Optimal p-persistent MAC algorithm for event-driven Wireless Sensor Networks

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1 Otimal -ersistent MAC algorithm for event-driven Wireless Sensor Networks J. Vales-Alonso,E.Egea-Lóez, M. V. Bueno-Delgado, J. L. Sieiro-Lomba, J. García-Haro Deartment of Information Technologies and Communications, Polytechnic University of Cartagena, Sain. Corresonding author. Address: Camus Muralla del Mar, 30202, Cartagena, Sain. hone: , fax: , Abstract In event-driven wireless sensor networks nodes transmit information only if the monitored hysical magnitude levels have triggered an alarm. In these networks, traffic exhibits a high satial correlation, since it is likely that neighbor nodes detect and try to notify the same events. Thus, the robability of acket collision raises u, as well as notification delay, just as oosite as required. In this work we roose to use a - ersistent mechanism in the access control layer. The aim is reducing collisions and saving energy. We comute the otimal for a coherent network deloyment and describe the exerimental imlementation of our roosal. Theoretical comutations redict a notable imrovement, secially in terms of energy, and exeriments reveal that our roosal achieves u to 67% of energy saving comared against a erfect (collision-free) mechanisms. Index Terms Wireless sensor networks, MAC rotocols, delay sensitive, ersistent I. INTRODUCTION Wireless Sensor Networks (WSN) are ad-hoc networks devoted to data gathering based on low cost and low transmission range (usually, less than 00 meters) sensor devices. Data are transmitted by means of multi-ho routing from sensing nodes to secial nodes, called sinks, which rocess them. In WSN networks, mainly two kinds of traffic are usually considered []: () eriodic data traffic, sensed data samles are eriodically transmitted by each sensor to the sink(s), and (2) event-driven traffic, in this case the hysical environment is continuously monitored, and if the sensed magnitude fulfills a qualifying condition (e.g. temerature is greater than 300 Kelvin degrees, ressure is lower than 00 kilo-ascal, etc.) an event is triggered, that is, an alarm is transmitted (a notification ) to the sink(s). Event-driven networks are usually associated with delay-sensitive alications, which require short notification delays. Besides, a major constraint in WSN is still the battery lifesan, which determines, in most cases, the rotocols oeration. At Medium Access Control (MAC) level, sensor devices must turn on radios only when strictly necessary, to avoid unnecessary energy waste. Indeed, avoidance of idle listening and utting devices to slee are the most widely used aroaches to reduce ower consumtion. That is, nodes coordinate their oeration in active/slee eriods (see figure ), which yields to time-slotted activity. There are several roosals for MAC contention rotocols adated to this kind Timeslot #i Timeslot #i Timeslot #i+ Timeslot #i K Data transmission Contention micro slots Active eriod Sleeing eriod time (+) Fig.. Nodes coordinate themselves in activity/slee eriods, which result in time-slotted oeration of oeration, e.g. [2], [3], [4]. In this case, data exchange can only take lace in the active eriods. Within this eriod, before starting data transmission, nodes erform some anticollision mechanism. For CSMA/CA (the most common aroach), the mechanism is as follows: backlogged nodes randomly select a number of contention micro-slots k =,...,K, and start transmission if medium kees idle after that number of microslots. Transmission lasts until the end of active eriod. A collision occurs if more than one node select the same initial micro-slot. If traffic shows an indeendent attern among nodes (a classical hyothesis in the literature), time-slotted oeration notably reduces consumtion and rovides a flexible access scheme. However, in networks where traffic is event-driven, transmissions exhibit a high satial correlation, that is,it is very likely that several nearby nodes cature the same event and, consequently, try to simultaneously notify it. Since timeslotted oeration grous communications in the active art of the frame, the robability of acket collision raises u, as well as notification delay, just as oosite as required. In this aer we roose a modification of activity-slotted contention rotocols to minimize the average latency of event notification and reduce energy consumtion. Our modification is based on the introduction of a -ersistent algorithm at the MAC layer. That is, at each time-slot, backlogged nodes decide to wake u (with robability ) or to kee on sleeing (robability ). We analyze the otimal ersistence, which minimizes the delay of the first notification of the event. In fact, the desired effect is twofold, because nodes that decide to kee on sleeing consume less energy. For examle, consider an event sensed by 5 nodes, in the best case (with a successful transmission at the first trial) 5 nodes consume We use the term micro-slot for a carrier sensing slot to distinguish from the active eriod slot

2 the energy of an idle listening activity eriod, whereas using ersistence, on average only 5 of the nodes wake u and consume energy. For a low value of, a considerable saving of energy can be obtained. In fact, as we will show later, the saving is greater as the number of backlogged nodes increases. A comutational feasible method for comutation of is rovided, as well as different analytic results that demonstrate the outerforming oeration (in terms of energy and latency) of the roosed algorithm versus the classical -ersistent aroach. The remainder of this work is organized as follows: Section II highlights related works for WSN. In Section III the otimal is comuted as a function of the number of nodes resent. Section IV describes the theoretical results in terms of time and energy of rotocols using the otimal ersistence. In section V the results of an exerimental imlementation of the -ersistent mechanism over S-MAC and MICA2 motes is discussed. Finally, Section VI resents the main conclusions of this work. Note: Hereafter the following notation and conventions are used: Probabilities are denoted as rob{event}. Random variables (rv) are denoted as x. Average values are denoted as x. II. RELATED WORK The number of MAC rotocols for Wireless Sensor Networks which have been roosed in the last years shows the interest this field has acquired. Most of them mainly focus on energy saving, which is often achieved by trading-off for acket delivery latency, usually considered of secondary imortance. WSN MAC rotocols can be classified into the classical categories of contention based rotocols and time division rotocols. Classical contention based rotocols are simle, scalable and flexible but at the exense of high idle listening time, that is, high waste of energy. WSN rotocols based on Carrier Sense Multile Access (CSMA) are designed with mechanisms to avoid overhearing and idle listening and, thus, decrease energy consumtion. The most used aroach is to make nodes turn off their radio during inactivity. S-MAC rotocol [2] is the first which roose to organize nodes in eriodic cycles of activity and slee (listen/slee), This mechanism makes nodes activate for a short time interval (listening time) and ut them to slee (turn off the radio) during the rest of the time (slee time). The ratio of the listen time and slee time is called duty cycle. Decreasing duty cycle results in a reduction of the energy consumtion. Nodes coordinate slee time with their neighbours by means of a synchronization broadcast acket (SYNC acket). This acket is eriodically rebroadcasted to maintain synchronization. Therefore, the activity eriod is slit into two suberiods: synchronization and data exchange. During data exchange, nodes use a variation of the CSMA/CA rocedure of IEEE 802.: the contention window is fixed. In addition, RTS/CTS acket avoid hidden node roblems. SMAC reduces energy waste considerably, but the constant slee and listen eriods increase the latency under variable traffic load. Minimizing latency has also been the focus in [5], where authors roose to use a non-ersistent CSMA but selecting the carrier sensing micro-slots with a nonuniform robability distribution function (f) which maximizes the robability of success when N nodes become simultaneously backlogged. Namely, rob{ Start transmission in microslot j } = f(j). The distribution (f) also minimizes latency of a successful transmission. However, this otimal distribution requires the knowledge of the real number of contenders (N), which is usually unknown. To avoid this roblem, the authors rovide an aroximation to the otimal distribution, called Sift distribution. Our mechanism is subotimal in comarison with f in terms of collision robability. However, in our case, not all nodes that sense an event will contend in the activity eriod. This roerty notably reduces ower consumtion as we will show. III. ANALYSIS In this section we comute the otimal for the -ersistent mechanism described in Section I, that minimizes the delay of the first notification. That is, the time elased since the hysical event takes lace until the notification of the event reaches the sink node. Before carrying out this analysis, it is necessary to assume a network model, since the otimal deends on the exected number of nodes sensing a triggering event. This model rovides a way to estimate the number of nodes needed to cover an interest area with a required quality. That is, the number of nodes to be deloyed to ensure that the robability of loosing an event of interest is below some target limit. A. Network model The network is formed by n sensor nodes, densely and randomly deloyed in a large area (of size A), since we consider that events occur equirobably in the area A. Therefore the number of nodes that cature each event is given by a random variable N, taking values on [0,,...,n]. Let us consider an uniform node distribution into the target area. To comute N, we assume that events are received by nodes within a certain radio r from the oint where the event takes lace, and that the radio communication coverage radius is R. The size of the area where the event is sensed is given by a = πr 2 A. Provided that r < R, all the nodes that receive the event content for its simultaneous transmission towards the sink. Then, the robability mass function of N is given by equation (). rob{n = i} = ( n i )( a A ) i ( a A) n i (n a A )i e n a A i! N P oisson{n a A } () 204

3 that such a reemtion mechanism is easily achieved by means of a variable delay before carrier sensing like the SIFS and DIFS delays in IEEE 802. or S-MAC adative sleeing. In this case, minimizing the delay in the first transmission is equivalent to minimizing end-toend delay Target α Fig. 2. versus target α In the former equation we have emloyed the Poisson aroximation for the binomial distribution. This aroximation is correct if a A n a A n, which is clearly fulfilled in WSNs since n is exected to be very large and the ratio a A very low. Based on the Poisson distribution nomenclature, let us define = n a A. Therefore, in our model can be interreted as the average number of nodes that receives each event. In addition, there is a relationshi between and the event coverage robability (α) that is, the robability that at least one sensor catures an event, α = rob{n =0} α = e { = ln( α) (2) n = A a ln( α) For instance, in a deloyment in an area A of one kilometer square, if the event cature radio is 20 meters, for a event loss robability of α =0.00, we get =6.9, and n 5500 nodes. With this numerical examle we can verify that a A = n a A =6.9 n = 5500, and therefore the Poisson aroximation holds. Hence, for a given coverage robability target we can comute the number of sensors to be deloyed, and the associated to such network configuration. Figure 2 shows the value versus a coverage robability target from 95% to almost 00%. The maximum notification time is much less than the inter-event time. This assumtion imlies that when a new event occurs the network is emty of notifications from other events. That is, we do not need to take into account the effect of simultaneous hysical events in our study. There exists a reemtion mechanism that allows forwarding nodes to acquire the channel without contention. This assumtion is added to avoid contention from nodes in the route to the sink. The inclusion of such mechanism is sound since delay is minimized if a node that receives a notification acket, and must forward it towards the sink, immediately wins the channel and relay it. Let us notice B. Average notification time At the beginning of each activity eriod, all the nodes (N) that have received an event contend to access the channel and transmit its notification. Let K be the number of contention micro-slots, and let q be the random variable which selects the initial contention micro-slot for node i =,...,N. Since contention micro-slots are usually chosen uniformly, q = Uniform{,K} for all nodes. Let us denote q k = rob{q = k} = K for every k [,...,K]. The robability of success in contention (one node wins) is a function of the number of cometing nodes (N). Obviously, for N =the robability is, and for N 2 is given by (see [5]): π(n) =N = N K K s= K q s ( s q r ) (N ) = r= (3) ( s K )(N ) s= Now, let us consider ersistence in the MAC algorithm, in this case the robability of success is comuted in exression (4). π(n,) = N ( ) N π(c) c ( ) N c (4) c c= For a given number of contending nodes (N), we can define the random variable T N reresenting the number of timeslots until one of the N nodes wins the channel and transmits. The mass robability function of T N is given by equation (5). rob{t N =j} = π(n,)( π(n,)) j (5) for all j 0. In the last exressions we have considered the arameter N as a constant. However, as we reviously discussed, it is in fact a random variable N. From equations () and (5) we can comute the average number of time-slots until a node wins contention (T ), for a random number of contenders N. Namely, T () = n T i rob{n = i} (6) Let us notice that the revious exression gives the average number of time-slots required for the transmission of the first notification. 205

4 ersistent = Average Time (timeslots) Fig. 3. Otimal versus Fig T () versus for the otimal C. otimization From the revious analysis we can exress our minimization criterion as, { } =argmin T () = { n } =argmin T i rob{n = i}} = { n ( ) } =argmin jrob{t i = j} rob{n=i} Simlifying, T () = n ( j= i c= π(c)( i c i e ) ) c ( ) i c i! = f() Deriving the revious equation and equalling to zero to comute the minimum, we obtain, dt () d = d(f()/) d (7) =0 = f() f = g() (8) () From equation (8) the otimal can be comuted using the Banach s fixed oint theorem [6]. This theorem states that for a contraction maing g(x) from a closed subset F of a Banach sace E into F there exists a unique x in F such that g(x) =x. In our roblem the contraction maing is g() = f() f ().In addition, the theorem rovides a constructive method to find out the fixed oint: setting an arbitrary initial 0 we comute i+ = g( i )= f(i) f ( i). Eventually, the succession i converges to the otimal. Furthermore, since the theorem guarantees that the solution is unique this oint is the minimum we look for. IV. RESULTS Figure 3 shows the otimal obtained using the fixed oint theorem. For values of lower than 3.5 we obtain a >, which has no hysical meaning. In these cases, we have to select =to achieve the best erformance. That is, the mechanism behaves as a -ersistent algorithm. However, notice that in any ractical deloyment the number of nodes must be selected so that the robability of loosing events is low enough (usually target values should be less than %). Looking at figure 2, we get that in this case that >4. For these values of we obtain <, and the use of the - ersistent aroach makes sense. Figure 4 shows the average number of activity eriods (time-slots) required for the event notification resectively for the -ersistent and -ersistent (i.e., no ersistence mechanism used) variant of the rotocol. As it is shown, the use of ersistence controls and adjusts contention, keeing the notification delay almost constant. On the contrary, with - ersistence, delay increases as the number of contenders raises (higher ). In fact, the increase may be higher, deending on the size of the contention window, that is, the available number of micro-slots (these results have been comuted for K =32). Finally, the energy saving can be aroximated as follows. Let us assume some energy consumtion er awake node and activity eriod: G. If no ersistence is emloyed, the energy consumed for the transmission of a notification is E = T ()G (let us recall that reresents the average number of nodes sensing an event). Whereas if -ersistence is used the energy consumed is E T ()G. Let us notice that the average time T () is different in each case. Thus, the benefit is twofold since energy is reduced because of both the aslet nodes and the fewer number of time-slots needed. As shown in figure 5, using -ersistence the energy consumed can be as just a 5% of the energy wasted by the common aroach for very high density networks. For a more realistic scenario, as the one rovided in section III-A, with =6.9, savings are around 50%. V. EXPERIMENTAL SET-UP We have imlemented our -ersistent aroach over a slotted oeration MAC (the S-MAC rotocol) using a common WSN hardware (the MICA2 latform). Our goal was to demonstrate the feasibility of imlementing the ersistence 206

5 E /E = Fig. 5. Ratio of energy consumtion by -ersistent and no ersistent rotocols versus for the otimal mechanism in actual WSN equiment. Indeed, the network model used is different from the one discussed in the revious section, since it is not ossible to reroduce such a big network in a lab environment. On the contrary, we aim at testing the mechanism reliability and its otential as a energy saving rocedure. As stated in II, SMAC [2] is a WSN MAC rotocol that coordinates nodes in a time-slotted fashion of active/slee eriods. S-MAC uses a fixed contention window of K =32 micro-slots selected uniformly, which allows seamless imlementation of a -ersistent modification. MICA2 motes are a widely distributed hardware solution for WSN develoed by Crossbow Inc. MICA2 are based on Chicon CC000 radio module which oerates in the 868/96 MHz band. In our exeriments (deicted in figure 6) we have: Onemote(coordinator) which acts as sink and which triggers events in the network. Coordinator incororates a MTS300 sensing board, which among other caabilities, has a tone buzzer and a tone detector hardware both at 4 KHz. U to 8 sensing nodes, incororating also MTS300 sensing boards. The exeriments roceed as follow: ) The coordinator emits a tone at 4 KHz. 2) All sensing nodes detect it with the tone detector. 3) All sensing nodes start contention to notify the sound detection to the coordinator using the -ersistent aroach. 4) When the first notification correctly reaches the coordinator it set u a flag in the next SYNC eriod (in our modification of SMAC all nodes kee listening during SYNC eriods) to avoid further notifications. Figure 6 shows our setu. We erformed this exeriment for different number of nodes (N =2, 4, 8). Let us remark that in this case all the nodes cature each event, and so traffic cannot be shaed as a Poisson attern, and the formulas derived in the last section can not be directly used. We tested the mechanism erformance for different ersistence levels ( =0.2, 0.5, 0.8). For each configuration we have gathered 30 samles of the Fig. 6. Exerimental set-u contains one sink node (bottom) and u to 8 nodes caturing acoustic events (to) =0.2 =0.5 =0.8 Delay Saving Delay Saving Delay Saving N= %.32 34% % N= %.4 43% 20% N= % % 20% TABLE I EXPERIMENTAL AVERAGE NOTIFICATION TIME (IN TIME-SLOTS) AND ENERGY SAVING notification delay (measured in time-slots). The average value is shown in table I. Indeed, we also deict the exected energy saving for each configuration, comared to a erfect access mechanism which is collision free. In this case, savings can be comuted as T, being T the average notification delay (in time-slots) and the ersistence level. As can be seen in table I, considerable saving can be achieved also in this configuration by means of the -ersistent mechanism. VI. CONCLUSIONS A feasible modification for WSN MAC rotocols that includes a ersistence mechanism has been analyzed in this aer as a solution to reduce notification delays and save energy. The -ersistent aroach notably reduces energy consumtion since: (i) the number of collisions is minimized, and (ii) nodes do not wake u in all the activity eriods. The otimal ersistence () according to the exected number of nodes sensing events has been comuted by means of a numerical algorithm based on the fixed oint theorem, for different realistic network configurations. Both analytical and exerimental results show a remarkable imrovement, in the order of 50%, in terms of energy saving. As a future work, we intend to extend our analysis to other environmental and oerational conditions, for instance, considering non-uniform node distributions. VII. ACKNOWLEDGEMENTS This work has been funded by Ministerio de Educación y Ciencia grant DEP C03-03/EQUI and grant 207

6 TEC /TCM (CON-PARTE-), by the Ministerio de Industria, Turismo y Comercio grant m:ciudad (FIT , artially funded by Euroean Regional Develoment Fund), and has been develoed within the framework of Programa de Ayudas a Gruos de Excelencia de la Región de Murcia, de la Fundación Séneca, Agencia de Ciencia y Tecnología de la RM (Plan Regional de Ciencia y Tecnología 2007/200). REFERENCES [] I. F. Akyildiz, I. H. Kasimoglu. Wireless sensor and actor networks: Research challenges, Ad Hoc Networks, Elsevier (forthcoming). [2] W. Ye, J. Heidemann, D. Estrin. Medium Access Control with Coordinated, Adative Sleeing for Wireless Sensor Networks, ACM/IEEE Transactions on Networking, vol. 2, , [3] T.V. Dam and K. Langendoen An Adatative Energy-Efficient MAC Protocol for Wireless Sensor Networks st ACM Conf. Embedded Networked Sensor Sys. Los Angeles, CA, Nov [4] C.C. Enz et al. WiseNet: An Ultralow-Power Wireless Sensor Network Solution IEEE Com., vol. 37, n0 8, Aug [5] Y.C. Tay, K. Jamieson and H. Balakrishnan, Collision-Minimizing CSMA and Its Alications to Wireless Sensor Networks IEEE Journal on Selected Areas in Communications, Vol. 22, No. 6, August 2004 [6] Debnath, L. and Mikusinski, P. Introduction to Hilbert Saces with Alications San Diego, CA: Academic Press,