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ichatz@cti.gr. Athanassios Kinalis .... and a central authority to assign the time schedules (which ... small homogeneous sensors, which we here call “grain” parti-.
Wireless Sensor Networks Protocols for Efficient Collision Avoidance in Multi-path Data Propagation ∗ Ioannis Chatzigiannakis

Athanassios Kinalis

Sotiris Nikoletseas

Computer Technology Institute 61 Riga Feraiou Str. 26110 Patras, Greece and Dept of Computer Engineering and Informatics, University of Patras 26500 Patras, Greece

Computer Technology Institute 61 Riga Feraiou Str. 26110 Patras, Greece and Dept of Computer Engineering and Informatics, University of Patras 26500 Patras, Greece

Computer Technology Institute 61 Riga Feraiou Str. 26110 Patras, Greece and Dept of Computer Engineering and Informatics, University of Patras 26500 Patras, Greece

[email protected]

[email protected]

[email protected]

ABSTRACT

Keywords

Data propagation in wireless sensor networks can be performed either by hop-by-hop single transmissions or by multipath broadcast of data. Although several energy-aware MAC layer protocols exist that operate very well in the case of single point-to-point transmissions, none is especially designed and suitable for multiple broadcast transmissions. In this paper we propose a family of new protocols suitable of multi-path broadcast of data, and show, through a detailed and extended simulation evaluation, that our parameterbased protocols significantly reduce the number of collisions and thus increase the rate of successful message delivery (to above 90%) by trading off the average propagation delay. At the same time, our protocols are shown to be very energy efficient, in terms of the average energy dissipation per delivered message.

Wireless Sensor Networks, Data Propagation, Multi-path Delivery, Collision Avoidance

Categories and Subject Descriptors C.2.1 [Computer-Communication Networks]: Network Architecture and Design—Wireless Communication

General Terms Algorithms, Design, Measurement, Performance, Experimentation ∗This work has been partially supported by the IST Programme of the European Union under contract number IST2001-33116 (FLAGS) and IST-2004-001907 (DELIS).

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. PE-WASUN’04, October 7, 2004, Venezia, Italy. Copyright 2004 ACM 1-58113-959-4/04/0010 ...$5.00.

1.

INTRODUCTION

Wireless Sensor Networks are visioned as very large collections of sensor nodes that form ad hoc distributed sensing and data propagation networks that collect quite detailed information about the physical environment. In a usual scenario, these networks are largely deployed in areas of interest (such as inaccessible terrains or disaster places) for fine grained monitoring in different classes of applications [1]. Certainly, a possible way to disseminate individual sensor observations to a control point in the network, is to use the simple approach of directly transmitting data to that point, i.e. with a single hop. However, single hop propagation consumes a lot of energy especially when the control point is at a high distance. A different approach is to use multi-hop data propagation over a single-path of intermediate nodes, where a data message is transmitted from one node to another, until the message reaches its final destination [7, 10, 11]. These, short-range, hop-by-hop transmissions consume less power and can effectively overcome some of the signal propagation effects in long-distance wireless transmissions. Furthermore, short-range hop-by-hop transmissions may help to smoothly adjust propagation around obstacles. The low energy transmission in hop-by-hop propagation may also enhance security, protecting from undesired discovery of the data propagation operation. Recently, a new approach has been developed, that uses multiple paths of intermediate nodes to propagate information [5, 4]. In this multi-path data propagation, information is broadcast to more than one nodes in each single hop, without, however, flooding the network. The receiving nodes continue to broadcast until the message reaches its final destination. In this approach, that trade-offs energy consumption and fault-tolerance, node failures do not need to be handled in a special way since a single successful delivery

is enough and the message is always propagated simultaneously to several nodes. Each approach above has different merits and flaws. The single-path hop-by-hop protocols tend to spend little energy during data propagation, but the selection of a route is a resource consuming process and is prone to single node failures. Such protocols may turn out to be energy efficient and energy balanced by ensuring (in the protocol design) that the average energy dissipation per sensor is the same throughout the execution of the protocol in all sensors [9]. On the other hand, multi-path protocols are easier to implement (due to absence of a next particle search phase) and may tolerate sensor faults but may spend more energy. A comparative study of single-path and multi-path protocols conducted in [4] shows that multi-path protocols can achieve high success rates in terms of time and hops efficiency, while single-path protocols manage to reduce the energy spent in the process by activating less particles. For a detailed discussion of energy efficiency aspects of data propagation, see [2]. Remark that these protocols can be used either directly to solve a data propagation problem or as part of a more general information dissemination paradigm (such as [11]). The need for an efficient MAC layer protocol: In all the above approaches, a crucial aspect affecting their performance and correctness is the use of an efficient MAC layer protocol that manages to resolve collisions that arise, particularly in the case of many nearby, simultaneous transmissions. Due to special features of sensor networks (such as dense deployment of many nearby sensors, common final destination of transmissions, severe energy limitations) the design challenges of MAC layers for wireless sensor networks are different to those in ad-hoc wireless networks. Two characteristic protocols designed for wireless sensor networks are the S-MAC [16] and T-MAC [8]. Both protocols use a carrier sense with control messages scheme, which is similar to the IEEE 802.11 protocol. However, in contrast to the IEEE 802.11 protocol, these protocols try to reduce energy dissipation, since energy resources are significantly more limited in sensor networks compared to ad-hoc mobile networks. Both protocols identify 4 main sources of energy waste: (a) idle listening, (b) collisions, (c) protocol overhead, (d) overhearing. The number of collisions and the protocol overhead are reduced by the CSMA scheme used. The other two factors are confronted by using sleep-awake schemes ([6]). Another interesting MAC layer protocol is B-MAC [15] which is implemented specifically for the TinyOS operating system, introducing a new carrier sense mechanism specifically designed for the limitations of the mica mote platform [12]. This new mechanism increases throughput by allowing smaller packet sizes and avoids the hidden terminal interference problem by avoiding the use of control messages. The Problem of Collisions in Multi-path Data Propagation: The MAC protocols discussed above are specifically designed for point-to-point communication (i.e. singlehop and single-path protocols) and are not suitable for applications that broadcast messages to more than one node (i.e. multi-path protocols). In multi-path data propagation, the sources of energy waste are similar to the four described earlier but differ significantly in some cases. The different nature of data propagation makes it harder for common CSMA protocols to be deployed efficiently, since

the protocols also relay on the broadcast of control messages between the sender and the receiver, in order for the sender to acquire the medium. Such schemes can’t be used in broadcast mode since the eventual broadcast transmission of multiple control messages would mean that these messages would collide with each other. Other collision avoidance mechanisms such as TDMA or CDMA could be deployed, but these are generally complex solutions since TDMA requires the synchronization of nodes and a central authority to assign the time schedules (which is not available in wireless sensor networks), while CDMA requires complex modulation hardware (which is difficult to implement due to the reduced size and capabilities of wireless sensor nodes). In multi-path data propagation protocols, delivery of the message to the final destination is assured when in every broadcast at least one node receives properly the message and performs the next broadcast. The main problem of such protocol, is that more than often several nodes in a confined area attempt to broadcast a message simultaneously. This results to all messages interfering with each other, a fact that the MAC layer in the destination nodes perceives as a collision. When a collision is detected the message is rejected and the result is that none of the messages is delivered. So, the ideal case for a multi-path protocol is to allow a significant number of nodes to receive a message, in order to achieve redundancy, but not too many so as to interfere with each other. Our Results: In this paper we deal with the problem of collision avoidance when nodes operate in broadcast mode. To our knowledge, no MAC layer protocol has been specifically designed for propagation of packets through a broadcast mechanism. To this end, we propose a set of new protocols, that, by reducing collisions, assist the efficient data propagation of multi-path delivery and can be incorporated into existing MAC layer protocols or be implemented in the application level. Our protocols form a family of protocols, since all of them use various Random Backoff schemes in order to reduce collisions resulting from concurrent broadcasts. The main idea is that each broadcast is delayed by a time period, called the backoff time period ; each protocol appropriately defines a different (depending on various network conditions) way to select, handle and adapt this backoff time period. Deploying these protocols, we investigate their impact on the performance of a multi-path protocol. Certainly, we can use any flooding protocol as multi-path protocol, if energy efficiency is not the primary goal. In this work we decided to use a characteristic multi-path protocol, the PFR protocol [5, 4] which is based only on local information (and thus it is necessary a probabilistic one) and succeeds to efficiently propagate information to the sink without flooding the network (although each transmitting particle broadcasts around it), by probabilistically favoring certain close to optimal “paths” towards the sink and also by avoiding any control messages. The analysis conducted in [5] shows that PFR is very efficient, in terms of energy consumption, while achieving high success rates even in the case where part of the network fails. Our results show the crucial impact of the MAC layer on the performance of the multi-path protocol; when the MAC layer is absent or does not handle the packet collisions that result from simultaneous broadcast of messages, the

success rate is at most 10%. On the other hand, when we apply our protocols presented in this paper, the success rate drastically improves (becomes greater than 80%), while for a particular protocol (ARBP presented in Sec. 4), the success rate measured by our experimentation achieves values higher than 90%. These results indicate that by suitably selecting an appropriate MAC layer protocol, the performance of the multi-path protocol can reaches as high as the theoretical maximum [5]. Particularly, our explicit measures of the number of collisions in the network shows that our protocols significantly reduce collisions. We furthermore note that our protocols (at the same time with reducing collisions) also manage to reduce (in some cases drastically) the average energy dissipation per delivered message. Our experimental evaluation has been very detailed, i.e. we measured extensive ranges of various network parameters (number of sensors, message generation rate). We here note that our protocols can also be used in combination with other information dissemination protocols. In fact, the design and implementation of such MAC layer schemes are left as a future work in [10], since SPIN protocols can be improved by taking advantage the MAC layer broadcast mode.

2.

THE MODEL

Sensor networks are comprised of a vast number of ultrasmall homogeneous sensors, which we here call “grain” particles (see also [7, 6]). Each grain particle is a fully-autonomous computing and communication device, characterized mainly by its available power supply (battery) and the energy cost of computation and transmission of data. Such particles (in our model here) do not move. Let n be the number of smart dust particles spread in an area and let d be the density of particles in the area (usually measured in numbers of particles/m2 ). There is a single point in the network area, which we call the sink S, and represents a control center where data should be propagated to. The particles are equipped with a set of monitors (sensors) for light, pressure, humidity, temperature etc. Each particle has a broadcast (digital radio) beacon mode of fixed transmission range R. In addition, the communication device provides a mechanism to measure the signal strength of received messages. Based on these measurements, the particle can estimate the distance of the sender of a message (within a certain accuracy factor, that depends on current technology advance). Let d(i, j) be the Euclidean distance of particles i, j and des (i, j) be the estimation of this distance measured by particles. Note that des is not necessarily an exact value but rather an estimate of the real distance d, since such kind of measurements are prone to random errors and in this sense, successive estimations of the same distance may differ. We however assume that measured distances are more or less analogous to real ones. Each particle is equipped with a power supply (battery), initially set to the same energy level for all particles, that offers a mechanism that provides measurements of its remaining energy supplies. Let E(i) be the available energy supplies of particle i at a given time instance. At any given time, each particle can be in one of four different modes, regarding the energy consumption: (a) transmission of a message, (b) reception of a message and (c) sensing of events.

In our model, for the case of transmitting and receiving a message, we assume that the radio module dissipates an amount of energy proportional to the message’s size. To transmit a k-bit message, the radio expends ET (k) = ²trans · k and to receive a k-bit message, the radio expends ER (k) = ²recv · k where ²trans , ²recv are constants that depend on the radio module and the transmission range of the particles. Concluding, there are three different kinds of energy dissipation: (a) ET , the energy dissipation for transmission, (b) ER , the energy dissipation for receiving and (c) Eidle , the energy dissipation for idle state. For the idle state, we assume that the energy consumed for the circuity is constant for each time unit and equals Eelec (the time unit is 1 second). We note that in our simulations we explicitly measure the above energy costs; the exact values of ²trans , ²recv and Eidle were set to match as close as possible the specifications of the mica mote platform [12]. Finally, we assume that a specific, high-level, application is executed by the particles that form the network. Applications for smart dust networks fall in three major categories [3]: (i) Periodic Sensing (the particles are always monitoring the physical environment and continuously report their sensors’ measurements to the control center S), (ii) Event driven (to reduce energy consumption, particles operate in a silent monitoring state and are “programmed” to notify about events) and (iii) Query based (queries can be propagated to the particles arbitrarily by the control center S, according to the application and/or user’s will). We model in an abstract way the kind of high-level application by the message generation rate in the network. Let I the global message generation rate of the smart dust network, measured in number of messages per time period.

3.

THE SIMPLE RANDOM BACKOFF PROTOCOL (SRBP)

The protocol SRBP is based on the observation that in multi-path data propagation, since particles operate without any coordination regarding message broadcasts, whenever more than one nearby particles receive a message M, their attempt to further propagate M independently from each other will lead to a high number of collisions. A typical way to avoid such cases of simultaneous multiple broadcasts is to employ a backoff scheme in which broadcast of data over the medium is delayed by a period tb . The use of such a backoff period will force the broadcasts to “spread” over time. Such a “spreading” will reduce the number of message collisions. Conventional schemes including Ethernet and IEEE 802.11 use an exponentially increasing congestion backoff. In such schemes, the transmitter delays after checking the status of a channel and determining that the channel is busy. In SRBP the backoff period tb is selected uniformly randomly from a continuous space of numbers which we call Tb and is defined as Tb = [Tb min, Tb max]. Randomized backoff schemes are very simple, assume only local knowledge and computation and tend to spread evenly the load, avoiding bad performance in the case of worst case (or adversarial) network inputs. Remark however that the size of Tb affects the maximum load that each particle may offer to the channel and also result in less throughput per particle and more particles to

saturate the channel. Clearly, the backoff period represents different trade-offs between fault-tolerance (collision avoidance) and efficiency (time, energy). If we tune the above parameters to reduce the collision rate, then there will be long delay in delivering messages. However, in Wireless Sensor Networks, the information is usually time-critical, the message with long delay will be out-of-date and have no use. In this sense, the selection of an appropriate Tb space is crucial to the overall performance of the network. In SRBP the values of Tb min, Tb max are embedded to each particle at the beginning of the network execution (i.e. during the setup phase) and remain fixed for the entire duration of the protocol execution. Note that since each particle decides on the random backoff period independently from the other particles, no coordination among the particles through message exchange is required. SRBP can be implemented at the low levels of the protocol stack by using a queue Q where all messages that need to be broadcast are stored. The messages stored in the Q are processed sequentially. The mechanism pops the message at the top of the queue, waits for a random period tb and then broadcasts the message.

4.

THE ADAPTIVE RANDOM BACKOFF PROTOCOL (ARBP)

The SRBP protocol is based on the assumption that the parameters that affect the number of multiple transmissions (e.g. density of the network, message generation rate) are (more or less) known in advance, thus Tb min, Tb max can be adjusted accordingly. For example, in sparse networks (i.e. low d) the number of particles that will simultaneously try to further propagate a message M will be small, thus a small space Tb will suffice for the multiple broadcasts to “spread” in time. On the other hand, in dense networks (i.e. high d) the number of particles propagating a message M will be larger, thus a larger space Tb will be required for the broadcasts to sufficiently spread over time and not collide. Similarly, in networks with high message generation rate I, since particles will be required to further propagate an increased number of received messages, a larger space Tb will be required, while for networks of low message generation rate a smaller space may suffice. However, in real environments, measuring the density of the smart dust plane may be a highly non-trivial task, especially if we consider cases where the particles are dropped randomly on the area of interest. Moreover, as the network evolves over time, particles will exhaust their limited battery resources and fail. It is also possible for particles to stop functioning due to physical damage (i.e. destruction by external factors) or failure on the (low-cost) equipment. Furthermore, it is possible to re-deploy additional particles [1] while the network is in operation to replace the malfunctioning particles or due to change in the task dynamics. In this sense, the density of the network will change over time. Similarly, the generation of messages (that need to be reported to S) depends on the local conditions of the smart dust plane. There may exist areas where messages are generated with high frequencies (compared to the rest of the network) or other areas that, because of their central position, experience high volumes of messages that pass through in order to reach S (e.g. particles that are near to S).

In the light of the above, we want the protocol to be capable of sensing and appropriately handling changes to the local conditions and suitably adjust the backoff period, otherwise, if values of Tb min, Tb max remain fixed for the duration of the protocol, any change on the local conditions of the network will not be reflected in the way the backoff period is selected. In order to sense the local particles’ density and message traffic, ARBP, builds upon the following subprotocols. • The Density-Sensing subprotocol (Pdensity ). We call dl the average number of neighbors a particle senses over a certain area (i.e., the local density). Initially dl = di , where di is set to reflect the (expected) conditions of the network; the expected degree of a particle is related to the network density, i.e. di ∝ d. Pdensity maintains a table where it stores all the sender’s ids encountered along with a time counter indicating the time the message was received. In fact, the subprotocol is continuously inspecting all packets received and updates the local table. For every entry in the table a counter is defined that is initialized to a predefined period of time called tinactive (e.g. tinactive = 1hr). Periodically, Pdensity will go through the list of ids and remove those neighbors whose counter has reached zero. Therefore, the Pdensity table only needs O(di ) entries, where di ¿ d. • The Message Traffic-Sensing subprotocol (Ptraffic ). We call Il the average number of distinct messages received per period of time by a particle (i.e., the local message traffic). Initially Il = Ii , where Ii is a set to reflect the (expected) conditions of the network. In fact, the expected message traffic handled by a particle is related to the global message traffic I, i.e. Ii ∝ I. Ptraffic maintains a variable that is used to count the total number of messages received within each time period (i.e. every 1sec the counter is reset). Every message received is considered in the calculation of Il besides the fact that in multi-path propagation several messages carrying duplicate data might exist. It’s application specific to suppress duplicate messages. Remark that the calculation of dl and Il is performed dynamically and is subject to change over time; in this sense, we introduce the notion of dl (t) and Il (t) where dl (0) = di and Il (0) = Ii . We fix the value of Tb min to a value little higher than the amount of time it takes to transmit a packet. On the other hand, the value of Tb max will change once the network is running, in order to adjust the space of Tb , and for this reason again we use the notion of Tb max(t). There are several ways to calculate a new value for Tb max; we here present the change of Tb max as a function of successive measurements of the local density, the local message traffic and the current value of Tb max: Cd (t) = Tb max(t − 1) ·

dl (t) − dl (t − 1) dl (t) + dl (t − 1)

(1)

Ct (t) = Tb max(t − 1) ·

Il (t) − Il (t − 1) Il (t) + Il (t − 1)

(2)

Then based on Cd (t) and Ct (t), Tb max(t) is calculated as follows:

Plain PFR SRBP

(3)

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where α ∈ [0, 1] and β ∈ [0, 1], two parameters that adjust the way Tb max(t) is calculated and its dependency on the two components; fine grained adjustment can be achieved for different kinds of application requirements. For applications with constant data generation rate, by setting β = 0 the dependence on the traffic rate is totally removed and ARBP adapts only based on the sensed local density change. Furthermore, α and β determine how drastically the protocol reacts to changes. For values close to 0 little adjustment is made, while values close to 1 allow more drastic adaptation.

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THE RANGE ADAPTIVE RANDOM BACKOFF PROTOCOL (RARBP)

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We now present RARBP, that is using information regarding the distance between the particle from which a message M was received in order to adjust the random backoff space Tb . The intuition here is that in multi-path data propagation protocols, such as the PFR protocol, it is desired that the particles that decide to further propagate a message M are the ones that are the most distant from the sender. If two particles p1 , p2 receive a message M sent by particle ps and d(p1 , ps ) < d(p2 , ps ), we want p1 , p2 to adjust their random backoff spaces Tb p1 , Tb p2 in a way such that IE(tb p1 ) > IE(tb p2 ), where E(·) is the expectation of the random variables measuring the backoff. We want particles that are about R distance away to select a small backoff value, maximizing in this way the distance travelled in each hop, thus improving efficiency. Furthermore, the latency introduced by the backoff mechanism is reduced by this scheme. Also note that it is possible to further reduce the number of nodes that forward the message, since the application can detect if a message has already been forwarded another particle. To this end, we design RARBP in a way such that the backoff is selected from the tb space in a non-uniform manner. We use the distance from the message’s sender to generate a new random backoff value for each message separately. Thus, as soon as a message M is processed, particle i calculates a number Tb sl(M), as follows: Tb sl(M) = Tb min + (Tb max − Tb min) ·

des (i, j) R

(4)

where j is the sender particle of M. The random backoff value is generated by a random variable that follows the normal distribution with µ = Tb sl and σ = dl1(t) . This method creates pseudo-time slots according to the spatial distribution of particles. Since particles that lay in the same distance from the message source get identical pseudo-time slots, we allow the random backoff value to vary to a limited degree based on the local density; a greater density means more strict bounds, prevent nodes that are about the same distance from the source, from selecting the same backoff values. Remark that since the particles cannot calculate precisely how far away is the sender of a message, we work using the estimate of the distance, as assumed in Sec. 2. Also note that RARBP can work in conjunction with the way that

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Figure 1: Success Rate and Average Delay of PFR, SRBP for various particle densities (n ∈ [500, 1500]) and fixed event rate (λ = 5)

ARBP calculates Tb max(t) and both protocols can be used together.

6.

EXPERIMENTAL EVALUATION

To evaluate the performance of the proposed protocols we conducted an extensive simulation analysis. In contrast to previous work of our team (see [4, 5, 6, 7, 13]) where we were using the lightweight LEDA environment to be able to study very large instance sizes, in this work we chose to use the Network Simulator (ns-2 version 2.26, [14]), a detailed network simulator that more accurately takes into account the network parameters. The ns-2 simulator provides a quite detailed implementation of the physical and MAC layers and allows detailed measurements of many variables (such as the energy dissipation) in simulations of wireless networks. We start our experimentation by investigating the improvement on the success rate of the original PFR when applying the Simple Random Backoff protocol SRBP. We generate a variety of sensor fields in a 500m by 500m square and in these fields, we drop n ∈ [500, 1500] particles uniformly distributed on the smart-dust plane. The sink is always positioned at point (0, 0) and the transmission range of each particle were set to 50m. In each execution, we generate 1, 000 events by randomly selecting one particle in the network for each event, with event generation rate λ = 5 (i.e. 5 events every 1 sec). The simulation duration is calcu-

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Figure 2: Success Rate and Average Delay of SRBP, ARBP (α = 1.0, β = 0.0) for various particle densities (n ∈ [500, 1500]) and fixed event rate (λ = 5)

Figure 3: Success Rate and Average Delay of SRBP, ARBP (α = 0.0, β = 1.0) for fixed Particle Density (n = 1000) and various event rates (λ ∈ [2, 10])

lated according to the event rate and is long enough to allow all messages to be generated. Another 15 seconds of simulation time are added to allow the arrival of delayed messages. The results of this experiments are shown in Fig. 1. Our first experiment clearly indicates the impact of the MAC layer (available by ns-2) on the performance of the PFR protocol. The inability of this MAC layer to handle the simultaneous broadcast of messages leads to situations where messages are rejected. The magnitude of this effect on the success rate of PFR is realized if we consider the theoretical analysis presented in [5], where the authors prove that the protocol always succeeds in sending the information to the control center when all collisions are handled properly at the MAC layer. This dependence of PFR to a proper MAC protocol is depicted in Fig. 1; the experimental results suggest that the success rate of the protocol is less than 10% when the particular MAC layer does not handle the collisions properly. Interestingly, when we apply SRBP, the success rate drastically improves and reaches as high as 80%. We here define success as the eventual data propagation of the messages to the sink. The above performance evaluation cannot be fully indicative if considered in isolation since the success rate of multipath and multi-hop transmission is inversely proportional to the delivery delay. This trade-off between collision avoidance and time efficiency is clearly shown in Fig. 1.

In the next set of experiments we evaluate the performance of the PFR protocol when applying the Adaptive Random Backoff protocol ARBP at the MAC layer. We start by setting α = 1.0 and β = 0.0 so that only the Density-Sensing component of ARBP is active. Fig. 2 clearly indicates the improvement on the success rate when the backoff time space adapts to the density sensed by the particles. In fact, as the density increases, ARBP seems to raise the success rate of PFR to values higher than 90%. This result is very promising in the sense that the simulated performance is close to the theoretical maximum as indicated in [5]. Again, the improvement on the success rate hinders the time efficiency of ARBP, however, the additional overhead on the propagation delay is at most 20%. We now set α = 0.0 and β = 1.0 so that only the Message Traffic-Sensing component of ARBP is active. In this case, we drop sensor fields of fixed number of particles (n = 1000) and vary the event generation rate λ ∈ [2, 10]. Fig. 3 shows that for low event generation rates, the success rate of PFR seems to be better when applying the simple backoff scheme at the MAC-layer. However, as the event generation rate increases, the results suggest that the adaptation mechanism improves the success rate of the backoff scheme; then it seems to remain unaffected by further increases of the rate of event generation, always higher than that of SRBP. This inability of ARBP to successfully adapt in the case

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Figure 4: Success Rate and Average Delay of ARBP (α = 1.0, β = 1.0) for various event rates (λ ∈ [2, 10]) and different particle densities (n ∈ {1000, 1500})

Figure 5: Success Rate and Average Delay of SRBP, ARBP, RARBP for various particle densities (n ∈ [500, 1500]) and fixed Event Generation Rate (λ = 5)

of low event generation rates may be partially explained by the fact that initially, each particle may sense a message rate that is lower to the actual one used; that is because the events generated are local to a specific area of the network, however as the network evolves in time, more propagation paths become active, thus the sensed message rate gets closer to the actual one used. Based on this observation, and by considering Eq. 2, an adaptation that reduces the backoff time space due to a reduction of the sensed traffic rate, is not matched at a latter point when the sensed traffic rate returns to the original levels. In the light of the above, it is interesting to also investigate other adaptation schemes (i.e. different α, β values and adaptation functions with respect to the network parameters). In Fig. 4 we activate both components of ARBP (i.e. we set α = 1.0, β = 1.0) and evaluate the performance of the protocol for different event generation rates and particle densities. The results depicted in Figs. 2,3 are somehow merged when both components are active. Notice in Fig. 4 that the case of 1500 particles achieves lower success rates than that of 1000 particles (due to more collisions), in contrast to Fig. 2. Also notice the curve of Fig. 4, that is initially increasing, reaches a maximum and then becomes decreasing with the event rate; a pattern similar to that of Fig. 3. Similar observations hold for the propagation delay metric.

This behavior seems very interesting to us, in the sense that it implies that the way of combining the DensitySensing (Pdensity ) and the Message Traffic-Sensing (Ptraffic ) subprotocols is not a straightforward issue and should be done in a very careful way in order to have the desired effect in each network setting. We plan to further investigate efficient combinations. We conclude by evaluating the performance of Range Adaptive protocol RARBP in combination with ARBP, along with the other two protocols. Fig. 5 depicts the case where we drop sensor fields of fixed number of particles (n = 1000) and vary the event generation rate λ ∈ [2, 10]. In this experiment both components of ARBP are active (i.e. α = 1.0, β = 1.0). In order to get a more complete view on the performance of the three protocols, in Figs. 6, 7, 8 we include three additional efficiency metrics: (i) the Average Number of Hops required for a message to reach the sink, (ii) the Average Energy Dissipated by the smart dust network (i.e. by all particles) while propagating a single message regarding the realization of one event and (iii) the Number of Dropped Packets (i.e. packets that were lost as a result of collisions) in the process of propagating each message towards the sink. In these figures we also include the second case where we drop sensor fields of fixed number of particles (n = 1000) and vary the event generation rate λ ∈ [2, 10]. Remark that in Fig. 6 the average was taken only for messages that were

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Figure 7: Average Energy Dissipation of PFR, SRBP, ARBP, RARBP for various particle densities (n ∈ [500, 1500]) and various event rates (λ ∈ [2, 10])

able to reach the sink, while in Figs. 7, 8 the averages were taken over all messages transmitted in the network. The results of these experiments suggest that the RangeAdaptive protocol RARBP successfully reduces the average number of hops required for a message to reach the control center (see fig. 6). However, in the process of favoring particles that are far away from the one that broadcasts the message, the performance of the protocol is hindered, compared to the adaptive protocol ARBP, while still performing better than the simple protocol SRBP (see fig. 5). Note that this observation on the reduction of the average number of hops holds for both cases, i.e. when varying the particles density and when varying the event generation rate. Regarding the energy consumption (see fig. 7) it is evident that the backoff protocols successfully reduce the average energy dissipated by the particles of the network. This improvement on the energy consumption is due to the reduction on the number of collisions, as shown in Fig. 8. It is clear that the number of dropped packets of the multi-path PFR protocol are significantly reduced when the family of Random Backoff protocol is used to handle collisions. Note that the number of dropped packets implicitly measures the actual number of collisions. Since the number of dropped packets are reduced, the total number of messages that get delivered to the control center increase. In this sense the energy of the particles is consumed more effectively.

7. CLOSING REMARKS In this paper we study the problem of collision avoidance in wireless sensor networks, especially when nodes use the broadcast communication mode. We present a family of protocols that try to minimize transmission collisions and reduce energy consumption by using time delay schemes. We have conducted extensive experiments to investigate the performance of the new protocols based on a characteristic multi-path propagation protocol PFR. Our results, clearly indicate the impact of the MAC layer on the performance of the PFR protocol. Our protocols manage to significantly reduce collisions and improve the success rate (in most cases to above 80%, and in some cases even to above 90%) by imposing a limited delay on the propagation of the messages. Our protocols are also found to be energy efficient, in terms of the average dissipated energy per delivered message. The detailed investigation we perform leads to interesting findings, showing that a careful, appropriate protocol design is needed in each network setting to get the desired results. There are several directions for future work. An obvious one is to analyze theoretically the performance of the proposed schemes. Another one is to further investigate efficient ways to take the network input into account in the design of even more efficient protocols.

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REFERENCES

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