Abstract—In this paper, the expected lifetime of a

wireless sensor network devoted to vineyard monitoring is considered. This network uses a technique called random or stochastic sampling for the continuous tracking of the air temperature across the vineyard, and a pure Aloha protocol without retransmissions for the delivery of data to the base station. The design is based on the fact that the reconstruction process at the application layer can tolerate certain jitter in the sampling process. This is completely acceptable because of the strong temporal and spatial correlations exhibited by the environmental conditions across the sensor field. In addition to simplicity, the proposed implementation provides excellent results in terms of network lifetime. The design can also be extended to broader contexts, such as precision agriculture and habitat monitoring in general.

Index Terms—Access protocols, energy consumption, environmental testing, sampling methods, wireless sensor networks.

I. INTRODUCTION

ONTINUOUS monitoring constitutes a key application class of wireless sensor networks.

Here, some environmental variable must be continuously monitored and reconstructed in real time at the management center. Thus, the sensor network must deliver a continuous flow of packets containing sample data and other logistic information to the base station. In this paper, a strategy that combines a new technique called random or stochastic sampling [1] and a pure Aloha-based access protocol [2] is used. This strategy is based on two assumptions: (1) the reconstruction process at the application site admits certain jitter on the sampling process and

This work was supported in part by the MCyT (Spanish Ministry of Science and Technology) under contract TIC2003-06293.

Sebastià Galmés is with the Department of Mathematics and Computer Science, University of Balearic Islands, Spain (phone: +34-971172989; fax: +34-971173003; e-mail: sebastia.galmes@uib.es).

certain packet losses, because of the strong temporal and spatial correlations that the monitored variable typically exhibits across the sensor field and (2) the time interval (defined as the period of time at which the application expects to receive updated information from the whole sensor field) is usually much greater than typical “network times” (this is particularly true in the context of vineyard monitoring, where the time interval may typically vary from 1 to 25-30 minutes, while packet durations are in the order of milliseconds).

More specifically, the proposed approach defines a cross-layered design with the following detailed functionalities:

--Each node samples the environment following a random pattern. The distribution of the inter-sampling periods is set to exponential, in order to facilitate the analytical treatment. Random sampling was preliminarily introduced in [1] under the theoretical perspective of the sampling theorem [3]. Here, a more practical point of view is considered, where the time interval is fixed by the user according to previous experimental knowledge. Since random patterns from different nodes are mutually independent, there is no requirement on synchronization at local/global scales.

--Each sample is immediately packed into a message and transmitted to the base station as in pure Aloha networks [2]. However, collided packets are not retransmitted.

--A static multi-hop routing strategy is assumed. A key node parameter here is the routing factor, which is defined as the number of nodes from which a given node forwards packets towards the base station.

--Since any given node generates internally the sampling/transmission instants, it can announce them to its successor node in the routing strategy. Thus, this node can shift to sleep

Lifetime Issues in Wireless Sensor Networks for Vineyard Monitoring

Sebastià Galmés

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mode until the announced instant, with the corresponding energy savings. Of course, there must be an initialization phase where all nodes are listening to expected announcements.

According to such premises, nodes only consume energy in two types of operations: (1) packet generation (energy consumed EG) and (2) packet forwarding (energy consumed EF). In the next section, an interesting application in the context of precision agriculture, such as vineyard monitoring, is considered. Based on the exponential assumption, it is possible to derive a linear pessimistic death Markov model [4] for the evolution of energy consumption on a per node basis, where the maximum between EG and EF is associated with any type of operation. The rate of the death process is state-independent and of value ( ) sλσ ⋅+1 , where σ denotes the routing factor and λs is the average reporting rate per node.

II. VINEYARD MONITORING

In this section, the implementation of the random sampling strategy and the evaluation of network lifetime are illustrated over a fictitious vineyard. Real or realistic data from other vineyards and network components are combined to produce also realistic results.

A. Preliminaries A promising application field of wireless

sensor networks is precision agriculture. Unlike current agricultural solutions based on large-scale averages taken from single weather stations, remote sensing of the environmental conditions across different parts of a farmland can greatly improve the quality of the final product and maximize benefits. This is especially true in the case of highly-sensitive plantations, such as vineyards. For instance, accurate monitoring of temperature can reveal significant variations in heat accumulation (hot and cold spots), and thus in grape maturity, even in small sections of a vineyard. Adapting right harvest dates to such variations (a process known as precision harvesting) is essential to keep the best quality of wine that a given land can produce (for more details in vineyard computing, see [5]).

In this paper, only air temperature is considered for simplicity, without any loss of

generality (the technique can be extended to other variables relevant to vineyards, such as soil temperature, humidity, solar radiation and others). As an example, Fig. 1 shows the evolution of temperature during a typical day in spring at a mild climate location. By examining it in more detail, we can detect that the maximum temperature variation is 3 centigrade degrees in half an hour, that is, 6ºC/hour (from 8:00 AM to 9:00 AM). Then, according to the sampling theorem [3], the required Nyquist rate is 12 samples per hour and the corresponding sampling period is 5 minutes (∆t = 5 min). This is in fact a representative order of magnitude of the time interval used in other experimental test-beds for vineyard monitoring.

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Fig. 1. Sample evolution of temperature during a spring day of 2005 at Palma de Mallorca, Balearic Islands. Temperature readings were taken every half an hour (expressed in ºC).

B. Numerical results Let us assume a fictitious vineyard of size 360

x 240 = 86400 m2 (approximately 21 acres). Let us also assume a subdivision into square cells of 225 m2, with a sensor node located at the center of each cell. Thus, the total number of nodes (or cells) is φ = 86400/225 = 384 (= 24 x 16). Fig. 2 shows the resulting grid topology. This structure should not surprise, since it adapts very well to reality in many cases. In fact, vineyards are frequently organized as rectangular farmlands with multiple parallel rows of vines using a trellis system. Table I reflects the rest of input data adopted in this example. For the packet duration, a rather large value has been adopted, yielding to pessimistic results (and still very good) with regards to more realistic scenarios. For instance, an 8 ms-packet could correspond to a packet size of 2000 bit (which could include readings of other environmental variables, in addition to air temperature) transmitted at 250 Kbps. The radio characteristics regarding energy consumption

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have been taken from [6-7]. Finally, an overall reliability (defined as the probability that at least one successful packet is received from every node per time interval) of 95% has been specified, leading to a strong requirement on node reliability (probability that any given node delivers a successful packet per time interval): about 99.99%.

Fig. 2. Organization of a sensor network deployed in a fictitious vineyard.

TABLE I INPUT DATA

Parameter Value Overall reliability 95% Packet transmission time (τ) 8 ms. Time interval (∆t) 5 min. Number of cells (φ) 384Battery (Berkeley MICA Motes) 15 kJ Energy dissipated by transmitter electronics (EdTx)

50 nJ/bit

Energy dissipated by receiver electronics (EdRx)

50 nJ/bit

Energy radiated by the transmitter amplifier (Eamp)

100pJ/bit/m2

Table II shows the results obtained analytically for the values adopted so far. In this table, ETdenotes the energy consumed per packet transmission, ER the energy consumed per packet reception and E the value of energy consumption associated with any operation (pessimistic approximation). The total number of operations (generation or forwarding) that any given node can perform is denoted by N.

A key aspect in determining the expected lifetime is the routing strategy, and more precisely the routing factor (σ). A simple way to implement a static routing strategy over a grid topology is also shown in Fig. 2. In this case, the routing factor for the worst case nodes is given by σ = (360/15) -1 = 23. Assuming that such

nodes determine the expected network lifetime ( )σl , a result of about 2 years is still obtained in

Table II (last row). This result is quite encouraging, especially if we take into account the hard operational conditions imposed on the network (strong reliability requirement, large number of cells, relatively small time interval and long packets).

TABLE II OUTPUT DATA

Parameter Value Node reporting rate (per min.) 2.243675

2xmEmEE ampdTxT ∆⋅⋅+⋅= (m = 2000,

∆x = 15) 145000 nJ

mEE dRxR ⋅= (m = 2000) 100000 nJ

TG EE ≅ 145000 nJ

TRF EEE +≅ 245000 nJ

GF EEE >= 245000 nJ

=EBN (B = 15 kJ) 61224489

( ) ( ) s

Nlλσ

σ⋅+

=1

(σ = 23, λs = 2.34) 1136983.052 min.≅ 2 years

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Fig. 3. Evolution of the expected lifetime (in years) as the packet size (in bits) decreases (φ = 384, ∆t = 5 min.).

A packet size of 2000 bit (250B) is relatively long for a sensor network. Thus, Fig. 3 shows the evolution of the expected lifetime as the packet size (m) decreases from 250 to 25 bytes, assuming a fixed bandwidth of 250 Kbps. The reason for the increase is double: the reduction on the necessary node reporting rate caused in turn by the reduction of packet collision probability when packet duration decreases, and the energy savings caused by transmitting and receiving fewer bits.

Another interesting analysis considers the influence of the time interval. Fig. 4 describes the evolution of the expected lifetime as the time interval varies from 1 to 30 minutes. The packet size has been set to 100B. By increasing the time

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interval, the necessary node reporting rate decreases and, again, this contributes to increasing the expected lifetime (about 6-7 years every 5 minutes).

Finally, a relevant experiment consists of varying the number of cells in the grid. The results depend, however, on how this variation is introduced. In the present experiment, the number of cells is modified by varying ∆x, which affects both the transmission range (precisely the value of ∆x) and the maximum routing factor (number of cells along x). More specifically, the number of cells along y has been set to 16 and the number of cells along x has been varied over the set {28, 24, 20, 16, 12, 8, 4}. Results are shown in Fig. 5.

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Fig. 4. Evolution of the expected lifetime (in years) as a function of the time interval (in minutes) (φ = 384, m = 100B, Bandwidth = 250 Kbps.).

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Fig. 5. Evolution of the expected lifetime (in years) in terms of the number of cells (m = 100B, ∆t = 5 min., Bandwidth = 250 Kbps.).

The evolution shown in Fig. 5 is explained by the fact that the requirement on node reliability and the potentially colliding traffic decrease as the number of cells decreases. However, with regards to energy consumption, two opposite factors come together: on the one hand, the energy consumption is proportional to the sensor reporting rate, but, on the other hand, it is also proportional to the range, which in turn increases as the number of cells decreases. Thus, Fig. 5 exhibits a maximum expected lifetime, beyond

which the effect of increasing the range becomes dominant.

III. CONCLUSIONS

In this paper, the application of a combined strategy consisting of random sampling and Aloha-based transmissions has been illustrated for a vineyard monitoring application. The proposed design is very simple, it does not require synchronization among nodes and other complex collaborating tasks, and it yields to excellent results in terms of network lifetime. Such design can be extended to other habitat monitoring scenarios.

REFERENCES[1] S. Galmés, R. Puigjaner, “Performance and Reliability

Analysis of Continuous Monitoring Sensor Networks Using Randomly Sensed Data”, in Proc. of the NAEC 2005 Conference, Riva del Garda (Italy), October 2005, pp. 409-422.

[2] A. S. Tanenbaum, Computer Networks. Prentice-Hall, 1998.

[3] J. R. Higgins, Sampling Theory in Fourier and Signal Analysis: Foundations. Oxford University Press, 1996.

[4] G. Bolch, S. Greiner, H. de Meer and K. Trivedi, Queueing Networks and Markov Chains. John Wiley & Sons, 1998.

[5] J. Burrell, T. Brooke and R. Beckwith, “Vineyard Computing: Sensor Networks in Agricultural Production”, in Pervasive Computing, IEEE CS - IEEE ComSoc, January-March 2004.

[6] W. R. Heinzelman, A. Chandrakasan and H. Balakrishnan, “Energy-Efficient Communication Protocol for Wireless Microsensor Networks”, in Proc. of the 33rd Hawaii Int. Conf. on System Sciences-2000.

[7] F. Zhao and L. Guibas, Wireless Sensor Networks.Elsevier, 2004.

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