The Hybrid Mobile Wireless Sensor Networks for Data Gathering Biao Ren
Jian Ma
Canfeng Chen
Beijing Univ. of Posts & Telecommunications, Beijing 100876, China +86-010-62282007
Nokia Research Center, Beijing 100013, China +86-010-65392828-2883
Nokia Research Center, Beijing 100013, China +86-010-65392828-2795
[email protected]
ext-canfeng.chen @nokia.com
[email protected]
bring a variety of new applications including habitat monitoring, soil quality monitoring, detection of hazardous chemicals and forest fires, military surveillance, seismic activity, etc. Such a network is comprised of a large number of sensor nodes deployed over a large area and collects information from the nodes for long periods of time.
ABSTRACT Introducing heterogeneous mobile devices, such as mobile phones into the large scale sparse wireless sensor networks is a promising research direction. These devices acting as mobile sinks offer many benefits to the network. For instance, they help to improve scalability, maintain load balance, conserve energy, prolong network lifetime and implement commercially. The paper investigates the impacts of different features and behavior of mobile sinks on the hybrid wireless sensor networks. Analysis and simulation results show that, instead of deploying mobile sinks as much as possible, choosing appropriate number, transmission range, velocity and gathering mode of the sink nodes can significantly decrease the average end-to-end data delivery delay and improve the energy conservation. The comparisons of performance metrics between fixed sinks and mobile sinks are also made in sparse networks along with the results that mobile sinks can bring higher data success rate and energy balance.
Traditional wireless sensor networks are regarded as a specific application and extension based on pure ad-hoc networks [1], where the dense distribution of sensor nodes and multi-hop transmission over the whole network are their outstanding characteristics. Although many distinguished researches have been carried out, some disadvantages still exist inherently on performance metrics, such as poor scalability, weak energy balance, as well as low network lifetime. Exploiting hybrid architecture in wireless sensor network is a promising research regime in the last few years. Hybrid wireless sensor network is usually comprised of some kinds of heterogeneous devices, which mainly act as sinks responsible for gathering and forwarding data from underlying sensor nodes. Some of them are energy-rich or rechargeable, some are capable of communication with better capability and some are mobility enabled. These features can not only improve the network performance such as energy-efficiency, throughput, reliability and scalability, but also extend the potential applications and make commercial implementation easy.
Categories and Subject Descriptors C.2.1 [COMPUTER-COMMUNICATION NETWORKS]: Network Architecture and Design –Wireless communication, Distributed networks
General Terms: Algorithms,
Performance, Design
Keywords: Wireless sensor networks, Hybrid network, Mobile phones, Energy conservation, Delay 1. INTRODUCTION Advances in device technology, radio transceiver designs and integrated circuit along with efficient network protocols have enabled the emergence of Wireless Sensor Networks [1,2], which _____________________
Fig. 1 Hybrid sensor network with mobile phone and cellular infrastructure In recent years, more and more novel portable devices such as mobile phone, PDA and Laptop are gaining more popularity. They are at the same time suitable for hybrid wireless sensor network thanks to their powerful computing and communicating capabilities. In particular, we think mobile phone is the preferred alternative since it is not only much popularized but also with comprehensive support of cellular infrastructure. An example for such architecture is shown in Fig. 1, which we refer to as Hybrid Mobile Wireless Sensor Networks. Some similar concepts, such as multi-tier architecture, heterogeneous network as well as hierarchical network are also presented in some literatures [11,14].
Supported by NSFC Grant No. 90204003, 60402012; Beijing Municipal Key Disciplines XK100130438; mWSN project sponsored by NOKIA China Research Center
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, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. IWCMC’06, July 3–6, 2006, Vancouver, British Columbia, Canada. Copyright 2006 ACM 1-59593-306-9/06/0007...$5.00.
1085
The paper investigates the impacts of the number, velocity, transmission radius and gathering mode of mobile sinks on largescale and sparse wireless sensor networks, in which the advantage of hybrid architecture is outstanding. We are mainly concerned with the performance metrics of end-to-end data delivery delay and energy balance. The mobility of sink nodes can benefit to load balance and energy balance. Better energy balance would improve the overall network lifetime which can be defined as the time elapsed until the first node depletes its energy. The sparse wireless network is characterized by loose connectivity, in which the process of data gathering is mainly performed by mobile sinks. It is much difficult to guarantee low data delivery delay in that each sensor node has to wait for a mobile sink to approach before the transfer occurs. Whereas analysis and simulation results demonstrate that by choosing the appropriate number, transmission range and velocity of mobile sinks, an acceptable end-to-end delay can be achieved, which is sufficient for many practical applications. The comparisons between fixed sinks and mobile sinks are also made with respect to data success rate and energy balance.
3. MODELS AND ASSUMPTIONS 3.1 Network Model The hybrid mobile sensor network consists of numerous static sensor nodes and some number of mobile sinks. The location of the static nodes are fixed and distributed uniformly at random. We concentrate on large scale and sparse network in which the sensor nodes are deployed with low density. The mobile sinks are randomly distributed at initial time. At later time their position and velocities are given by the mobility model. In order to comparison, we also consider the fixed sinks where the velocity of mobile sinks is set to zero. Each fixed sink is arranged at a grid point to optimize the performance.
3.2 Mobility Model Similar to random waypoint model [17,18, 19], in our mobility model, each of the total m mobile sinks pick a direction uniformly at random from (0, 2π ] and moves in that direction for a distance d at speed v , where d is a exponentially distribution. If the sink hits the boundary of the sink, it is reflected at the boundary. Under this model, the positions of mobile nodes are independent of each other. The steady state distribution of the mobile nodes over the area is uniform. The direction of the mobile node is also uniformly distributed in (0, 2π ] all the time [16].
2. RELETED WORKS Existing literature utilizes mobile nodes as mobile sinks. In [3], R.C Shah presents a novel architecture to collect sensor data in sparse networks. Mobile sinks called data MULEs are used which pick up data from the sensors when in close range and drop off the data at access points. Different from us, this paper assumes a two dimensional grid and does not consider the load balance and the lifetime of network. Yu Wang and Hongyi Wu [4] focus on the Delay and Fault Tolerant Mobile Sensor Network (DFTMSN) for pervasive information gathering. They develop two approaches tailored for DFT-MSN, that is, directed transmission and optimized flooding. Similar to us, DFT-MSN has several unique characteristics such as sensor mobility, loose connectivity, fault tolerability and delay tolerability. Fall [5] proposes the concept of a delay-tolerant sensor network (DTN). DTN would typically be deployed to monitor an environment over a long period of time, and characterized by non-interactive sensor data traffic. Sensors are randomly scattered and organized into one or more clusters that may be disconnected from each other. Sensor information is typically aggregated at the cluster heads, which are responsible for communicating data to outside world. Wireless mobile robots (e.g. robomote [6]), unmanned aerial vehicles can roam around the network to collect data from cluster heads. Examples of DTNs in existence are Sammi[7], Zebranet[8]. Authors in [9] explore the idea of exploiting the mobility of sinks for the purpose of increasing the lifetime of a wireless sensor network with energy-constrained nodes. Mobile sinks with predictable and controllable movement patterns are studied in [10,11,12]. In these approaches, the static sensors only send out their data when the sink is moving close enough to them. The disadvantage of such proposals is that there will be considerable delay in acquiring sensed data, since a node need to wait for the sink to approach it. In order to minimize the delay, several methods of delivering the sensing data through multi-hop communication to the mobile sink are proposed [13,14,15].
3.3 Traffic Model In dense sensor network, data gathered from environment is forwarded to sink node in multi-hops fashion. Although it can provide low data delivery delay, the energy consumption per bit is much higher due to the multi-hop forwarding of one packet. We adopt the limited k-hop scheme for data gathering from sensor nodes, as shown in Fig.2. That is, the data transmission of a sensor node will not happen until at least one mobile sink approach to it within at most k-hop distance. In general, gathering data within one-hop neighborhood can minimize the average energy consumption coupled with more delay, while k-hop forwarding would lead to more overhead for routing.
4. ANALYSES 4.1 Delay Analysis In our analysis, time is divided into consecutive slots, so that delay is counted by the number of time slots. In addition, since
Fig. 2 one-hop and limited multi-hop transmission the mobile sinks are responsible for gathering data from their nearby sensor nodes in one-hop or k-hop fashion, and the number of mobile sinks is very small as compared to sensor nodes, the end to end data delivery delay is dominated by the duration
1086
during which sensor nodes are waiting for a sink to approach. So in terms of delay, this waiting duration is our primary concern.
d X ( d ) = ∑ j =1 ∑im=1 X i , j
d is a variable denoting the
number of rings far from S. In order to obtain a bound on d such that X ( d ) >1 , Use the second Chernoff bound Equation [20] as [16], we get the probability that X ( d ) < 1 for d = 4 f log m / rc is
Now we will deduce the mean value of delay that a mobile sink firstly come into the range of a sensor node. The results show that the delay for which sensor node has to wait is related to the number and the velocity of mobile sinks as well as the transmission radius of sensor nodes.
less than m
Theorem Given a sensor node S. Let m denotes the number of mobile sinks, r is the range of transmission and v is the velocity of mobile sinks. With high probability, the average duration D until which a mobile sink first enters the field of sensor node S is
−f
, which means
⎡ 4 f log m 1 ⎤ −f . Pr ⎢ D ≥ ⎥≤m crv m ⎣ ⎦ Thus a sensor node can take time less than 4 log m 1 to wait for
4log m 1 D≤ crv m
crv
cr l m
4 log m
either increasing the radius r of sensor and mobile sink, or increasing the number m as well as the velocity v of mobile sink can all decrease the waiting duration D to some extent.
4.2 Velocity Impact on Delay High velocity can increase the probability for the sensor and mobile sink meet with each other, on the other hand, it can result in mobile sinks passing through the effective region of a sensor node so fast that there is no adequate time to perform continuous transmission. The data delivery delay would increase inevitably since one message has to be sent more than one time. So, increasing velocity will increase the service probability whereas decrease the service duration of each time.
, where c < 1 . The
related notations are alse illustrated in Fig.3. Defining concentric rings R1 , ..., R i , ... with width
1 m
m
a mobile sink reaching it with high probability. The result follows. Then the service probability that a sensor is within the coverage of at least one mobile sink p = crv m . Furthermore,
Proof: Let M be some mobile sink at a distance l from an intended and static sensor node S. The position and moving direction of M is uniformly and independent distribution. For simplicity, assume M does not change its moving direction until reaching the network boundary. Then the probability that M enters the neighborhood of S is equal to the angle subtended by the neighborhood of S at M, see Fig.3. we use the constant c as a scaling factor defined in [lemma 4, 16] and substitutes c with cr. Then this subtended angle is at least
， where
. Each
Given velocity v and a mobile sinks can move into the transmission region of a sensor node from any direction, the average travel distance through the region is equal to r π . The available time for message transmission is proportional to r π . v
That is, the travel times that are required to finish a integrated message is proportional to
w
probability p, the service time of the message is a random variable with Pascal distribution. That is, the probability that the message can be transmitted within no more than x time slots, is
R i is centered at S and R i consists of points which are at a i −1 m
and
i m
from S. Let X i , j be a random
x−s s + i − 1 ⎛ ⎞ s i FX ( x) = ∑ ⎜ ⎟ p (1 − p) i =0 ⎝ s − 1 ⎠
th
variable such that X i , j =1 if the i mobile sink is in R j and it
This is the Pascal distribution with mean value of s . Under an p average Poisson arrival rate λ and a Pascal service time with μ = p . Data generation and transmission can be modeled as s an M/G/1 queue. But [4] didn’t take the impact of sink mobility on delay into consideration. Herein we substitute the value μ as follows:
will enter neighborhood of S. X i , j = 0 otherwise. Since the uniform distribution of mobile sinks, the probability that M i ∈ R j is
2 ( j −( j −
1 2 which is approximately ) )
−
1
2 jm . Moreover, each 2
m
mobile sink in R j has a probability of at least
cr j m
. In [4], the authors assume
message length of L, channel bandwidt w , the number of time slots required to transmit a message s = L . Then with a service
Fig. 3 The illustration of notations
distance between
v r π
of reaching S,
the event X i , j has an expected value of 2cr . Thus X i , j are m independent Bernoulli random variables. Define
μ=
wr π p Lv
The average message delivery delay can be expressed as follows:
1087
D=
section 3.2. The data generation of each sensor nodes follows a Poisson process with an average arrival interval of 1s. Firstly we vary the number of mobile sinks to observe the change of average data delivery delay. Apparently the end to end delay would decrease with the increase of the number of mobile sinks as shown in Fig.4. This trend would become stable when the number is near to 40, which is approximately equal to the square root of the number of sensor nodes ( 1500 ≈ 39 ). It can also be regarded as a trade-off point at which some degree of low delay can be guaranteed at cost of the least number of mobile sinks. At the same time, adding additional expensive mobile sinks would not significantly reduce the delay any more. From Fig. 4 we can also see that increasing the number of the hops is another effective approach to obtain low delay, especially when the fraction of mobile sinks is small. With the increase of the number of mobile sinks, the performances corresponding to 4-hop and 6-hop fashions are prone to get closer, and the larger hop would result in extra overhead for routing and data forwarding. Fig.5 shows the energy expenditure under various numbers of mobile sinks. When adopting the one-hop fashion, the energy consumption is constant, also it is minimum compared to those by other multi-hop forwarding. Comparing with the performance obtained by the one-hop fashion, we can see that the 6-hop fashion can achieve the lowest degree of delay but the most energy is consumed as seen in Fig.4 and Fig 5. The impact of velocity of mobile sinks on data delivery delay is evaluated in Fig.6, in which the x axis value means the ratio of the velocity of mobile sinks to the transmission radius of nodes. The change trend of delay in the figure verifies the results deduced from section 4.1 and section 4.2. At beginning, with the increase of the velocity of mobile sinks, the average delay is decreasing
1⎛ ρ 2 + λ2ρ 2 ⎞ ⎜ρ + ⎟ λ⎝ 2(1 − ρ ) ⎠ ,
λ
where ρ = μ . For simplicity, we neglect the impact of arrival rate and set λ = 1 , thus 1 D= μ −1 . On one hand, large v can improve the service probability p , on the other hand it increases the required times of mobiles sinks reaching it in order to finish a message transmission. Both sides of the impacts should be considered when choosing the appropriate velocity value of mobile sinks.
5. SIMULATIONS Extensive Simulations have been carried out. We evaluate three different performance metrics which are crucial to improve the quality of service and prolong the lifetime of wireless sensor network. The average data delivery delay is referred to the duration from data generation to data reception by mobile sinks. The data success rate is the ratio of the number of message generated by sensor nodes to the number of message received by mobile sinks. For evaluating the lifetime of the network, we also consider the minimal nodal remaining energy, which is set to 1000 initially. Totally 1500 sensor nodes are deployed uniformly at random in the determined area. Varying transmission radius is chosen properly to assure some degree of connectivity of network. Mobile sinks move according to mobility model mentioned in 1 2 4 6
200
hop hops hops hops
350
5 mobile sinks 10 mobile sinks 15 mobile sinks
300
Average Delay (units)
Average Delay (Units)
250
150
100
50
250
200
150
100
50
0 10
20
30
40
50
0
Number of Mobile Sinks
0
10
20
30
40
50
60
Ra tio of Veloci ty to Radius of Sensor Nno des
Fig. 4 Impact of the number of mobile sinks on delay
Fig. 6 Impact of velocity of mobile sinks on delay
35
1.00
1 2 4 6
25
20
hop hops hops hops
0.95
Data Success Rate
Energy Consumption (per message)
30
15
10
5
0.90 0.85 0.80 0.75
5 mobile sinks 10 mobile sinks 15 mobile sinks
0.70 0.65
0 10
20
30
40
50
0.60
Number of Mobile Sinks
0
10
20
30
40
50
60
70
Ratio of Velocity to Radius of Sensor Nodes
Fig. 5 Energy consumption under varying number Fig. 7 Data success rates under varying velocities
of mobile sinks
1088
significantly. The reason is that increasing the velocity can increase the service probability that some mobile sinks come into the range of a sensor nodes. Consequently the waiting duration is shortened greatly. However, this trend is reversed when the number of mobile sinks exceeds some value of about 10. Then the value of delay is prone to increase. This is attributed to the fact that, the increased velocity would shorten the duration of passing through the effective region of a sensor node. It results in no adequate time to perform continuous transmission and hence the message (see section 4.2, herein we use message instead of packet since a packet can not be partitioned when transmitting) has to be segmented and sent over several times by several sinks. At this moment the increased service probability can not offset the decreased service time. So it is important to choose a reasonable velocity of mobile sinks when deploying network and gathering data. Similar delay change trends can also be found under different numbers of mobile sinks in Fig.6. Too large value of velocity is not practical in reality, we use it here only for the evaluation of delay performance. Fig. 7 depicts the data success rates corresponding to various velocities. It shows the same trend as described in Fig. 6. A message with large delay would be discarded from the queue in sensor nodes. We also make the comparison of data success rates between fixed sinks and mobile sinks in spare network, where the sensor nodes are not fully connected with each other. In this case, the data success rate produced by mobile sinks is much better than that by fixed sinks, as shown in Fig. 8. One of the advantages of mobile sinks is that they can approach to such sensor nodes that are disconnected with others, that is, those sensor nodes are isolated. Using fixed sinks, the data success rate decreases since those isolated node can not find a path to delivery their data to any sink.
1.0
Data Success Rate
0.9
20
Minimal Remaining Energy
30
Sucess Data Rate
Number of Sink Nodes
Fig. 8 Data success rates in loose-connectivity network 280
Average Delay (units)
260 240
5 mobile sinks 20 mobile sinks
220 200 180 160 140 120 100 80 60 40 20 10
15
20
25
30
500 400 300
fixed sinks mobile sinks with one hop mobile sinks with four hops
200 100
10
15
20
25
30
In general, the large transmission radius can obtains the better network performance such as low delay and high data success rate. In ad-hoc networks, although large transmission radius can reduce the end to end delay (for example, hops), it also leads to the decrease of throughput of pre node [17] since the interference from each other. But in the fashion of limited k-hop transmission, the interference is reduced and localized, so we don't have to consider it too much. Furthermore, adding transmission radius can also increase the service probability and prolong the service time. But note that, sensor nodes are resource constrained and large transmission power would consume more energy. Fig. 9 depicts the impact of the transmission radius on delay. Fig.10 shows the data success rates under varying transmission radius. Both of them present the similar characteristics of performance enhancement. Fig. 11 shows the minimal nodal remaining energy. More remaining energy of each node means the prolonged lifetime of wireless sensor network. The advantage brought by mobile sinks is that it can achieve load balance over all the sensor nodes. The load balance is associated with energy balance, which is unreachable by fixed sinks. The mobile sinks with one-hop fashion gives the best energy reservation and it doesn't scale with the number of mobile sinks. The four-hop fashion also performs well. The performance corresponding to fixed sinks is poor since the pure multi-hop forwarding can lead to more energy consumption of some sensor nodes around the fixed sinks, which is referred to as traffic or routing hot spots.
hop hop hop hop
25
600
Fig. 11 Minimal nodal Remaining Energy
0.20 15
700
Number of mobile and fixed sinks
0.25 10
35
800
5
0.60
5
30
0
0.65
0.30
25
900
0.70
0.35
20
1000
0.75
1 2 4 6
15
transmission radius
0.80
0.40
0.4
Fig. 10 Data success rates under varying
0.85
fixed sinks mobile sinks, mobile sinks, mobile sinks, mobile sinks,
0.5
Radius of Sensor Nodes
0.90
0.45
5 mobile sinks 20 mobile sinks
0.6
10
0.95
0.50
0.7
0.3
1.00
0.55
0.8
35
Radius of Sensor Nodes
Fig. 9 Impact of the transmission radius on delay
1089
[7] D. T. N. R. Group, “The sammi network,” http://www. cdt.luth.se/babylon/snc/.
6. CONCLUSIONS Incorporating mobile phones into large-scale and sparse wireless sensor network will form a novel hybrid mobile wireless sensor network, which offers much benefit to network performance. The paper investigates the impacts of mobile sinks on such hybrid wireless sensor networks. The results show that, instead of deploying as much expensive mobile sinks as possible, choosing appropriate number, transmission range, velocity as well as gathering fashion of mobile sinks can significantly guarantee lower end-to-end data delivery delay and achieve better energy conservation. For many applications such level of delay and lifetime of network is sufficient. In addition, mobile sinks can also bring higher data success rate and energy balance as compared to those obtained by the same amount of fixed sinks.
[8] P. Juang, H. Oki, Y. Wang, M. Martonosi, L. Peh, and D. Rubenstein, “Energy-efficient computing for wildlife tracking: Design tradeoffs and early experiences with zebranet,” in Proceedings of ASPLOS-X. ACM, October 2002. [9] Z. M. Wang, S. Basagni, E. Melachrinoudis, and C. Petrioli, “Exploiting sink mobility for maximizing sensor networks lifetime,” in Proceedings of the 38th Hawaii International Conference on System Sciences (HICSS), 2005. [10] A. Chakrabarti, A. Sabharwal, and B. Aazhang, “Using Predictable Observer Mobility for Power Efficient Design of Sensor Networks,” in The second International Workshop on Information Processing in Sensor Networks (IPSN), Palo Alto, CA, April 2003.
A promising direction for future work is to explore the use of cooperative mobility. Since mobile sinks usually operate under centralized control, the cooperative mobility is possible and can also improve the coverage and efficiency of mobile sinks for gathering data, along with the decrease of data delivery delay and energy dissipation. An effective data dissemination protocol is under consideration which can reduce the broadcast and routing load. Moreover, utilizing the mobile sinks to improve the throughput capacity of hybrid sensor network is another challenging regime.
[11] A. Kansal, A. Somasundara, D. Jea, M. Srivastava, and D. Estrin, “Intelligent fluid infrastructure for embedded networks,” in Proceedings of the 2nd international conference on Mobile systems, applications, and services (MobiSYS), 2004. [12] W. Zhao, M. Ammar, and E. Zegura, “A message ferrying approach for data delivery in sparse mobile ad hoc networks,” in Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing (MobiHoc). ACM Press, 2004, pp.187–198.
7. ACKNOWLEDGMENTS Thanks to Dr. Jian Ma at Nokia China Research Center for giving me much help to finish my work.
[13] S. Gandham, M. Dawande, R. Prakash, and S. Venkatesan, “Energy-efficient schemes for wireless sensor networks with multiple mobile base stations,”in Proceedings of IEEE GLOBECOM, Dec 2003.
8. REFERENCES [1] J. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A survey on sensor networks,” IEEE Commun. Mag., vol. 40, pp. 102–114, Aug. 2002.
[14] Sankaranarayanan, L.; Kramer, G.; Mandayam, N.B. “Hierarchical sensor networks: capacity bounds and cooperative strategies using the multiple-access relay channel model,” 1st Annu. IEEE Conf. on Sensor and Ad Hoc Communication and Networks (SECON'04), Santa Clara, CA, USA, Oct. 4-7, 2004..
[2] Ren FY, Huang HN, Lin C. Wireless Sensor Networks. Journal of Software, 2003,14(7):1282~1291. [3] R. C. Shah, S. Roy, S. Jain, and W. Brunette, “Data MULEs: Modeling a three-tier architecture for sparse sensor networks,” in Proceedings of the First IEEE International Workshop on Sensor Network Protocols and Applications, SNPA 2003, Anchorage, AK, May 11 2003, pp. 30–41.
[15] J.Luo and J. P. Hubaux, “Joint mobility and routing for lifetime elongation in wireless sensor networks,” in Proceedings of the 24th IEEE INFOCOM, Mar 2005. [16] N. Bansal and Z. Liu, “Capacity, delay, and mobility in wireless ad hoc networks,” in Proc. IEEE INFOCOM, vol. 3, 2003.
[4] Y. Wang and H. Wu, "DFT-MSN: The Delay Fault Tolerant Mobile Sensor Network for Pervasive Information Gathering", to appear in IEEE INFOCOM'06, Barcelona, Spain, April 23-29, 2006.
[17] P. Gupta and P. R. Kumar, “The capacity of wireless networks,” IEEE Transactions on Information Theory, vol. 46, no. 2, Mar 2000.
[5] K.Fall, “A delay-tolerant network architecture for challenged internets,” Intel Research Berkeley, Tech. Rep. IRB-TR-03003, February 2003.
[18] X. Hong, M. Gerla, G. Pei, and C. Chiang. A group mobility model for ad hoc wireless networks, 1999.
[6] G. Sibley, M.H.Rahimi, and G.S.Sukhatme, “Robomote: A tiny mobile robot platform for large-scale ad-hoc sensor networks,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA-2002), vol. 2. Washington D.C, USA: IEEE, May 11-15 2002, pp. 1143– 1148.
[19] David B Johnson and David A Maltz. Dynamic source routing in ad hoc wireless networks. In Mobile Computing, volume 353. Kluwer Academic Publishers, 1996. [20] H. Chernorff. A measure of aymptotic e_ciency for tests of a hypothesis based on the sum of observations. Annals of Mathematical Statistics.
1090
