� � E½X�: ð41Þ

J.J.P.C. Rodrigues et al. / Computer Communications 35 (2012) 1819–1827 1827

In order to calculate E[N � X], the joint probability distribution ofN and X has to be defined. Clearly, P[N = njX = x] = 1 if sgb + (n � 1) �tslot 6 x < sgb + n � tslot, otherwise, P[N = njX = x] = 0. Therefore,fN,X(n,x) = l � e�l�x.

Then, the expected value of N � X is

E½N � X� ¼P1n¼1

n �Z sgbþðnÞtslot

sgbþðn�1Þtslot

x � l � e�l�xdx ð42Þ

and from the previously defined expected values of N and X, thecovariance of N and X reduces to Eq. (31), and all the dependenciesof the variance of random variable W can be calculated. Finally,since the standard deviation of W is the square root of its variance,the derivation of Eq. (29) is complete.

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