Distributed media-aware flow scheduling in cloud computing ...

Computer Communications 35 (2012) 1819–1827

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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, Portugal Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, China c Dalian University of Technology, China d Polytechnic University of Valencia, Spain b

a r t i c l e

i n f o

Article history: Available online 15 March 2012 Keywords: Body area network Cloud computing Media-aware scheduling Multimedia application

a b s t r a c t Media-aware flow scheduling in cloud computing environment has attracted much attention nowadays because of the new possibilities they bring to many research and industry fields. Particularly, body area networks, as a typical computing environment application in healthcare, allow ubiquitous monitoring of patients, and more thorough patient diagnoses can be done with the help of multimedia service. In this work, we propose a novel media-aware flow scheduling architecture with the aims of improving the multimedia quality and increasing the network’s lifetime. In order to avoid interfering with the multimedia applications’ delay requirements, this work also proposes to analyze frames delay and jitter. The proposal has proven to improve the multimedia quality and decrease the transmission delay in a controllable manner, and thus the tradeoffs between QoS, lifetime, and delay requirements can be achieved according to the considered scenario. In addition, extensive simulation results validates the efficiency of the proposed method. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Cloud computing environment (CCE) has received much attention recently since it viewed as an alternative to conventional office-based computing [1]. As CCE becomes more widespread, the demand of the multimedia service in CCE has increased dramatically [2]. Typically, the architecture of CCE is comprised by restrained devices called sensor nodes, which can sense environmental conditions, perform local processing, and send the acquired data to a base station through wireless links. It is foreseen that these devices can be used in several fields, such as in medicine [3], security [4], industry [5], and others. Currently, body area network (BAN) is developed as a typical application scenario in CCE [6]. Despite the advantages that the use of BAN can bring to multimedia applications, there are some problems that limit their dissemination. The main concern is that sensor nodes are small and have limited battery as power source. Hence, the lifetime of the BAN is dependent of the used routing protocol, modulation, frames scheduling, security mechanisms, and the application requirements. With regard to a specific video application, quality of service (QoS) is also a problem, since video packets cannot experience long delays, or the goal of the network ⇑ Corresponding author. Tel.: +351 275 319 891. E-mail addresses: [email protected] (J.J.P.C. Rodrigues), [email protected] (L. Zhou), [email protected] (L.D.P. Mendes), [email protected] (K. Lin), [email protected] (J. Lloret). 0140-3664/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comcom.2012.03.004

may be compromised [14]. Therefore, all solutions for the aforementioned problems need to be energy efficient. One of the techniques that has proven to use sensors resources more efficiently in BAN is cross-layer design [7]. Cross-layer design states that parameters of two or more layers can be retrieved and/ or changed in order to achieve an optimization objective. This concept has been first proposed for TCP/IP networks, when wireless links were deployed [8], and it has been used not only to overcome energy limitations, but also increase network throughput and to improve quality of service. It can be seen in the literature on cross-layer design that two medium access methods are generally considered – carrier sense multiple access (CSMA) and time division multiple access (TDMA). The first is frequently considered in wireless sensor networks with a large number of nodes [9]. However, the scenarios considered in this work are comprised of at most 20 sensor nodes, and thus the use of CSMA would incur in unacceptable medium contention overheads. The second provides a simpler analysis, but at the cost of synchronization overhead. Achieving nodes synchronization is not an easy task, and it is a research field by itself [10]. Thus, in order 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 consumption reduction through sleep periods is proposed. In particular, a media-aware low scheduling scheme is presented by joint considering the characteristics of network and applications. Also, analytical expressions are derived in order to analyze frame delay and

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jitter, and they are validated through simulations. Slotted ALOHA medium access method is considered for the reasons given previously, using body area networks and multimedia sensor networks as scenarios for performance assessment. The remainder of the paper is organized as follows. Preliminaries related to this work is presented in Section 2. In Section 3, the system model, the considered characteristics of IEEE 802.15.4 and IEEE 802.15.3 protocols are shown, and the problem is formulated. The distributed media-aware flow scheduling scheme is proposed in Section 4. The analytical expressions and delay and jitter analysis methodology are presented in Section 5. Extensive simulation results of frame delay and jitter analysis, and also the analytical expressions validation, are shown in Section 6. Finally, the conclusions 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 challenges imposed by these applications. Some of the challenges identified by Akyildiz et al. [7, 11] are resource constraints, quality of service (QoS) requirements, high data transmission rates, variable wireless channel capacity, parameters interdependence across the layers, and data coding and processing. As also pointed by the aforementioned authors, multimedia applications in CCE are used for many different applications, including surveillance and health-care. An example of these applications is given next section. Luo et al. [24] have proposed a new mannerless human gait tracking system that simplifies the expensive and lengthy process used in clinics. Their cross-layer transmission process determines the video quantization step and the adaptive modulation and coding (AMC) scheme according to the channel bit error rate. Thus, the delay and video distortion bounds are respected while transmission is adapted according to the channel state. In their experiments, video playback deadlines of 20, 30, and 40 [ms] have been defined, and they have proven to achieve gains of 3–5 [dB] in the peak signal-to-noise ratio of the video transmitted frames. A scenario with 18 video sensor nodes with a central processing unit has been defined by Wang et al. [18] in order to assess the visual recognition efficiency of their proposed algorithm. The video sensor nodes are trained by using raw data in order to recognize human targets and objects. Then, when acquiring data for classification, the irrelevant set of data for target recognition is detected and discarded, and the relevant part is compressed. A decision is made by each sensor node and transmitted to the central processing unit, which is responsible for combining the observations to achieve a final result. Their new algorithm has proved to greatly reduce the training and classifying time, and thus sensors spend less energy on data processing. In another paper by the same authors [19], the effects of the adopted computing paradigm on the recognition accuracy and delay is assessed. The comparison has been carried out considering centralized client/server (C-CS), distributed client/server (D-CS), mobile agent (MA), and peer-to-peer (P2P) paradigms. Then, it has been pointed out that the P2P paradigm could yield the best accuracy and delay on the target recognition process. However, these authors have not addressed the issues on 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 the use of a few sensors and a coordinator that receives data from

the sensors and have some degree of control over them. This common topology for BSNs has been used to define the behavior of the wireless channel near the human body. Chen et al. [20] have considered only one sensor communicating with a gateway node through the ultrawideband (UWB) technology. Also, they have proposed the use of cooperative nodes to relay data from the sensor to the gateway, increasing the diversity gain and improving the quality of the signal received at the gateway. Furthermore, Reusens et al. [21] have characterized the channel model considering different parts of the body – legs, arms, torso, and back. They have also considered the impact of the sensors topology on the sensors energy consumption, arguing that multihop communication is needed. However, for multihop communication, a larger number of sensors is needed, and in their work they have even considered 6 node levels, which is generally not the scenario seen in BSNs. Thus, in this work single-hop transmission will be considered. Su and Zhang [17] have proposed a cross-layer time division multiple access (TDMA) method considering the battery discharge dynamics, the healthcare applications quality of service (QoS) requirements, and the channel quality to control the used modulation. They have proven that their proposal outperforms IEEE 802.15.4 [22] and Bluetooth in terms of delay and packet loss rate. In order to carry out the performance assessment, the authors have considered a case with Poisson packet arrival and an electrocardiogram (ECG) application, with constant packet arrival. These scenarios will be revisited in this work considering the cross-layer solution explained in a later section. Furthermore, some scenarios for multimedia applications will be considered, and some of these applications 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 applications need only a few sensors to work [16], e.g. in ECG [17] (Fig. 1(a)), human recognition [18] (Fig. 1(b)), and surveillance of small areas, the network topology can be generalized as a central sink node with surrounding sensor nodes, as shown in Fig. 1(c). The transmitted frames will follow either the IEEE 802.15.4 data frame 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 destination part of the addressing fields to be omitted and for the chosen topology there is only one destination, it can be seen in Fig. 2a that the destination part has 0 octets. The adopted medium access method is slotted ALOHA and some considerations have been made in order to analyze it. First, the frame size cannot change during the network operation. Thus, if the size for IEEE 802.15.4 is considered, it keeps this size until the end of the analysis. In another analysis, the same scenario can be investigated with the use of IEEE 802.15.3, as long as it does not change during the network operation. Second, sensors cannot generate frames while transmitting. This also implies that no queues are considered at the link layer level, and that all data arriving 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 perform this calculation, a free space attenuation channel model has been selected. Thus, considering a R = 30 [m] range for the sensors transmission (suiting all the scenarios explained later), the transmission power Pt can be calculated by Friss’ transmission equation [25], given by

Pt ¼

P r  ð4pRÞ2 Gt  Gr  k2

;

ð1Þ

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

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Fig. 1. Examples of body area networks.

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

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

where Pr is the required received power, Gt is the transmission antenna gain, Gr is the reception antenna gain, and k is the transmitted signal wavelength. 3.2. Application requirements According to Su and Zhang [17], the delay of ECG signals in a myoelectric prosthesis control application should be less than 300 [ms], considering a constant packet arrival. Also, they have considered a number of sensors varying from 2 to 16, and packet arrival rates of 10 and 20 [arrivals/s]. The packets are encapsulated in frames without packet fragmentation. Although they have considered shorter packets, in this work it is considered that the packet will occupy the whole IEEE 802.15.4 frame payload. These mentioned parameters will be designated by Scenario 1. In the same paper [17], a Poisson arrival process has been considered, which is also studied in this proposal, but focusing on optimal frame generation rates instead of varying these rates within a range of values. This will be called Scenario 2. In the work by Luo et al. [24], the gait tracking application discussed before has been discussed. Three video playback deadlines have been defined – 20, 30, and 40 [ms], resulting in delivery rates of 100, 33.333, and 25 [video frames/s]. Here, it is considered that each video frame will occupy the whole IEEE 802.15.3 frame payload, even if a very efficient video compression is needed to realize that. Furthermore, video frames are considered to arrive at the link layer at a constant rate, defining Scenario 3, and according to a Poisson process, defining Scenario 4. 3.3. Problem formulation We model a general BAN as a graph G ¼ fV; E; Ag, where V ¼ f1; . . . ; i; . . . ; Ng is the set of network nodes, E is the set of links and A ¼ ½aij  2 RNN is the weighted adjacency matrix of G. A link denoted 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 a P set of other nodes in V, which we denote as Ni. deg i ¼ Nj¼1 aij 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 connection. In particular, ! ¼ D  A, where D ¼ diagðdeg 1 ; . . . ; deg N Þ. In BAN, there are S ¼ f1; . . . ; s; . . . ; Sg sources and Z ¼ f1; . . . ; z; . . . ; Zg hybrid flows. Each flow z is assumed to be classified into one of K classes (i.e., C ¼ fC 1 ; . . . ; C K g). A class Ck can be modeled as (Dk, Rk, kk): Dk represents the delay deadline of Ck; Rk is the average source rate of Ck; kk denotes the quality impact factor of Ck. We employ kkRk as the average quality gain when the flows of Ck with source rate Rk are received by the receiver. Let Nsk denote the number of flows in class Ck streaming from s, and Cs denotes the subset of classes for s (e.g., Cs  C). T(i,j),k is the maximum transmission rate supported by the modulation and coding scheme for Ck, so the effective transmission rate for a flow z 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) is the end-to-end delay for transmitting the flow z based on qz. We define ETT(i,j),z as the effective transmission time (ETT) [12] of the link (i, j) for the flow z

ETT ði;jÞ;z ¼

Lk ; tði;jÞ;z  T ði;jÞ;k

for z 2 C k ;

ð2Þ

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

dz ðqz Þ ¼

P

ETT ði;jÞ;z ðqz Þ:

ð3Þ

ði;jÞ;t ði;jÞ;z >0

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

Qs ¼

Nsk P P C k 2C s z¼1

kk  Rk  Iðdz ðqz Þ 6 Dk Þ;

ð4Þ

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where I() is the indicator function [13]. Based on the joint allocation q, the proposed scheduling paradigm can be formulated as a generalized optimization problem:  S  P qopt ¼ arg max Q s ðqÞ ; q s¼1 ð5Þ Z P tði;jÞ;z 6 1; 8ði; jÞ 2 E; dz ðqz Þ 6 Dk ; 8z 2 C k ; z ¼ 1; . . . ; Z: s:t:

hðtÞ ¼ hð0Þ/t ;

gðtÞ ¼ gð0Þut ;

ð10Þ

where h(0) and g(0) are the inial values at t = 0, while / and u are the gain factor and scaling factor, respectively. Lemma 1. Suppose that Assumption 1 holds and the system is stable, let the stable factor qh ¼ max26i6N j 1  hðtÞN i j. We can get

z¼1

Specifically, the first constraint is the resource constraint for each network link, and the second constraint is the delay constraint for each flow. To get the solution of (5), two types of information are needed, namely network and source information. Roughly speaking, network information includes the transmission rate T(i,j),k over each link ði; jÞ 2 E to calculate the delay dz. On its side, the source information 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 presented to seek for the optimal solution of (5). Generally speaking, no matter what kind of method, the core idea aims at allocating appropriate resource to appropriate flow. Let xi,k(t) denote the packet number of class Ck in the node i’s queue at time t. The weighted queue length of node i at time t, xi(t), can be given by [12]

xi ðtÞ ¼

K k R P k k xi;k ðtÞ: k¼1 Dk

ð6Þ

Therefore, the optimal scheduling measures how to achieve a balance value of xi(t) for all i 2 V. Definition 1. Optimal scheduling solution [14]The solution of (5) satisfies:

limxi ðtÞ ¼

t!1

1 P xj ð0Þ; jNi j j2Ni ;j–i

8i 2 V:

ð7Þ

As stated previously, the flow scheduling over CPE is characterized by constrained communication link. In particular, we employ the scaling factor function (SFF) g(t) to capture the characteristics of constrained communication link [15]. From the perspective of controlling, xi(t + 1) can be written as:

xi ðt þ 1Þ ¼ xi ðtÞ þ hðtÞ  ui ðtÞ;

ð8Þ

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

ui ðtÞ ¼ g 1 ðtÞ

P

xj ðtÞ:

ð9Þ

(1) If hðtÞ > D2 , then qh < 1; 2 (2) If hðtÞ < AþD , then qh < 1/2; 2 dj . (3) If AþD 6 hðtÞ 6 D2 , then qh < jC xCC x

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

Zð/; uÞ ¼ bMð/; uÞ þ /dc; pffiffiffiffi 2 N/ ! 1 þ 2/d Mð/; uÞ ¼ : þ 2u 2uju  /j

ð11Þ ð12Þ

In this case, the minimum bit number of information exchange between each node to achieve Definition 1 is dlog2jZ(/, u)je. Proof 1. The proof process is similar to that of in [15, Theorem 3.1], so we omit it here. h Lemma 3. Suppose Assumption 1 holds. When

 Cx 2ðC d u þ C x /ÞD ; ; jMð/; uÞj jZð/; uÞj   Cd 2ðC d u þ C x /ÞA ; ; hð0Þ > max jZð/; uÞj jMð/; uÞj

gð0Þ > max



ð13Þ ð14Þ

there exists h(t) and g(t) to achieve the optimal scheduling as described in (7). Outline of the proof: The idea of optimal scheduling is to decouple the coupled objective function (7) by introducing auxiliary variables and additional constraints, and then use Lagrange dual decomposition to decouple all of the constraints. There are two exact steps: (1) introducing new variables to enable decoupling; (2) employing dual decomposition and gradient descent method to derive (7). h Theorem 1. Suppose Assumption 1, Lemmas 1, 2 and Lemma 3 hold. For any given E½gðtÞ ¼ WðW > 0Þ, let



XW ¼ ð/; uÞj/ 2



  2 2 1 ; u 2 ðqh ; 1Þ; Zð/; uÞ < W þ : ; AþD D 2

j2N i

ð15Þ

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

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

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:

maxjxi ðtÞj 6 C x ; maxjli ðtÞj 6 C d ; i

i

t ¼ 0; 1; . . . ;

where Cx and Cd are known nonnegative constraints. To design a distributed algorithm to achieve the optimal scheduling scheme as described in Definition 1, the core points are to shape a reasonable CGF h(t) and a scaling function g(t). According to [13], an exponential model can be achieved by

Proof 2. (1) Noting that

! pffiffiffiffi N/A 1 þ /D 1 þ ¼ ; lim /!1 2N 2 2 we know that for any given W P 1, there exists / 2 that

pffiffiffiffi  N/ A 1 þ / D 1 þ 1 

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

This leads to the conclusion of this lemma. h

1 Zð/ ; u Þ < W þ : 2 ⁄

⁄

Therefore (/ , u ) 2 XW, that is, XW is nonempty. h i 2 (2) For any (/, u) 2 XW, by (15), we know that / 2 AþD ; D2 , and u 2 [qh, 1], and

1 1 < Zð/; uÞ < W þ ; 2 2

2Wð1  ÞA WA pffiffiffiffi P 1  pffiffiffiffi : ND 2 ND

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

inf

2½0;1;/2½0;2D

½1  ð1  Þ/A 6 1 

WA pffiffiffiffi : 2ð N þ 2WÞD

Proof 4. From Lemma 1, we have

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

( )   2 1 2W A 1 2W A ; pffiffiffiffi ¼ min ; pffiffiffiffi P min D ND þ 2WD D ð N þ 2WÞD D 2W A ¼ pffiffiffiffi : ð N þ 2WÞD

4.2. Performance analysis In this section, we first define the asymptotical convergence rate, then we provide the main result on that. Definition 2. Asymptotical convergence rate [15]The asymptotical convergence rate r of the scheduling scheme can be defined as:



kXðtÞ  J N Xð0Þk2 r ¼ sup lim Xð0Þ–J N Xð0Þt!1 kXð0Þ  J N Xð0Þk2

Together with Lemma 4, we have

2ð1  ÞWA inf ½1  ð1  Þ/A 6 1  pffiffiffiffi : 2  /2½0; D  ð N þ 2WÞD From this, it follows that

1=t :

ð17Þ

2ð1  ÞWA 2ð1  ÞWA WA 6 1  max pffiffiffiffi ¼ 1  pffiffiffiffi : 1  pffiffiffiffi 2½0;1 ð N þ 2WÞD ð N þ 2WÞD 2ð N þ 2WÞD

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

Thus, the lemma holds. h

inf ð/;uÞ2XW r lim pffiffiffi g N!1 expf WA 2 ND

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

¼ 1:

ð18Þ

The proof of Theorem 2 needs the following lemmas which can be obtained from [15,13]. Lemma 4. For any given W P 1, and

 2 [0, 1], let

pffiffiffi inf 2½0;1;/2½0;2D ½1  ð1  Þ/A 1  2WA n o n ND o ; P pffiffiffi pffiffiffi exp  2WA exp  2WA ND ND

inf 2½0;1;/2½0;2 ½1  ð1  Þ/A D n o P 1: pffiffiffi exp  WA

lim inf N!1

2 ND

Then we have

XW ¼

XW; :

ð19Þ

2½0;1

Lemma 5. Format of the asymptotical convergence rateSuppose Assumption 1 and Lemma 4 hold, the convergence rate of the method in Lemma 3 satisfies

r/

8N P 1;

pffiffiffi ! 0, one can then get together with limN!1 2WA ND

  2 2 XW; ¼ ð/; uÞj/ 2 ½ ; ; u ¼ 1  ð1  Þ/A : AþD D S

ð22Þ

jZð/; uÞj : jMð/; uÞj þ jZð/; uÞj

ð20Þ

Similarly, by Lemma 7, we have pffiffiffi N inf 2½0;1;/2½0;2 ½1  ð1  Þ/A 1  WA pffiffiffi pffiffiffiffiffiffiffiffiffiffi D 2 ND Nþ2W n o n o ; 6 WA pffiffiffi pffiffiffi exp  2WA exp  ND 2 ND

which together with

lim sup N!1

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

! 0, when N ? 1 gives

inf 2½0;1;/2½0;2 ½1  ð1  Þ/A D n o 6 1: pffiffiffi exp  WA 2 ND

By Lemmas 4 and 5, we get that

inf

WA inf ½1  ð1  Þ/A P 1  pffiffiffiffi : 2½0;1;/2½0;2D 2 ND

Wk2 ðLÞ pffiffiffi 2 ND

8N P 1;

ð/;uÞ2XW

r ¼ inf

2½0;1

inf

ð/;uÞ2XW ;

r¼

inf

½1  ð1  Þ/A:

2½0;1;/2½0;2D

ð21Þ Therefore, we get the result of Theorem 2. h

Proof 3. From Lemma 1, we have

4.3. Cross-layer adaptation mechanism

2W A / < pffiffiffiffi ; ND

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

Then for any get

8/ 2 ½0;

2 : D

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

thpslotted ¼ G  eG ;

ð23Þ

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where G is the number of transmission attempts per slot time. The curve that represents the throughput as a function of the offered load (G) can be seen in Fig. 3. It is clear that there is an optimal offered load for the network throughput, which is proportional to the sensors frame generation rate (l). Nonetheless, finding the function that relates the frame generation 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 results according to the number of nodes in the network are shown in Fig. 4, with the previously considered parameters regarding IEEE 802.15.4. 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 ALOHA with IEEE 802.15.4. Thus, it can be inferred that the optimal mean frame inter-arrival rate can be achieved by using the lowest optimal mean frame inter-arrival time and spending slots in sleep mode to result in the other inter-arrival time according to the number of nodes. Thus, when a frame is generated at the link layer, it waits until the boundary of the next time slot, then the sensor sleeps for j = [number of nodes in the network minus the minimum number of nodes] time slots, and finally it is transmitted through the medium. Moreover, j can be adjusted to save more energy according to the application delay requirements instead of according to the number of nodes. This approach will be considered in the simulation of the previously proposed scenarios since the number of nodes is not supposed to change during the use of the application.

Fig. 4. Optimal mean time between frames generation.

5.2. Poisson data generation In this case, frames will be generated according to a Poisson distribution, resulting in exponential time between frames generation. Thus, the number of time slots since the last transmission and the frame waiting time will be random. Hence, the time since the last transmission will be represented by the random variable X, the number of time slots since last transmission will be represented by the random variable N, and the waiting time by the random variable W, as shown in Fig. 6. More precisely, the probability density function of X is given by

5. Delay and jitter theoretical analysis

 fX ðxÞ ¼

5.1. Constant data generation Considering that a new frame will be generated every 1/l seconds after the last frame has been transmitted, the transmission process can be represented as shown in Fig. 5, in which the frame wait time is represented by w and it can be calculated by

  t gen  sgb  tslot  ðtgen  sgb Þ þ n  t slot ; w¼ t slot

ð24Þ

where sgb is the guard bit duration, dxe represents the least integer that exceeds x, and the other variables have already been defined previously. If the frame generation rate does not change directly and if the number of nodes does not change regularly, thus varying the frame generation rate indirectly, w is constant and there is no jitter.

l  elx ; if x P 0; 0;

ð25Þ

otherwise:

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

W ¼ N  t slot  X þ k  t slot ;

ð26Þ

8 lsgb ; if n ¼ 0; > 0; > : 0; otherwise:

ð27Þ

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

E½W ¼

1 P



1 n  el½sgb þðn1Þtslot   elðsgb þntslot Þ  t slot  þ k  t slot :

l

n¼1

ð28Þ Finally, the jitter can be inferred from the standard deviation of the mean frame wait time, which is given by

rW

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ¼ t 2slot  r2N þ 2  2  tslot  Cov ðN; XÞ:

ð29Þ

l

In particular, rW depends on the variance of Nðr2N Þ and on the covariance of N and X, which are given in Eqs. (30) and (31), both developed in Appendix C.

r2N ¼

1 P



n2  el½sgb þðn1Þtslot   elðsgb þntslot Þ

n¼1



1 P



n  el½sgb þðn1Þtslot   elðsgb þntslot Þ

2 ;

ð30Þ

 E½N:

ð31Þ

n¼1

Cov ðN; XÞ ¼ Fig. 3. Slotted ALOHA throughput as a function of the offered load (G).

1 P n¼1

n

Z sgb þðnÞtslot sgb þðn1Þtslot

x  l  elx dx 

1

l

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Fig. 5. Representation of constant frame generation.

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

6. Simulation results Simulations have been run using the OMNeT++ simulator [27]. The considered scenario consists of a wireless sensor network using the IEEE 802.15.4 with the slotted ALOHA medium access method with exponential time frame generation. The network comprises a sink node and from 7 to 20 sensors. The mean frame wait time for this scenario is shown in Fig. 7. It can be seen from Fig. 7 that the delay boundary of 20 [ms] is respected up to 12 sensors, the boundary of 30 [ms] is respected up to 14 sensors, and the boundary of 40 [ms] is respected up to 17 sensors in the network. Also, it can be seen that the analytical model matches the results achieved by simulation. Moreover, the jitter can be inferred from the wait time standard deviation, shown in Fig. 8. From Fig. 8, it is possible to see that the increase in the number of slots spent on sleep mode does not affect the standard deviation of the wait time, and thus does not affect jitter. Furthermore, the analytical model could predict the results with good approximation. Finally, we test the proposed scheduling in BAN, which is a classic CCE. There are multiple media flows in this BAN, and each flow belongs to one of four classes (their parameters are listed in Table 1). To demonstrate the effectiveness of our algorithm, we use the Additive-Increase-Multiplicative-Decrease (AIMD)-based rate allocation method [28], which is used by TCP congestion control for comparison. There are 10 nodes with 0–1 weights, which means

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

that aij = 1 if ði; jÞ 2 E, otherwise, aij = 0. The initial states are chosen as xi(0) = i, i = 1, . . . , 10, and ! = 1.5683. The control gain is h = 0.75 and the mean of scaling function is W = 0.5. To give a reasonable evaluation for hybrid media flows, we evaluate a concrete quality metric based on MOS (Mean Opinion Score) value. MOS reflects the average user satisfaction on a scale from 1 to 4.5 [13]. Fig. 9 presents the average MOS for the 4 flows of different classes obtained by the AIMD method and the proposed method, respectively. It is observed that the proposed method outperforms the AIMD method on the aspect of constant performance. That is because our proposed method manages to keep a rather constant application quality for all active flows by constantly adapting and redistributing the control gain h to all the media flows. 7. Conclusions and future work Given the fast growth of cloud computing environment and its different applications, particularly for healthcare and multimedia, this work has proposed a media-aware flow scheduling scheme

Table 1 Video sequence’s parameters.

Fig. 7. Mean frame wait time.

Ck

C1

C2

C3

C4

kk(dB/Kbps) Rk(Kbps) Dk(ms)

0.0170 550 350

0.0105 500 370

0.0064 400 400

0.0060 400 420

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Fig. 9. Average performance comparison based on MOS.

and an analysis of the frame delay and jitter in body area network using slotted ALOHA as the medium access method. Analytical expressions to calculate these two metrics when the cross-layer solution is used have been derived. Moreover, according to the results shown, it can be seen that the cross-layer solution creates a tradeoff between the frame delay and energy consumption. Also, the analytical expressions have proven to predict the results achieved by simulations correctly. Finally, it has been shown that the frame wait time jitter is kept at a low and constant level. Future work might consider the use of other medium access methods like TDMA and CSMA. Thus, new analytical expressions will have to be derived, including cross-layer dependencies on the analysis. Moreover, multi-hop communication, routing protocols, and cross-layer solutions involving the network layer could be proposed.

Appendix B. Calculation of the mean of random variable W The random variable W has been related to the other random variables in Eq. (26). Using the mean operator on both sides of the equation results in

E½W ¼ E½N  tslot  X þ k  tslot :

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

E½W ¼ E½N  t slot  E½X þ k  tslot :

This work has been partially supported by Instituto de Telecomunicações, Next Generation Networks and Applications Group (NetGNA), Portugal, and by National Funding from the FCT – Fundação para 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 the next time slot, resulting in n time slots since the last frame transmission. If the random variable X randomly selects the next frame generation to be within the guard bit duration of the current transmission, 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  ¼

Z sgb

l  elx dx ¼ 1  elsgb :

E½N ¼

þ1 P

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

Z sgbþtslot

ð36Þ

and since pN(n) has no negative part, and for n = 0 the multiplication nullifies 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 wellknown to be 1/l, and the mean of the constant part is the value of the constant, the remainder of Eq. 28 is proven. Appendix C. Calculation of the standard deviation of random variable W Before calculating the standard deviation, the variance is calculated, and it is represented by

r2W ¼ VarðWÞ ¼ VarðN  tslot  X þ k  tslot Þ;

ð37Þ

where the function Var(A), represents the variance of the random variable A. According to the following variance property [29], we can have

2

þ b  VarðBÞ þ 2  a  b  Cov ðA; BÞ;

ð38Þ

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

VarðWÞ ¼ t2slot  VarðNÞ þ VarðXÞ  2  t slot  Cov ðN; XÞ:

l  elx dx

ð39Þ

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

sgb

¼ elsgb  elðsgb þtslot Þ :

n  pN ðnÞ

Varða  A þ b  B þ cÞ ¼ Varða  A þ b  BÞ ¼ a2  VarðAÞ ð32Þ

0

P½N ¼ 1 ¼ P½sgb 6 X < sgb þ t slot  ¼

ð35Þ

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

n¼1

Acknowledgments

ð34Þ

ð33Þ

Analogue to the previous case, the boundaries of the random generation of X will vary in multiples of tslot. Thus, if sgb + 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 negative result, n will never be negative, and since the n = 0 case does not follow the progression for n > 0, the probability mass function can be generalized by the three cases of Eq. (27) shown previously.

VarðNÞ ¼ E½N2   E½N2 ¼

þ 1 P n¼1

n2  pN ðnÞ  E½N2 ;

ð40Þ

where E[N] has been defined in Appendix B. From the discussion in Appendix B on the sum limits, it can be inferred that r2N ¼ VarðNÞ reduces to Eq. (30). The variance of the exponential random variable X is well-known to be 1/l2. Finally, Cov(N, X) can be calculated by

Cov ðN; XÞ ¼ E½N  X  E½N  E½X:

ð41Þ

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

In order to calculate E[N  X], the joint probability distribution of N 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  elx. Then, the expected value of N  X is

E½N  X ¼

1 P n¼1

n

Z sgb þðnÞtslot

x  l  elx dx

ð42Þ

sgb þðn1Þtslot

and from the previously defined expected values of N and X, the covariance of N and X reduces to Eq. (31), and all the dependencies of 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. References [1] J. Baliga, R.W.A. Ayre, K. Hinton, R.S. Tucker, Green cloud computing: balancing energy in processing storage and transport, Proceedings of the IEEE 99 (1) (2011) 149–167. [2] W. Yi, M.B. Blake, Service-oriented computing and cloud computing: challenges and opportunities, IEEE Internet Computing 14 (6) (2010) 72–75. [3] X. Teng, Y. Zhang, C.C.Y. Poon, P. Bonato, Wearable medical systems for phealth, IEEE Reviews in Biomedical Engineering 1 (2008) 62–74. [4] H. Liu, P. Wan, X. Jia, Maximal lifetime scheduling for K to 1 sensor-target surveillance networks, Computer Networks 50 (15) (2006) 2839–2854. [5] V.C. Gungor, G.P. Hancke, Industrial wireless sensor networks: challenges, design principles, and technical approaches, IEEE Transactions on Industrial Electronics 56 (10) (2009) 4258–4265. [6] M. Chen, S. Gonzalez, A. Vasilakos, H. Cao, V. Leung, Body area networks: a survey, ACM/Springer Mobile Networks and Applications 16 (2) (2010) 171– 193. [7] I.F. Akyildiz, T. Melodia, K.R. Chowdhury, A survey on wireless multimedia sensor networks, Computer Networks 51 (4) (2007) 921–960. [8] V. Srivastava, M. Motani, Cross-layer design: a survey and the road ahead, IEEE Communications Magazine 43 (12) (2005) 112–119. [9] R.W. Ha, P.-H. Ho, X.S. Shen, Cross-layer application-specific wireless sensor network design with single-channel CSMA MAC over sense-sleep trees, Computer Communications 29 (17) (2006) 3425–3444. [10] H. Kwon, T.H. Kim, S. Choi, B.G. Lee, A cross-layer strategy for energy-efficient reliable delivery in wireless sensor networks, IEEE Transactions on Wireless Communications 5 (12) (2006) 3689–3699. [11] I.F. Akyildiz, K.R. Chowdhury, Wireless multimedia sensor networks: applications and testbeds, Proceedings of the IEEE 96 (10) (2008) 1588–1605.

1827

[12] H.-P. Shiang, M. van der Schaar, Informationally decentralized video streaming over multi-hop wireless networks, IEEE Transactions on Multimedia 9 (6) (2007) 1299–1313. [13] L. Zhou, B. Zheng, J. Cui, B. Geller, Media-aware distributed scheduling over wireless body sensor networks, in: Proceedings of IEEE ICC 2011, Kyoto, Japan, June, 2011, pp. 5–9. [14] L. Zhou, X. Wang, W. Tu, G. Mutean, B. Geller, Distributed scheduling scheme for video streaming over multi-channel multi-radio multi-hop wireless networks, IEEE Journal on Selected Areas in Communications 28 (3) (2010) 409–419. [15] T. Li, M. Fu, L. Xie, J. Zhang, Distributed consensus with limited communication data rate, IEEE Transactions on Automatic Control 56 (2) (2011) 279–292. [16] L. Zhou, N. Xiong, L. Shu, A. Vasilakos, S.-S. Yeo, Context-aware middleware for multimedia service in heterogeneous networks, IEEE Intelligent Systems 25 (2) (2010) 40–47. [17] H. Su, X. Zhang, Battery-dynamics driven TDMA MAC protocols for wireless body-area monitoring networks in healthcare applications, IEEE Journal on Selected Areas in Communications 27 (4) (2009) 424–434. [18] X. Wang, S. Wang, D. Bi, Compacted probabilistic visual target classification with committee decision in wireless multimedia sensor networks, IEEE Sensors Journal 9 (4) (2009) 346–353. [19] X. Wang, S. Wang, D. Bi, Distributed visual-target-surveillance system in wireless sensor networks, IEEE Transactions on Systems, Man, and Cybernetics 39 (5) (2009) 1134–1146. [20] Y. Chen, J. Teo, J.C.Y. Lai, E. Gunawan, K.S. Low, C.B. Soh, P.B. Rapajic, Cooperative communications in ultra-wideband wireless body area networks: channel modeling and system diversity analysis, IEEE Journal on Selected Areas in Communications 27 (1) (2009) 5–16. [21] E. Reusens, W. Joseph, B. Latre, B. Braem, G. Vermeeren, E. Tanghe, L. Martens, I. Moreman, C. Blondia, Characterization of on-body communication channel and energy efficient topology design for wireless body area networks, IEEE Transactions on Information Technology in Biomedicine 13 (6) (2009) 933– 945. [22] IEEE 802.15.4, Part 15.4: Wireless medium access control (MAC) and Physical layer (PHY) specifications for low-rate wireless personal area networks (WPANs), IEEE Computer Society, September 2006. [23] IEEE 802.15.3, Part 15.3: Wireless medium access control (MAC) and physical layer (PHY) specifications for high rate wireless personal area networks (WPANs), IEEE Computer Society, September 2003. [24] H. Luo, S. Ci, D. Wu, N. Stergiou, K. Siu, A remote markerless human gait tracking for e-healthcare based on content-aware wireless multimedia communications, IEEE Wireless Communications 17 (1) (2010) 44–50. [25] J.D. Kraus, R.J. Marhefka, Antennas for All Applications, 3rd ed., McGraw Hill Science, Engineering, Math, 2001. [26] A.S. Tanenbaum, Computer Networks, 4th ed., Prentice Hall PTR, 2003. [27] ‘‘OMNeT++ 4.1. Available at: .’’ [28] E. Altman, K. Avrachenkov, Performance analysis of AIMD mechanisms over a multi-state Markovian path, Computer Networks 47 (3) (2005) 307–326. [29] A. Papoulis, S. Pillai, Probability Random Variables and Stochastic Processes, 4th ed., McGraw Hill, 2002.