Combined analysis of contention window size and duty cycle for throughput and energy optimization in wireless sensor networks

Computer Networks 57 (2013) 1101–1112

Contents lists available at SciVerse ScienceDirect

Computer Networks journal homepage: www.elsevier.com/locate/comnet

Combined analysis of contention window size and duty cycle for throughput and energy optimization in wireless sensor networks Mehmet Yunus Donmez a, Sinan Isik a,b,⇑, Cem Ersoy a a b

NETLAB, Department of Computer Engineering, Bogazici University, Istanbul, TR-34342, Turkey Department of Mathematics, Bogazici University, Istanbul, TR-34342, Turkey

a r t i c l e

i n f o

Article history: Received 3 April 2012 Received in revised form 25 September 2012 Accepted 5 November 2012 Available online 22 December 2012 Keywords: Wireless sensor networks Multimedia Duty cycle Medium access Contention window size

a b s t r a c t The main objective in a wireless sensor network design is to minimize the energy expenditure for sustaining a long lifetime. Moreover, some recent multimedia applications require the network to satisfy specific throughput and delay constraints for large data sizes. In this paper, we analytically derive the expected throughput and the expected energy expenditure for a synchronized contention-based duty cycled MAC protocol. Our analysis explores the combined effect of contention window size, duty cycle and data size on throughput and energy expenditure for a successful transmission. We show that the performance of the network in terms of both metrics fluctuates with increased duty cycle as opposed to the general intuition that an increase in duty cycle increases the throughput and decreases the energy expenditure in the network. The results, validated by simulations, show that in order to provide an efficient MAC operation, the contention window size and the duty cycle should be optimized together for a given data size. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction In wireless sensor networks (WSNs), energy efficiency is the primary concern in all protocol designs regarding the communication of the data generated by the sensors with limited energy budgets. Two primary approaches have been considered in the MAC layer for energy efficiency in WSNs. The first one is the synchronous approach used in SMAC [1], T-MAC [2] and SCP-MAC [3] which adopts common sleep/wakeup schedules to remain awake only for the contention periods to coordinate and transmit data. The second approach is the asynchronous approach used in B-MAC [4] and X-MAC [5] which adopts asynchronous sleep/wakeup schedules to transmit data by using preamble sampling. The first group of protocols are designed for ⇑ Corresponding author at: NETLAB, Department of Computer Engineering, Bogazici University, Istanbul, TR-34342, Turkey. Tel.: +90 212 3597330; fax: +90 212 2877173. E-mail addresses: [email protected] (M.Y. Donmez), isiks@ boun.edu.tr (S. Isik), [email protected] (C. Ersoy). 1389-1286/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comnet.2012.11.016

periodic traffic whereas the second group is proposed to handle seldom traffic. The addition of visual sensing modality to the sensor nodes has extended the capability of WSNs to support multimedia adaptations of typical WSN applications [6,7], which introduce a many-fold increase in the volume of data traffic with larger data size and more stringent QoS requirements. In a typical sensor network application, the network usually generates light traffic for periodic reports. In light to moderate traffic conditions, the use of an asynchronous MAC protocol may be ideal to provide a low latency and high throughput operation. However, a multimedia sensor network usually operates with light traffic such as control and periodic report messages of small size and generates bursty traffic of large size in the vicinity of a detected event. The situation gets worse around the sink due to the funneling effect caused by the convergecast communication pattern resulting with high traffic density approaching to a saturation load [8]. In such traffic conditions, it is beneficial to use a synchronized scheme to adapt quickly to the traffic

1102

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112

changes and regulate the medium access for maximum throughput and minimum energy consumption in the network. In synchronous MAC protocols, a neighborhood can be informed about traffic changes via broadcast messages. However, in asynchronous approaches it is difficult to inform the neighborhood about the changes in traffic patterns and to tune the parameters of the MAC protocol in the whole neighborhood. Being the ancestor of many duty-cycled, contention based and synchronized MAC protocols [2,3,9,10] in the literature, we inspect the performance of the SMAC protocol [1] under saturated heavy load traffic conditions. SMAC aims to reduce the energy consumption in WSNs by periodically putting sensors into sleep state to enable low-dutycycle operation in a multi-hop network. Even though low duty cycle of SMAC is efficient in terms of energy conservation, it results in high latency and lower throughput, which are the key factors affecting the functionality of some delay-sensitive applications, such as border surveillance, target tracking and fire detection. Although, some recent proposals [11–14] uses SMAC as the underlying MAC protocol for multimedia sensor networks, the duty cycled operation should be reconsidered to improve the performance of the sensor network regarding the high volume of traffic and large data size. The duty cycle concept of SMAC is extended in [15] to support multiple duty cycles dynamically adjusted by the sensors to adapt to different traffic conditions. Dynamic approach alleviates the high latency problem when the traffic load is high, while still keeping the energy efficiency when the traffic load is low. However, the contention window size and the data size should also be considered in the determination of duty cycle, since improper duty cycle configurations may lead to significant performance degradations in terms of latency and throughput. In SMAC protocol, the time is partitioned into constantlength frames which is further divided into synchronization, listen and sleep periods. In the synchronization period, sensors exchange their sleep schedules via the periodically broadcasted SYNC packets to their immediate neighbors. Consequently, virtual clusters are formed by the sensors following the same sleep schedule. In the listen period, the nodes having data packets contend for the medium, while the remaining nodes listen to the medium for possible incoming packets. The node that wins the contention and the destination node stay awake during the data transmission, whereas other nodes sleep to the end of the sleep period that is scheduled after the end of transmission. The performance of the network is tightly bound to the performance of virtual clusters, which is determined by the node density, the contention window size, the duty cycle and the data size. Certain subsets of these parameters jointly determine the time components that constitute the throughput performance of a virtual cluster. The contention window size and duty cycle determines the SMAC frame duration. On the other hand, the density of the contending nodes and the contention window size determine the fail probability in a contention period of an SMAC frame, and hence the expected number of frames to elapse till a successful contention. In addition, the data size, jointly with the contention window size and duty cycle,

determine the number of frames required for a successful transmission to finalize. The paper provides an analytical model for the expected throughput and the expected energy expenditure of an SMAC virtual cluster under saturated conditions to evaluate the worst case performance. The model is constructed for the virtual cluster that is formed in the neighborhood of the sink since the performance of the whole network is highly determined by the performance in the neighborhood of the sink. The model is based on the number of nodes in a cluster, the number of contending nodes, the contention window size, the duty cycle and the data size. It derives the expected time and expected energy expenditure for a successful transmission to finalize including retrials caused by collisions. Using the expected time, it introduces the throughput metric for a virtual cluster. In that way, the model enables us to investigate how the cross relationship among the operational parameters of SMAC affects the performance of the network. The strength of this paper is that it is the first analysis in the literature that concentrates on the combined effect of duty cycle and contention window on the throughput and energy consumption for given data size and number of contenders. The paper raises an objection to the general intuition that the throughput of the network increases with an increase in the duty cycle. via analysis validated by simulations, the paper presents that the throughput and energy expenditure of the network fluctuates while increasing the duty cycle and it shows that in order to improve the efficiency of the operation of SMAC, a proper adjustment of duty cycle and contention window size pair is required. The results of the paper can serve as a guide for the selection of appropriate values for operational parameters when deploying a sensor network that uses SMAC as the underlying MAC protocol. Moreover, another outcome of this paper is that it is most beneficial to transmit packets in a regulated manner by minimizing the sleep durations for the transmitter at the end of transmissions till the end of the MAC frame by adjusting the contention window and duty cycle parameters properly. This result provides a hint for the parameter optimization of synchronization based sensor MAC protocols exposed to the saturation load to maximize their throughput. The rest of the paper is organized as follows. An overview of the related works on the analysis of the duty cycled MAC protocols are presented in Section 2. In Section 3, the operation of SMAC protocol is summarized and the duty cycle related system parameters required for the analysis are introduced. Our analysis of throughput and energy expenditure of SMAC for the steady state is presented in Section 4. The analysis is supported by simulations and the effect of contention window size on time, throughput and energy expenditure for various number of contending nodes is explored in Section 5. Section 6 concludes the paper. 2. Related works on the analysis of SMAC and duty cycle optimization SMAC introduces the low-duty-cycle operation for energy conservation in sensor networks using periodic

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112

listen/sleep schedules. An analysis based on Markov models for wireless sensor networks that contains nodes with sleeping behavior is proposed in [16]. However, the proposed sensor model is not suitable for the analysis of SMAC since this common model ignores some protocol details such as fixed duty cycle, overhearing avoidance and message passing. An analytical model for the energy consumption of sensors using SMAC for different traffic conditions and network topologies is proposed in [17]. The analytic model can estimate the energy consumption under different duty cycles for sensor nodes and evaluate the design trade-offs. In addition to the energy consumption, in order to evaluate the service delay and throughput of SMAC protocol under unsaturated conditions, [18] provides an M/G/1 queuing model using the classical Bianchi model [19] for IEEE 802.11 protocol. The model takes into account the impact of several factors together, including periodic listen and sleep cycle, various incoming traffic loads, the backoff mechanism, the queueing behavior at the MAC layer, and the non-independent nature of service delay distributions of nodes. A similar study based on Markov model is proposed in [20] to analyze the packet delay and energy consumption of the SMAC protocol for a successful packet transmission in one-hop under unsaturated conditions. The analysis is based on the architectural characteristic of the SMAC protocol with a fixed frame length, and it reflects the probability that contending nodes attend the backoff procedure, depending on the offered load. By using the analytic forms, the packet delay and the energy consumption can be numerically evaluated under various parameters, such as duty cycle, and offered load. In [21], the analysis in [18] is extended to model the multi-hop network performance of SMAC, which can take the node active/sleep and contention backoff mechanism into account. In this model, each node is regarded as a finite single server queue with server shutdown and the node state is modeled as a two-dimension continuoustime Markov chain (CTMC). The analytical model enables the investigation of the performance tradeoff between energy efficiency and QoS requirement, and gives theoretical insight into the optimal parameters such as duty cycle, mean active period and buffer size in multi-hop wireless sensor networks. The behavior of SMAC with a finite queue capacity is evaluated in [22] using a model based on [19]. A 1-D Markov model is proposed to describe the behavior of SMAC without retransmissions, and a 2-D Markov model is used to describe the behavior of SMAC with retransmissions. The throughput of SMAC is obtained from the proposed models. Markov model and throughput analysis can be used to estimate the performance of SMAC, optimize the SMAC parameters, and optimize the duty cycle to arbitrate the tradeoff between throughput and network lifetime. In [23], various MAC protocols including SMAC are analyzed for low data rate applications without considering the effect of contention resolution and large data sizes on throughput and energy consumption. These models explore the effects of different parameters such as the number of nodes, queue capacities, contention window sizes,

1103

and data arrival rates on the service delay, throughput and energy consumption. However, they do not consider the interdependency between duty cycle, contention window size and data size which significantly affects the throughput and energy expenditure of SMAC. In addition, these studies ignore the time and the energy spent in the synchronization period, which actually affects the contention window size and the duty cycle configurations for the optimal throughput and the energy expenditures of the SMAC protocol. The duty cycle optimization for SMAC is studied in [24], which argues that when designing the listening time, SMAC fails to consider the traffic distribution factor. This work considers a Gaussian traffic distribution and proposes an optimization approach for the listening time in SMAC based on energy and latency models. It is found that SMAC with optimized listening time outperforms SMAC with those values in [1], with less energy waste, lower latency and higher average delay/energy saving efficiency. In [25], the average packet delivery latency of RMAC [9], a successor of SMAC, is numerically analyzed in a probabilistic manner to obtain the the average packet latency which can be easily applied for any multi hop transmission methods. The paper also mathematically obtain an optimal duty cycle value that minimizes the average power consumption while satisfying a given delay bound. The optimal duty cycle found by the analysis provides a significant reduction in the power consumption compared to the setting in [9]. In addition, a duty cycle optimization approach is presented in [26] for the unslotted IEEE 802.15.4 based wireless sensor networks, where the objective function is the total energy consumption subject to the constraints of delay and reliability of the packet delivery. The protocol resulting from the optimization minimizes the energy consumption while guaranteeing delay and reliability requirements. The the optimization problem is approximated by deriving empirical explicit models for cost function and constraints as function of sleep and wake time. With this simplification the optimization problem is solved in closed form, which makes it possible to compute the optimal solution at sensor nodes online. In [27], an analytical approach that is not based on a Markov model is introduced. This study aims to derive energy and delay optimized contention window sizes for nonsleeping contention based sensor network MAC protocols. Our study incorporates the contention analysis approach of [27] into the analysis of the duty cycled operation of SMAC by taking the data size into account which has a joint impact with the duty cycle and the contention window size on the throughput and the energy expenditure of an SMAC cluster. In this work, we inspect the worst case performance of the SMAC protocol under saturated load conditions with large data size different from the studies analyzing the performance of SMAC. As some of the presented work, we analyze the one hop performance of a virtual cluster around the sink node since we believe that the performance in the neighborhood of the sink node significantly affects the overall network performance. Different than each presented approach, our approach is the first that analyzes

1104

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112

the combined effect of contention window size and duty cycle on throughput and energy performance of SMAC.

3. SMAC model For the sake of completeness, we will briefly describe the SMAC operation and introduce the system parameters that will be used in the analysis. The basic scheme of SMAC [1] is shown in Fig. 1. Each node sleeps for a duration of T sleep and then wakes up to see if any other node wants to talk to it. During the sleep period, the node turns off its radio, and sets a timer to awake itself later. The complete cycle of awake and sleep is called a frame. The awake interval is composed of synchronization and listen periods. In the synchronization period, nodes exchange their schedules by periodically broadcasting a SYNC packet to their immediate neighbors. In the listen period, if a node has data to deliver, it contends for the medium, otherwise it listens to see if a neighbor wants to deliver a packet to it. Each period has a contention window with many time slots for senders to perform carrier sense. For example, if a sender wants to send a SYNC packet, it starts carrier sense when the receiver begins listening. It randomly selects a time slot to finish its carrier sense. If it has not detected any transmission by the end of that time slot, it wins the contention and starts sending its SYNC packet. A similar procedure is followed while sending data packets. If two or more awake nodes have data packets to send, and select the same slot in the contention period, these nodes experience a collision in that frame. Hence, the data transmission in that SMAC frame fails due to collision and all nodes in the neighborhood of collision sleeps till the next SMAC frame. The medium access attempts by the nodes to transmit packets are postponed to the contention period of the subsequent SMAC frame. If no collision occurs in the contention, the winner node transmits its data packet, while the other nodes not involved in the communication sleep till the end of the transmission according to the overhearing avoidance mechanism of SMAC. At the end of the data transmission, the communicating nodes sleep until the beginning of the subsequent SMAC frame. SMAC applies message passing to reduce applicationperceived latency and control overhead. A message is the collection of meaningful, interrelated units of data. SMAC fragments the long message into many small fragments, and transmit them in a burst to decrease the penalty of accumulated contention latency for individual fragments. Only one RTS packet and one CTS packet are used. They reserve the medium for transmitting all the fragments. Every time a data fragment is transmitted, the sender waits for an ACK from the receiver. If it fails to receive the ACK, it

CWforSync

SyncPeriod

RTS ListenPeriod

T frame ¼ T activ e =rdc   ¼ T sync þ T listen =r dc ¼ ððW s  1Þ  tslot þ t SYNC ðW  1Þ  tslot þ t RTS þ t CTS Þ=r dc ð1Þ T sleep ¼ T activ e  ð1  rdc Þ=r dc

ð2Þ

T tr ¼ n  ðtDATA þ t ACK Þ

ð3Þ

where tslot ; tSYNC ; t RTS ; tCTS ; t DATA and tACK are the durations for a single contention slot and the packets of SMAC in a channel of bitrate c in terms of bits per second. 4. Throughput and energy expenditure analysis of SMAC In this section, we will derive the expected time and the expected energy expenditures of a virtual cluster of SMAC to finalize a transmission successfully. The analysis aims to inspect the interdependency between the number of contenders, contention window size, duty cycle and data size. The throughput of the virtual cluster is obtained using the expected time analysis. 4.1. Expected time to finalize a transmission The expected time in terms of SMAC frames required for a successful data transmission, X, is defined as the duration between the start of the frame where the contention for the data begins to the end of the frame, in which the data transmission is finalized. Hence X can be decomposed into two phases: K, the expected duration consumed for the frames in which collision occurs and C, the expected duration of the frames in which the contention is successful and transmission is finalized. If the transmission duration is longer than the sleep interval which is determined by the duration of active interval and the duty cycle, data transmission may last more than one frame, which should be considered in the derivation of C. The equations for these components are derived in terms of the contention

Transmissionduration(ttr)

CWforDATA SYNC

will extend the reserved transmission time for one more fragment, and re-transmit the current fragment immediately. Typically, the duration of synchronization (T sync ) and listen periods (T listen ) are determined as the time required for the contention window in that period plus the time required to send a SYNC packet or the time required to send RTS and CTS packets, respectively. The duty cycle (rdc ) is defined as the ratio of the awake interval (T activ e ) to the frame length (T frame ). The size of each period is normally fixed according to physical-layer and MAC parameters such as the radio channel bitrate (c) and the contention window sizes for the data period (W) and the SYNC period (W s ). The frame length, the duration of the sleep period and the transmission duration (T tr ) can be calculated as:

CTS

DATA

ACK

DATA SleepPeriod

Fig. 1. Frame structure of SMAC [1].

CWforSync ACK

1105

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112

window size, W, number of contending nodes, N, and SMAC duration parameters. We assume that each contending node selects a slot independently and uniformly from the slots 1; . . . ; W. (See Table 1). The derivations of K and C are based on the probability of a contention to be successful, n. Since the successful contention means that the first occupied slot w is selected by only one node, we need the probability of successful slot selection for each w. As in the analysis in [27], given the random variables W as the first occupied slot number in a slot selection and  as the status of the slot selection, the success probability, n, and therefore the collision probability, f are found as:

Hence, the expected time spent for collisions and retrials, K, equals the expected number of SMAC frames elapsed before the frame in which the successful data transmission starts, b, times the time elapsed in each retrial, T frame .

K ¼ b  T frame ¼

W X Pr½W ¼ w;  ¼ success w¼1

PW

¼N

w¼1 ðW

W

 wÞ

aw ¼

N1

ð4Þ

N

NðW  wÞN1 WN

ð5Þ

In SMAC, if a collision occurs in a slot selection in a frame, the retrial will be postponed to the next frame. Therefore, the derivation of K is based on the expected number of SMAC frames, b, in which the contention resolution results with collision before a successful data transmission. Since contentions in each SMAC frame are independent and random events, contentions can be modeled as a Bernoulli trial with success and fail probabilities of n and f as in [27], and therefore

1 b ¼  1; n

  T sync þ ðw  1Þt slot þ tRTS þ t CTS þ T tr T frame

Pr½W ¼ wj ¼ success ¼

Pr½W ¼ w;  ¼ success Pr½ ¼ success

ðW  wÞN1 ¼ PW N1 f ¼1 ðW  f Þ

C¼

ð6Þ

W X Pr½W ¼ wj ¼ success  aw  T frame w¼1

Symbol

Explanation

Symbol

Explanation

aw

Expected number of SMAC frames required to finalize a data transmission Expected number of collisions before a successful contention Expected time for a successful transmission after collisions Expected carrier sense time elapsed until w Probability of collision in the contention Expected energy consumption in a frame with collision Energy consumption until w where m nodes collide

Etot Etx Lsync m M n N

Cluster energy consumption for a successful transmission including collisions Energy consumed for transmission by a node per second Expected number of lost synchronization periods Number of colliding nodes Number idle nodes in the neighborhood Number of data packets in a message Number of contending nodes in the data period

Expected energy consumption during frames with collisions Expected time for collisions before a successful transmission Probability of success in the contention The period of SYNC message generation Random variable indicating the status of the slot selection Expected energy consumption during successful transmission Random variable representing the first occupied slot First occupied contention slot number Expected first occupied slot in a successful contention Expected time for a successful transmission including collisions

N sync r dc t slot t ACK t CTS t DATA t RTS t SYNC T activ e T frame

Initial number of nodes in the synchronization period Duty cycle Duration of a single contention slot Duration of an ACK packet Duration of a CTS packet Duration of a DATA packet Duration of an RTS packet Duration of a SYNC packet Duration of the awake period Duration of an SMAC frame

T listen T sleep T sync T tr W Ws

Duration of the listen period Duration of the sleep period Duration of the synchronization period Duration of message transmission Contention window size for the data period Contention window size for the synchronization period

b

f h hðw; mÞ

H K n

ssync 

U W

w w X

c C Eidle Erx Esync

Radio channel bitrate Random variable for the number of colliding nodes Energy consumed in the idle state by a node per second Energy consumed for reception by a node per second Average energy consumed by a node in the synchronization period

ð9Þ

Therefore,

Table 1 List of symbols.

C C0

ð8Þ

Since we know that the contention is successful in the current SMAC frame, now we need to calculate the probability of the first selected slot to be w given that it is selected by only one node. By the definition of the conditional probability,

where

Pr½W ¼ w;  ¼ success ¼

ð7Þ

In order to derive C, initially we need to calculate the expected number of SMAC frames required to finalize a data transmission, aw . Since the winner node transmits its RTS packet in the slot w, the time required for the medium access is ðw  1Þt slot . The duration of synchronization period (T sync ) and transmission duration of data packets (T tr ) can be calculated as presented in (1) and (3). Hence,

n ¼ ð1  fÞ ¼ Pr½ ¼ success ¼

  1  1  T frame n

ð10Þ

1106

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112

Since we have derived the durations of the phases K and C, we combine (7) and (10) to find the expected time in terms of SMAC frames required for a successful data transmission, X:

P½W ¼ w; C ¼ m;  ¼ fail f   N ðW  wÞNm m ¼ N P N1 W N W w¼1 ðW  wÞ

P½W ¼ w; C ¼ mj ¼ fail ¼

X¼KþC ¼

!   X W 1 ðW  wÞN1  T frame  a 1 þ PW w N1 n w¼1 f ¼1 ðW  f Þ

ð14Þ ð11Þ

T frame and therefore aw in (8) depends on r dc in (1). The transmission duration, T tr is independent from T sync and T listen which are constant for a given W and W s values. However, the duration of SMAC frame, T frame , is determined by T sync and T listen together with the duty cycle, r dc . W and N parameters jointly determine the number of collisions before successful contention and the expected slot number, w , where the successful slot selection occurs. w and r dc jointly determine the number of SMAC frames required for the transmission to finalize. Note that, 1=X gives the system throughput of the contending neighborhood in terms of message per second where a message is the data unit composed of many packets via the message passing function of SMAC. 4.2. Expected energy expenditure to finalize a transmission As in Section 4.1, the energy consumption of a virtual cluster till the end of successful data transmission, Etot , can be decomposed into two components: H, as the total energy consumption in the neighborhood during collisions and, U as the total energy consumption in the neighborhood within the SMAC frames containing the successful contention and the data transmission. The equations for these components are derived in terms of the contention window size, W, number of contending nodes, N, number of idle nodes that do not have data to send, M and SMAC duration parameters. We assume that each contending node selects a slot independently and uniformly from the slots 1; . . . ; W. In order to derive the energy consumption in the H component, we need to calculate the probability of collision in a contention period of an SMAC frame. Assuming that m of N contenders collide in the first occupied slot w; w should be chosen by any m nodes and the slots w þ 1 to W, i.e., W  w slots, should be chosen randomly by the remaining N  m nodes. Since there are W N different slot assignment possibilities,

 Pr½W ¼ w; C ¼ m;  ¼ fail ¼

N m

 ðW  wÞNm W

ð12Þ

N

The probability of collision in a contention period of an SMAC frame (f) can be obtained from (4) as

f ¼ 1  n ¼ Pr½ ¼ fail ¼

WN  N 

PW

w¼1 ðW N

W

 wÞN1

ð13Þ

Since H component is composed of the energy consumption in the presence of collision, now we need to calculate the probability of the first selected slot to be w given that it is selected by m nodes. By the definition of the conditional probability,

In each collision, the energy consumption is determined by the number of nodes (m) colliding in the first occupied slot w and is calculated as:

hðw; mÞ ¼ ðN þ M ÞEsync þ ðN þ MÞðw  1Þt slot Eidle þ mt RTS Etx þ ðN þ M  mÞt RTS Erx

ð15Þ

where Erx ; Etx and Eidle are the energy consumed in reception, transmission and idle states of SMAC frame per unit time respectively. Esync is the average energy consumption per node in the synchronization period of an SMAC frame. The derivation of Esync can be found in Section 4.3. Hence the expected energy consumption in any collision, h, is:

h¼

W X N X

P½W ¼ w; C ¼ mj ¼ fail  hðw; mÞ

w¼1 m¼2

¼



W X N X w¼1 m¼2 W

N m

N

 ðW  wÞNm

N

PW

f ¼1 ðW

 f ÞN1

ð16Þ  hðw; mÞ

As in Section 4.1, the retrials will continue until a slot selection without collision. In SMAC, if collision occurs in a slot selection in a frame, the retrial will be postponed to the next frame. Therefore, the expected energy consumption for collisions and retrials equals to the expected number of SMAC frames elapsed before the frame where successful data transmission starts, b, times the expected energy consumption in each retrial, h. Substituting b from (6),

H¼hb¼h

  1 1 n

ð17Þ

The energy consumption in the U component can also be decomposed into three parts: the energy consumptions during the synchronization period, during the carrier sensing in the successful contention period and during data transmission. N þ M nodes are involved in the first two parts, whereas only the communicating parties are involved in the transmission phase, since all other nodes sleep according to the overhearing avoidance mechanism of SMAC after the reception of RTS message. Firstly, we need to calculate the expected carrier sense time, C0 , elapsed until the first occupied slot, w selected by only one node in the SMAC frame where the data transmission starts. The carrier sense duration of a successful contention is ðw  1Þtslot . Then by using (9),

C0 ¼

W X Pr½W ¼ wj ¼ success  ðw  1Þt slot w¼1

¼

W X

ðW  wÞN1  ðw  1Þt slot PW N1 w¼1 f ¼1 ðW  f Þ

ð18Þ

1107

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112

Hence, 0

U ¼ ðN þ MÞ  Esync þ ðN þ MÞ  C  Eidle þ Etr

ð19Þ

Et ¼ Nsync  t SYNC  Etx :

where

Etr ¼ ðN þ M  1ÞErx tRTS þ Etx t RTS þ Erx t CTS þ n  ðEtx tDATA þ Erx tACK Þ ð20Þ

4.3. Derivation of energy expenditure in the synchronization period Finally, we will derive the expected energy consumed per node in the synchronization period, Esync . Each node is assumed to transmit a SYNC message in every ssync seconds. We assume that all nodes create their SYNC packets in the same SMAC frame. Hence N sync nodes (which is equal to N þ M for our case) in the neighborhood start contending in the subsequent synchronization period and the winner nodes transmit their SYNC messages. Colliding nodes are assumed to transmit their packets regardless of the occurrence of a collision and do not contend in the following synchronization periods until a new SYNC packet is created. The remaining nodes contend in the subsequent synchronization periods in the same way until all nodes transmit their SYNC packets. We can model this process as a discrete time Markov chain (DTMC) where the time unit is an SMAC frame duration. There are N sync þ 1 states, each representing the number of remaining nodes to contend in that synchronization period. A state si (i ¼ 0 . . . N sync ) represents the case where N sync  i nodes remains in the contention of that synchronization period. The state N sync , representing 0 nodes is the absorbing state of the DTMC. The state transition probabilities of the transition matrix P for the absorbing DTMC are given as:

pij ¼

8   Nsync  i > > > ðW s wÞNsync j Ws > X > ji > < Nsync i w¼1

> > > > 0; > > : 1;

Ws

P¼

Er ¼ Nsync  ðt 1  1Þ  t SYNC  Erx :

ð25Þ

In case of a transmission or reception, the idle waiting time reduces to tslot  W s per node per synchronization period. Since the number of communicating nodes is N sync and the expected number of synchronization periods required to exhaust all messages is t1 , the total idle time energy expenditure of the synchronization periods with communication is:

Eci ¼ Nsync  t 1  tslot  W s  Eidle

ð26Þ

On the other hand, in each synchronization period without a transmission or reception, the total idle waiting time is t slot  W s þ tSYNC where W s is the contention window size for synchronization period. Hence, in case of an idle synchronization period, the total energy expenditure is:

Ei ¼ ðt slot  W s þ t SYNC Þ  Eidle :

ð27Þ

Combining (24)–(26), the total energy consumed for communication in the synchronization period is calculated as:

Ec ¼ Et þ Er þ Eci ¼ Nsync  t SYNC  Etx þ N sync  ðt 1  1Þ  tSYNC  Erx þ Nsync  t 1  tslot  W s  Eidle

ð28Þ

ð22Þ

synchronization periods per success is

!

l

frame

where there are N sync transient states and only one absorbing state. The fundamental matrix M of P can be found as:

M ¼ ðI  Q Þ1 ;

The expected number of nodes that transmit SYNC mesN sages in a synchronization period is found to be tsync . Con1 sequently, the total number of SYNC message receptions N is found as ðN sync  tsync Þt 1 . Hence, the total energy con1 sumed for the receptions is

ð21Þ

j>i i P j; j – Nsync i; j ¼ Nsync

RNsync 1 I11

ð24Þ

m s Each node generates its SYNC message in every T sync frame SMAC frames. The expected number of synchronization periods to finalize N sync transmissions is t 1 . Hence, each node consumes energy for communication in t 1 SMAC frames. According to (8), when the data cannot be transmitted in one SMAC frame, the transmission will continue to the following SMAC frames until the transmission is finished. In this case, no synchronization period is scheduled in those SMAC frames. The number of SMAC frames per successful data transmission is T C . Hence the number of lost

The matrix P has the canonical form [28]

Q Nsync Nsync 01Nsync

Since the number of SYNC messages is N sync , the total energy consumed for the transmissions of these messages is

ð23Þ

where the entry mij of M gives the expected number of times that the process is in the transient state sj if it is started in the transients state si . Then the ith entry t i of the column vector t ¼ M  c, where c is a column vector all of whose entries are 1, gives the expected number of steps before the chain is absorbed given that the chain starts in state si . Hence, t 1 gives us the expected number of SMAC frames required for N sync nodes to finish the transmissions of their SYNC messages.

C T frame

 1. Since the

number of frames that will elapse due to successful contention and collision are C and T frame respectively, the expected frame duration elapsed per data contention attempt is C  n þ T frame  f. Therefore, the number of contention attempts in ssync seconds can be found as l m ssync  n. As a result, the average number of lost synCnþT f frame

chronization periods (Lsync ) in

Lsync ¼



C

T frame

  1 

ssync seconds are: 

ssync

C  n þ T frame  f

n

ð29Þ

The number of synchronization periods that a node will l m ssync  Lsync  t 1 , since no T

stay idle can be found as

frame

synchronization energy is consumed in Lsync periods and

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112

transmission energy is consumed in t1 periods. Hence, the expected energy expenditure per SMAC frame per node in the synchronization period is:

l Esync ¼

ssync

m

 Lsync  t1  Ei þ Ec l m ssync  ðN þ MÞ T

T frame

ð30Þ

frame

5. Effect of contention window size and duty cycle on SMAC operation In this section, we explore the effect of contention window size and duty cycle on time, throughput and energy expenditure for a successful transmission for various number of contending nodes and message sizes. In addition, we verify the analytical results derived in Section 4 using the simulations implemented in MATLAB [29]. The process that we are trying to analyze is the contention process in a neighborhood. Since the virtual cluster mechanism synchronizes the nodes in the neighborhood, the simulated process is a simple stochastic process which initiates the contention process at the same time. Since the time frames are synchronized, the system can be simulated using Monte-Carlo simulation in MATLAB. In our simulations, the total simulation duration is partitioned into SMAC frames. In each phase of the SMAC operation the simulation time is progressed by the duration of the current events such as carrier sense operations, overhearing mechanisms, packet transmissions/receptions and resulting sleeping actions in the SMAC model (Section 3) which can be easily calculated with the given simulation parameters. Since the durations of these events are known in the simulation, the nodes affected by these events are determined at the end of each event and the related energy consumptions are calculated for the transmitting, receiving and overhearing nodes separately. The contention process that is analyzed in this paper is simulated by letting nodes randomly select a slot number from the contention window. The time is progressed in terms of slot durations until the first occupied slot is encountered. Depending on the results of contention which are either collision or success, the data delivery procedures of SMAC model are simulated similarly.

Table 2 Simulation parameters. Simulation parameters #Sensors in neighborhood #Contending nodes Duty cycle #Data packets per message Data packet size RTS/CTS/ACK/SYNC size Slot size DATA contention window size SYNC contention window size Channel bitrate TX power RX power IDLE power

30 sensors 5/10/15 sensors 1–100% (Default:15%) 1/5/10 packets 1000 bits 200 bits 20 bits 2–150 slots 32 slots 250 Kbps 81 mW 30 mW 30 mW

The duration of the simulation is configured to be 30 min. Along each run, we collect the number of successful contentions and number of collisions per success for a fixed contention window size (W), number of contending nodes (N), duty cycle (rdc ) and message size (n). In addition, the energy expenditures and the time required for a successful data transmission is gathered counting in the statistics collected for collisions prior to a successful contention. Each simulation instance is repeated 10 times and their averages are presented. The simulation parameters are listed in Table 2. The radio power consumption parameters are set as in [30], which are typical values for Mica2 Mote sensors. The figures in this section presents the analysis and simulation results for the statistics related with energy expenditure and throughput. We observe that the simulation results matches with the analytical results supporting the validity of the analysis for the assumptions given in Section 4.1. Fig. 2 presents the effect of contention window size for different number of contenders on X, which is the expected time per successful data transmission. In the test case for this figure, the data message is composed of 10 data packets which corresponds to 10 Kbits. We observe that there is a common behavior of a sharp decrease for X at the contention window size of 40. In order to inspect this behavior, for the instance of 15 contending nodes, we decompose X to its components, K and C in terms of the expected number of SMAC frames, size of which is determined by the corresponding contention window size. Fig. 3 presents the expected number of SMAC frames for K; C and X. The sharp decrease in Fig. 2 is also observed in Fig. 3 as a decrease from two to one SMAC frame for C. From (8) and (10), C is the expected duration in terms of the SMAC frames which contains the duration of the synchronization period, the carrier sense duration of a successful slot selection in the contention period and the transmission 0.3

Time per Successful Transmission (sec)

1108

Analysis (N=5) Simulation (N=5) Analysis (N=10) Simulation (N=10) Analysis (N=15) Simulation (N=15)

0.25

0.2

0.15

0.1

0.05

10

20

30

40

50

60

70

80

Contention Window Size (slots) Fig. 2. The effect of contention window size on X for N = 5, 10, 15.

1109

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112 9

Expected Number of SMAC Frames

8

7

6

5

4

3

2

1

0

10

20

30

40

50

60

70

80

Contention Window Size (slots) Fig. 3. The expected number of SMAC frames for K; C and X for N = 15.

duration. As shown in (1) and (2), the durations of the active and sleep periods, and consequently, the duration of an SMAC frame is extended by the increase in the contention window size for a given duty cycle. Since the transmission duration is constant, the transmission is expected to be finalized in less than two SMAC frames if the contention window size is extended to 40 slots and beyond. From our analysis, we find out that the expected transmission duration decreases to one frame at the size of 42 slots. The reason of the difference in the number of SMAC frames between the sizes of 40–42 slots is the result of likelihood of the selection of higher indexed slots (which depends on W and N) causing the transmission to extend to more than one frames, which affects the value of aw . The increase in the SMAC frame duration caused by an increase in W is reflected on X as a multiple of the number of expected SMAC frames required per successful transmission (Fig. 3). On the contrary, the expected number of collisions decreases as W increases since the collision probability for the first occupied slot for fixed number of contenders decreases. Hence, the contention window size causes a tradeoff on X between the expected number of collisions and the duration of an SMAC frame. When the contention window size is less than 40 in a neighborhood of 30 nodes containing 5,10 and 15 contenders, the optimal contention window sizes minimizing X values presented in Fig. 2 are 11, 16 and 20 slots, and otherwise, the optimal contention window sizes are 43, 42 and 41 slots respectively. Note that the order of optimal contention window size are reversed. As the number of contenders increases the index of the first occupied slot in a successful slot selection decreases and hence C decreases, which is the dominant component of X for W values greater than 40. For the contention window size less than 40, as the window size is increased to the optimal values, the effect of the decrease in the collision probability, and consequently the

Energy Expenditure per Successful Transmission (mJ)

14 Ω (Analysis) Ω (Simulation) Λ (Analysis) Λ (Simulation) Γ (Analysis) Γ (Simulation)

Analysis (N=5) Simulation (N=5) Analysis (N=10) Simulation (N=10) Analysis (N=15) Simulation (N=15)

13

12

11

10

9

8

20

40

60

80

100

120

140

Contention Window Size (slots) Fig. 4. The effect of contention window size on U for N = 5, 10, 15.

effect of the decrease in the number of collisions dominates the effect of the increase in the frame size. The dominance is reversed after the optimal window sizes. For contention window sizes greater than 40, the transmission is finalized in one SMAC frame, which decreases the effect of increase in SMAC frame duration on X. As W increases beyond 40, the collision probabilities for 5, 10 and 15 contenders approach to each other. Hence, the gap between the expected time per successful transmission curves decreases. Fig. 4 presents the effect of the contention window size for different number of contenders on Etot , which is the expected energy consumption in the neighborhood per successful data transmission. A tradeoff similar to the one observed on X is also observed on Etot between the expected number of collisions (increasing the energy for retransmissions) and the duration of an SMAC frame (increasing the energy for carrier sensing). We observe that the optimal contention window sizes which minimize Etot in a neighborhood of 30 nodes containing 5, 10 and 15 contenders are 30, 57 and 85 slots respectively. Up to the optimal W values for each curve, the energy consumption due to the retrials is dominant and as the number of contenders decreases, the number of collisions decreases. On the contrary, beyond the optimal W values, the energy consumption due to carrier sensing is dominant and as the number of contenders decreases, the expected carrier sense duration increases by (18). As a consequence, we observe that for the contention window sizes smaller than 45, the order of the energy expenditures is ascending in the number of contenders, whereas the order is totally reversed beyond the contention window of size 73. Note that the optimal contention window sizes differ for time and energy expenditure cases (Figs. 2 and 4). Depending on the application requirements, the preference between the two metrics varies. Hence, a joint metric

1110

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112 160 Analysis (10 pkts) Simulation (10 pkts) Analysis (5 pkts) Simulation (5 pkts) Analysis (1 pkt) Simulation (1 pkt)

140

Throughput (kbps)

120

100

80

60

40

20

0

10

20

30

40

50

60

70

80

Contention Window Size (slots) Fig. 5. The effect of contention window size on message throughput (1/ X) for message sizes of 1, 5 and 10 packets for N = 15.

should be introduced to optimize the contention window size including both metrics whose weights are determined regarding the application requirements. X  Etot is a simple example for the joint metric [31,32] where time and energy expenditures have equal weights in the optimization. In Fig. 5, the number of data packets per message is varied to present the effect of the contention window size on 1 X, which is the system message throughput of the contending neighborhood in terms of Kbps. We observe that when the duty cycle is 15%, transmission of messages of 1 and 5 packets are finalized in one SMAC frame regardless of the contention window size. However, in the 10 packets case,

450

160

400

Energy Expenditure per Second (mJ)

180

140

Throughput (kbps)

the transmission finalizes in two SMAC frames for the contention window sizes less than 40, which is the reason for the sharp increase in the throughput. We observe that the optimal contention window sizes which maximize the throughput in a neighborhood of 30 nodes containing 15 contenders for the message sizes of 1, 5 and 10 packets are 27, 27 and 41 slots respectively. However, when the contention window size is less than 40, the optimal throughput for the message size of 10 packets is obtained for the window size of 19 slots. Since for this message size, the transmission finalizes in two SMAC frames when the window size is less than 40, the increase in W increases the frame duration and X increases at least by a factor of two frame durations. Hence, the optimal window size that maximizes X1 is obtained at a smaller value as compared to smaller message sizes. Figs. 6 and 7 present the analysis results obtained for the effect of duty cycle on the expected throughput and on the expected energy expenditure of an SMAC virtual cluster for messages of size 1, 5 and 10 packets. In these figures, the contention window size for each curve is set as the optimal value determined for the corresponding message size in Fig. 5. In addition, the combined effect of the duty cycle and the contention window size on throughput and energy is presented in Fig. 8 for message size of five packets. A common intuition on the effect of duty cycle is that the throughput and the energy expenditure of the cluster monotonically increase with the increase in the duty cycle. However, we observe that the curves in both figures exhibits a sawtooth behavior. As the duty cycle is increased, the duration of the sleep period decreases and therefore the expected throughput and the expected energy expenditure increase since more messages are transmitted per second. However, when the sleep period duration is smaller than the message size, we observe a sudden decrease followed by a gradual

120

100

80

60

40

20

0 20

30

40

50

60

70

80

90

300 250

200 150 100 50

10 packets (W=41) 5 packets (W=27) 1 packet (W=27)

10

350

100

Duty Cycle (%) Fig. 6. The effect of duty cycle on message throughput (1/X) for message sizes of 1, 5 and 10 packets for N = 15.

0

10 packets (W=41) 5 packets (W=27) 1 packet (W=27)

10

20

30

40

50

60

70

80

90

100

Duty Cycle (%) Fig. 7. The effect of duty cycle on energy expenditure for message sizes of 1, 5 and 10 packets for N = 15.

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112

1111

consumption, we can conclude that the initial duty cycle value for which the desired level of throughput and energy consumption is observed should be selected as the system duty cycle in order to optimize the SMAC operation for the given application constraints. 6. Conclusion

Fig. 8. Combined effect of duty cycle and window size on (a) throughput and (b) energy expenditure (N = 15).

increase till the next duty cycle value where the expected carrier sense duration together with the data transmission are finalized in exactly two frames. The same pattern is observed for higher duty cycle values where a transmission is finalized in multiple frames. As stated in Section 3, the nodes not involved in the communication sleep during transmission according to the overhearing avoidance mechanism of SMAC. Moreover, at the end of the data transmission, all nodes sleep until the beginning of the subsequent SMAC frame. Hence, due to the under-utilization of the channel, the curves in each figure exhibits rapid degradation in the throughput and the energy expenditure. The number and location of the of peaks varies with respect to the message size which determines the transmission duration. It should be noted that as the duty cycle increases, the decrease in the duration of SMAC frame leads to an increase in the number of frames per second. Such an increase in the number of frames lead to an increase in the idle state energy consumption since the energy consumption per frame remains constant for fixed contention window sizes for data and synchronization periods. Considering both figures together with the idle energy

In this paper, we introduce an analytical model for the duty cycle based operation of SMAC with the message passing function enabled including the contention resolution and synchronization mechanisms. The analysis assumes a heavily loaded system such that the system is saturated with constant number of contenders at any time, which results with the worst case stable system performance in the steady state. We derive the expected time and the expected energy expenditure for a successful transmission to finalize which are corroborated by our simulation results. Considering the analysis results, the general intuition about the duty cycle that the throughput of the network increases by increasing the duty cycle is falsified. via analysis and simulation, the paper presents that the throughput and energy expenditure of the network fluctuates while increasing the duty cycle. In order to provide an efficient operation of SMAC in terms of energy expenditure and throughput, the contention window size and the duty cycle should be optimized together to provide a proper adjustment of both parameters for a given number of contenders and number of data packets per message. More specifically, for any contention window size under saturation load conditions, we should find the duty cycle value for which the transmission is expected to be finalized in multiples of one SMAC frame, which maximizes the throughput by minimizing sleep time. The paper also provides an intuitive hint for the parameter optimization of synchronized CSMA based sensor network protocols exposed to the saturation load to maximize their throughput. Acknowledgment This work is supported by The Scientific and Technological Council of Turkey (TUBITAK) under the Grant No. 108E207 (COST Action IC0906, WINEMO), by Bogazici University Research Fund (BAP) under the Grant Nos. 5146 and 5344, and by the European Community’s Seventh Framework Programme (FP7-ENV-2009-1) under the Grant agreement FP7-ENV-244088 FIRESENSE. References [1] W. Ye, J. Heidemann, D. Estrin, Medium access control with coordinated adaptive sleeping for wireless sensor networks, IEEE/ ACM Trans. Netw. 12 (3) (2004) 493–506. [2] T. van Dam, K. Langendoen, An adaptive energy-efficient MAC protocol for wireless sensor networks, in: International Conference on Embedded Networked Sensor Systems (SenSys), 2003, pp. 171– 180. [3] W. Ye, F. Silva, J. Heidemann, Ultra-low duty cycle MAC with scheduled channel polling, in: International Conference on Embedded Networked Sensor Systems (SenSys), ACM, New York, NY, USA, 2006, pp. 321–334. [4] J. Polastre, J. Hill, D. Culler, Versatile low power media access for wireless sensor networks, in: Proceedings of the 2nd International

1112

[5]

[6] [7] [8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21] [22]

[23] [24]

[25]

[26]

M.Y. Donmez et al. / Computer Networks 57 (2013) 1101–1112

Conference on Embedded Networked Sensor Systems, SenSys ’04, 2004, pp. 95–107. M. Buettner, G.V. Yee, E. Anderson, R. Han, X-mac: a short preamble mac protocol for duty-cycled wireless sensor networks, in: Proceedings of the 4th International Conference on Embedded Networked Sensor Systems, SenSys ’06, 2006, pp. 307–320. I. Akyildiz, T. Melodia, K.R. Chowdhury, A survey on wireless multimedia sensor networks, Comput. Netw. 51 (4) (2007) 921–960. S. Soro, W. Heinzelman, A survey of visual sensor networks, Advan. Multimedia 2009 (2009) 1–21. G.-S. Ahn, S.G. Hong, E. Miluzzo, A.T. Campbell, F. Cuomo, Funnelingmac: a localized sink-oriented mac for boosting fidelity in sensor networks, in: International Conference on Embedded Networked Sensor Systems (SenSys), ACM, 2006, pp. 293–306. S. Du, A. Saha, D. Johnson, RMAC: A routing-enhanced duty-cycle MAC protocol for wireless sensor networks, in: IEEE International Conference on Computation Communication (INFOCOM), 2007, pp. 1478–1486. Y. Sun, S. Du, O. Gurewitz, D.B. Johnson, DW-MAC: a low latency, energy efficient demand-wakeup MAC protocol for wireless sensor networks, in: ACM International Symposium on Mobile Ad Hoc Network and Computation (MobiHoc), ACM, New York, NY, USA, 2008, pp. 53–62. J. Wang, M. Masilela, J. Liu, Supporting video data in wireless sensor networks, in: Ninth IEEE International Symposium on Multimedia, 2007. ISM 2007, 2007, pp. 310–317. H. Alemdar, Y. Durmus, C. Ersoy, Wireless healthcare monitoring with rfid-enhanced video sensor networks, Int. J. Distrib. Sensor Netw. 2010 (2010) 1–10. Y. Durmus, A. Ozgovde, C. Ersoy, Distributed and online fair resource management in video surveillance sensor networks, IEEE Trans. Mobile Comput. 11 (2012) 835–848. S. Isik, M.Y. Donmez, C. Ersoy, Multi-sink load balanced forwarding with a multi-criteria fuzzy sink selection for video sensor networks, Comput. Netw. 56 (2) (2012) 615–627. P. Lin, C. Qiao, X. Wang, Medium access control with a dynamic duty cycle for sensor networks, in: Wireless Communications and Networking Conference, 2004. WCNC. 2004, vol. 3, IEEE, 2004, pp. 1534–1539. C.-F. Chiasserini, M. Garetto, An analytical model for wireless sensor networks with sleeping nodes, IEEE Trans. Mobile Comput. 5 (12) (2006) 1706–1718. H.-W. Tseng, S.-H. Yang, P.-Y. Chuang, H.-K. Wu, G.-H. Chen, An energy consumption analytic model for a wireless sensor MAC protocol, in: IEEE Vehicular Technical Conference (VTC), vol. 6, 2004, pp. 4533–4537. Y. Zhang, C. He, L. Jiang, Performance analysis of S-MAC protocol under unsaturated conditions, IEEE Commun. Lett. 12 (3) (2008) 210–212. G. Bianchi, Performance analysis of the IEEE 802.11 distributed coordination function, IEEE J. Sel. Areas Commun. 18 (3) (2000) 535– 547. S. Sung, S. Woo, K. Kim, Packet delay and energy consumption based on Markov chain model of the frame-based S-MAC protocol under unsaturated conditions, in: Information Networking. Towards Ubiquitous Networking and Services, LNCS, vol. 5200, SpringerVerlag, Berlin, 2008, pp. 604–613. J. Luo, L. Jiang, C. He, An analytical model for SMAC protocol in multihop wireless sensor networks, Sci. China Inf. Sci. (2010) 1–9. O. Yang, W. Heinzelman, Modeling and throughput analysis for SMAC with a finite queue capacity, in: Internnational Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), 2009, pp. 409–414. K. Langendoen, A. Meier, Analyzing mac protocols for low data-rate applications, ACM Trans. Sen. Netw. 7 (2010) 1–40. C. Li, K.-R. Wang, J.-L. Zhang, D.-X. Zhao, W. Li, Optimization of listening time of S-MAC for wireless sensor networks, The J. China Univ. Posts Telecommun. 16 (5) (2009) 41–45. K.-T. Cho, S. Bahk, Duty cycle optimization for a multi hop transmission method in wireless sensor networks, IEEE Commun. Lett. 14 (3) (2010) 269–271. S. Ergen, C. Fischione, D. Marandin, A. Sangiovanni-Vincentelli, Dutycycle optimization in unslotted 802.15.4 wireless sensor networks,

[27] [28] [29] [30]

[31]

[32]

in: IEEE Global Telecommunication Conference (Globecom), 2008, pp. 1–6. I. Demirkol, C. Ersoy, Energy and delay optimized contention for wireless sensor networks, Comput. Netw. 53 (12) (2009) 2106–2119. C.M. Grinstead, J.L. Snell, Introduction to Probability, second ed., American Mathematical Society, 1997. MATLAB, The Mathworks Inc., 2010. M. Miller, N. Vaidya, A MAC protocol to reduce sensor network energy consumption using a wakeup radio, IEEE Trans. Mobile Comput. 4 (3) (2005) 228–242. G. Lu, B. Krishnamachari, C.S. Raghavendra, An adaptive energyefficient and low-latency MAC for tree-based data gathering in sensor networks: research articles, Wirel. Commun. Mob. Comput. 7 (7) (2007) 863–875. Y.-F. Wen, Y.-Q. Chen, M. Pan, Adaptive ant-based routing in wireless sensor networks using energy⁄delay metrics, J. Zhejiang Univ. – Sci. A 9 (2008) 531–538.

Mehmet Yunus Donmez received his B.S. degree in mathematics and his M.S. and Ph.D. degrees in computer engineering from Bogazici University, Istanbul, Turkey in 1999, 2003 and 2011 respectively. He is currently a Postdoctoral Researcher at Computer engineering Department, Bogazici University. He worked as a Research Assistant at Mathematics Department in the same university, from 1999 to 2011. His research interests include design and analysis of QoS-aware cross-layer algorithms/protocols for wireless ad hoc and sensor networks, performance evaluation in computer networks, pervasive and ubiquitous computing, green networking and healthcare applications.

Sinan Isik received the B.S. degree in mathematics, and the M.S. and Ph.D. degrees in computer engineering from Bogazici University, Istanbul, Turkey in 1999, 2003 and 2011, respectively. He currently works as an Instructor at Bogazici University, Mathematics Department, where he also worked as a Research Assistant from 1999 to 2011. His research interests include reliable data delivery in wireless networks, design and analysis of cross-layer protocols for wireless ad hoc and sensor networks, performance evaluation in computer networks.

Cem Ersoy received his BS and MS degrees in electrical engineering from Bogazici University, Istanbul, in 1984 and 1986, respectively. He worked as an R&D engineer in NETAS A.S. between 1984 and 1986. He received his PhD in electrical engineering from Polytechnic University, Brooklyn, New York in 1992. Since then, he has been a professor of Computer Engineering and the leader of the Wireless Sensor Networks Research Group in Bogazici University. His research interests include wireless sensor networks, activity recognition and ambient sensing for healthcare, urban and participatory sensing with smartphones and green computing applications. Dr. Ersoy is the chairman of the IEEE Communications Society Turkish Chapter.