A Turnover based Adaptive HELLO Protocol for Mobile Ad Hoc and Sensor Networks

Transcription

1 A Turnover base Aaptive HELLO Protocol for Mobile A Hoc an Sensor Networks François Ingelrest, Nathalie Mitton, Davi Simplot-Ryl To cite this version: François Ingelrest, Nathalie Mitton, Davi Simplot-Ryl. A Turnover base Aaptive HELLO Protocol for Mobile A Hoc an Sensor Networks. MASCOTS, Oct 2007, Istanbul, Turkey. IEEE Computer Society, pp.9-14, <hal > HAL I: hal Submitte on 14 May 2009 HAL is a multi-isciplinary open access archive for the eposit an issemination of scientific research ocuments, whether they are publishe or not. The ocuments may come from teaching an research institutions in France or abroa, or from public or private research centers. L archive ouverte pluriisciplinaire HAL, est estinée au épôt et à la iffusion e ocuments scientifiques e niveau recherche, publiés ou non, émanant es établissements enseignement et e recherche français ou étrangers, es laboratoires publics ou privés.

2 A Turnover base Aaptive HELLO Protocol for Mobile A Hoc an Sensor Networks François Ingelrest LCAV, I&C School, EPFL CH-1015 Lausanne, Switzerlan Francois.Ingelrest@epfl.ch Nathalie Mitton an Davi Simplot-Ryl IRCICA/LIFL, Univ. Lille 1 CNRS UMR 8022, INRIA Futurs, France {Nathalie.Mitton,Davi.Simplot}@lifl.fr Abstract We present a turnover base aaptive HELLO protocol (TAP), which enables noes in mobile networks to ynamically ajust their HELLO messages frequency epening on the current spee of noes. To the best of our knowlege, all existing solutions are base on specific assumptions (e.g., slotte networks) an/or require specific harware (e.g., GPS) for spee evaluation. One of the key aspects of our solution is that no aitional harware is require since it oes not nee this spee information. TAP may be use in any kin of mobile networks that rely on HELLO messages to maintain neighborhoo tables an is thus highly relevant in the context of a hoc an sensor networks. In our solution, each noe has to monitor its neighborhoo table to count new neighbors whenever a HELLO is sent. This turnover is then use to ajust HELLO frequency. To evaluate our solution, we propose a theoretical analysis base on some given assumptions that provies the optimal turnover when these assumptions hol. Our experimental results emonstrate that when this optimal value is use as the targete turnover in TAP, the HELLO frequency is correctly ajuste an provies a goo accuracy with regars to the neighborhoo tables. I. INTRODUCTION AND MOTIVATION In mobile a hoc an sensor networks, because of the path loss of raio communications, only close hosts may irectly communicate to each other. Long-istance communications require packets to be forware by multiple intermeiate noes. While sensor networks are generally static, some applications involve mobility (e.g., her health control as targete by the WASP European project 1 ). Localize routing schemes are a resource-efficient way of achieving communication between two en hosts. In such schemes, each intermeiate noe is only expecte to maintain knowlege about spatially nearby noes (its neighbors). In most existing works, this knowlege is acquire thanks to beacon messages (the well-known HELLO messages): all noes maintain a neighborhoo table, an any localize protocol may make ecisions base on it [3], [8]. In this paper, we are intereste in stuying how noes may ynamically ajust the frequency of HELLO messages. Inee, because of mobility, neighborhoo tables have a limite lifetime an must be regularly upate. However, fining the correct frequency is not obvious: if it is too low (i.e., with regars to the spee of hosts), then tables quickly become obsolete. On the contrary, if it is too high, then tables will be up to ate but a high part of the available banwith will 1 be waste to the etriment of ata traffic. There obviously exists a trae-off between these behaviors, but fining the optimal one is not trivial. Moreover, this trae-off actually epens on network characteristics (e.g., ensity, spee) that may evolve over time, an a constant frequency is then not the best choice. An efficient HELLO protocol shoul thus be aaptive. A straightforwar solution might be to let noes know their spee an choose the correct frequency base on this information, but of course there is no easy an cheap way for a noe to etermine its spee. In this paper, we propose the Turnover base Aaptive HELLO Protocol (TAP), an elegant solution that let noes ynamically ajust their HELLO frequency base on the turnover of their neighborhoo. One of the key aspects of our solution is that it highly fits mobile wireless networks since it is fully localize an oes not require aitional harware. Our solution is inepenent of any routing protocol. Noes only nee to perioically make samples of their table to compute the current turnover an aapt their HELLO frequency. TAP may actually be seen as a generic framework rather than a frozen protocol, since it is inepenent of the functions use to ajust the HELLO frequency. Any such functions may be use epening on the require behavior (e.g., favor banwith usage to the etriment of up to ate tables). To evaluate our proposal, we provie a theoretical analysis in orer to compute the optimal turnover for the consiere environment. This allows to check the correctness of our scheme by means of simulation results using the same assumptions. We give the neee preliminaries in the next section, while Section III proposes a literature review of relate work. In Section IV, we escribe TAP an provie a theoretical analysis that aims at fining the optimal turnover uner known parameters. We then give experimental results about the effectiveness of TAP in Section V, an show that it is inee able to ynamically aapt the HELLO frequency without spee information. We finally conclue in Section VI. A. Network Moel II. PRELIMINARIES Wireless networks are represente by a graph G = (V, E) where V is the set of noes an E V 2 the set of eges: (u,v) E means that u an v are neighbors (i.e., close enough to communicate). The neighborhoo set N(u) of a vertex u is

3 equal to {v : (u,v) E (v,u) E}. The ensity is the average number of neighbors per noe. Each noe is assigne a unique ientifier (e.g., a MAC aress). Wireless links are etermine by the physical moel. The most frequent one is the unit isk graph moel [2]: E = {(u,v) V 2 u v uv R}, uv being the Eucliean istance between noes u an v, an R the maximum communication range. B. Plain Perioic HELLO Protocol The basic HELLO protocol, first escribe in OSPF [7], works as follows. Noes regularly sen HELLO messages to signal their presence to close noes, an maintain a neighborhoo table. The frequency of these messages is note f HELLO an the elay between them HELLO (i.e., HELLO = 1/f HELLO ). When a noe u receives such a message from a noe v, u as v to its table, or upates the timestamp of the entry if v was alreay there. We o not make assumptions about the content of HELLO messages, but they must contain the ientifier of the sener. III. RELATED WORK In [1], authors claim that the usefulness of a HELLO protocol epens on the size of the beacon messages, their transmission rate an the lifetime of eprecate entries of the neighborhoo table. While these aspects are important, only a few stuies have been performe about them. Among the propose enhancements of the basic HELLO protocol, most of them require a slotte network. For instance, [6] aims at reucing the overall energy consumption, assuming a static network. Noes can be in three ifferent states: sening, listening or sleeping. At each slot, noes choose a state with a probability p state : the ifficulty is then to etermine optimal values of p smboxstate. In [10], [12], three ifferent protocols are propose for both single channel an multichannel networks. In the first one (RP), noes sen a HELLO at each slot with probability p an listens with probability 1 p. In the secon one (AP), noes immeiately answer upon reception of a message. In the last one (LP), the following conition is ae to RP: noes listen the carrier if they have sent a HELLO on the slot before. Upon reception of a HELLO, noes trigger a backoff time an sen a new HELLO when the countown expires. As a result, LP presents the best traeoff when the number of noes is known. Of course, knowing the number of noes in a ecentralize an ynamic network is a rather unrealistic assumption. Moreover, all the proposals assume a slotte network, which means that synchronization among noes is neee, which is by itself not a trivial problem. As state earlier, a low HELLO frequency leas to obsolete tables while a high one may saturate banwith to the etriment of ata traffic. The trae-off epens on characteristics (e.g., ensity, spee) that may evolve over time, leaing to the nee for an aaptive protocol. Nevertheless, only a few stuies have trie to tackle this problem. In [5], a simple aaptive protocol is propose, in which noes evaluate two values by monitoring their neighborhoo: the time link failure (TLF) an the time without change (TWC). Moreover, they perioically sen HELLO at a frequency f low again. If a noe notices that the measure TWC becomes greater than a given threshol, it switches to the high ynamics rate an sens HELLO messages at a frequency f high. On the contrary, if the estimate TLF becomes smaller than a threshol, it goes back to the low ynamics rate an sens HELLO at a frequency f low. In this solution, fining the correct threshols is not obvious since the threshols themselves may nee to evolve over time. In [4], authors propose three protocols in orer to approach the best trae-off. The first one is calle Aaptive HELLO protocol: each noe simply sens a HELLO each time it has gone through X meters. Though straightforwar, this scheme assumes that noes are aware of their spee an their location. The secon protocol is calle Reactive HELLO protocol. It is base on the iea that noes shoul buil their neighborhoo table only when neee. Thus, when a noe sens a ata packet, it first sens a HELLO message an waits uring a time t for an answer. If no answer is receive, then it repeats the same behavior up to X times. Upon reception of a HELLO message, noes trigger a timeout before answering, to avoi collisions. While this scheme minimizes the quantity of HELLO messages, it introuces a high latency before sening ata packets, an shoul not be use in networks with high mobility. The thir protocol propose in [4] is calle eventbase HELLO protocol. Noes perform the classic perioic HELLO protocol, but if they o not receive any message an o not nee to sen ata packets uring a given time perio, then they stop sening beacon messages until reception of a HELLO message. The main rawback of this protocol is that some noes may never be etecte by mobile noes. In [11], an optimal HELLO frequency which epens on the relative spee between objects is escribe. The iea is that a noe which stries more than a given istance in the communication area of another noe has to be etecte by the latter. If the two noes move with a spee S, the optimal frequency f opt is equal to: f opt = 2S ar, (1) where ar is the threshol istance in communication area to be etecte (a < 1). A. Description IV. THE TAP PROTOCOL We suppose that each noe sens HELLO messages at the frequency f HELLO. Whenever a noe receives a HELLO message, it upates its neighborhoo table, thus generating some turnover. We assume in this paper that given a perio of time t, the turnover r t is equal to the ratio between the number of new neighbors (i.e., noes that were not yet neighbors t units of time earlier) an the current total number of neighbors. Obviously, the turnover epens on both t an f HELLO, but if we assume that t = 1/f HELLO (that is, the turnover is compute each time a HELLO message is

4 R u1 u0 k ω C u1, v1 θ v0 C v1 C u0, R u0 k ω u1 R â v1 θ max C v1, C u1, R C u0, R Fig. 1. A new neighbor v of a noe u - Global view. Fig. 2. A new neighbor v of a noe u - Zoom. sent), then it only epens on f HELLO. For the sake of clarity, we enote the turnover by r through the rest of this paper. The protocol we propose is base on the iea that noes can aim at the optimal HELLO frequency f opt (see (1)) by measuring the turnover. The analysis given in the next section shows the relationship between the optimal turnover r opt an the optimal frequency. Inee, if a noe aims at keeping r constant, then it has to moify f HELLO. Keeping the turnover close to r opt shoul make f HELLO ten towar an optimal HELLO message frequency f opt. Noes shoul thus compute the current turnover r each time they sen a HELLO message. To o so, they just have to make a backup of their table before sening a HELLO message, in orer to ientify new neighbors which will appear. Once r is compute, two cases may happen: When r is too small (r < r opt ), this means that f HELLO is too high an there are not enough changes in the table. The frequency f HELLO shoul be ecrease. When r > r opt, f HELLO is too low an there are too many changes. The frequency f HELLO shoul thus be increase. One can note that this escription is generic, an oes not epen on any external upate function. It simply assumes that noes are aware of the value of r opt an are able to observe their neighborhoo table to etermine the number of new neighbors each time a new HELLO is sent. We will later provie in Section IV-C some possible functions that may be use to aapt f HELLO base on the observe turnover r. B. From optimal frequency to optimal turnover The principal issue that remains opene is: what is the optimal frequency? Fining the correct value for f opt is inee not trivial an may epen on a lot of parameters. We propose in this section to theoretically compute r opt to erive f opt by setting these parameters. We thus assume a Unit Disk Graph an a mobility moel where noes move at a constant spee s in a ranom irection. While these assumptions may not be the most realistic ones, we use them as a first step in orer to experiment our HELLO protocol. In this analysis, we suppose that noes are ranomly eploye in a 1 1 square using a Poisson Point Process (noe positions are inepenent) with an intensity λ > 0, λ being the mean number of noes per surface unit. We are first intereste in fining the mean number of new neighbors of a noe after a time perio t. Let v be a point at istance R from noe u at time t 1 = t 0 + t (v is thus a neighbor of u). We nee to compute the probability P() that noe v is actually a new neighbor of u. Once P() is known, the mean number of new neighbors of a noe u after a time perio t (note E[N] t ) is simply equal to: E[N] t = R =0 2λπ P(). (2) Let u 0 (resp. v 0 ) be the position of noe u (resp. v) at time t 0 an u 1 (resp. v 1 ) its position at time t 1. Let also be = S t. We are thus intereste in fining the probability that u 0 v 0 > R knowing that u 1 v 1 < R. We enote by ω the irection u 0 u 1 an θ the irection v 0 v 1. ω an θ are chosen in a uniformly ranom fashion in [ π, π] (each irection has the same probability to be chosen). Fig. 1 illustrates our moel. C u,r is the circle centere at u with raius R an k = u 0 v 1. The blue ashe circle C u1, (resp. re otte circle C v1, ) represents the possible position of u 0 (resp. v 0 ). We can first notice that the shorter t, the less likely v is to be a new neighbor of u. This leas to the fact that there exists min = min(0,r 2 ) s.t. if < min, P() = 0 whatever ω an θ. Given an ω, computing the probability P(,ω) that noe v is a new neighbor of noe u amounts to computing the probability that noe v comes from the otte blue angular sector of Fig. 2, Thus, we have: P(,ω) = θmax 0 θ 2π. (3) By using notations on Fig. 2, we have 2π = θ max + 2â an â = arccos( 2 R 2 +k 2 2k ). We euce : θ max = 2arccos( R2 2 k 2 ). (4) 2k Given an ω, noe v can be a new neighbor iff C u0,r an C v1, intersect (see Fig. 2). If not, that means that noes v an u were alreay neighbors at t 0. C u0,r an C v1, intersect only if: R k R +. (5)

5 R = 75m R = 150m R = 100m R = 60m ropt Fig. 3. Probability to be a new neighbor as a function of = uv - S = 2 m.s R(m) Fig. 4. Theoretical values of r opt as a function of R for a =. 3 From (5), we can euce the angular sector Ω = [ω min,ω max ] of ω for which noe v is a new neighbor. We have k = cos(ω) an k < + ω {0,π}. Since < R, we have k < R + ω {0,π} an so ω max = π. We can also notice that k > R for ω > ω min such that k(ω = ω min ) = R. R = k ω min = arccos( 2 + 2R R 2 ) 2 Thus, given a istance, noe v is a new neighbor of u iff ω Ω = [ω min,ω max ]: ω min = arccos( 2 + 2R R 2 ) ω π. 2 Now, we can compute the probability P() that a noe v is a new neighbor of u: π P(, ω) P() = 2 ω 0 π { 1 π π θ = 2 ω max ω if min R, min 0 otherwise. Fig. 3 plots P() for several values of R, t = 0.2s, S = 2m.s an λ = As expecte, P() increases when or S increases an is proportional to R. From (6), we can euce the number of new neighbors that noe u encounters uring a time perio t: R E[n] t = 2πλ P() = λ R π θ max ω. min π min ω min (7) Equation (7) allows us to theoretically compute r opt (see Section IV-A). Inee, r opt is the ratio obtaine between two HELLO packets sent at frequency f opt. Thus: E[n] t= 1 r opt = f opt λπr 2. The spee parameter S appears in the result of E[n] t only through = S t. For t = 1 ar, we have = S fopt 2S = ar 2. Thus, since oes not epen on S anymore, r opt is inepenent of the spee an only epens on R. Fig. 4 an 5 plot the theoretical values of r opt as a function of R for ifferent values of a. Note that with the help of (6) ropt a = a = 0.3 a = Fig. 5. Theoretical r opt as a function of R for ifferent values of a. this stuy, by watching its neighborhoo uring t, a noe can count the number of new neighbors an from this quantity, euces its relative spee S (from corresponence tables). This can help for many applications. C. Implementation There are still some remaining issues regaring how our TAP protocol may be implemente. One of them is about how a noe may obtain a correct turnover value. In the previous section we inee showe that this value may be very small (e.g., ) while it is nearly impossible for a noe to observe a so small turnover between two successive HELLO messages. A solution to this problem is to let noes archive more than one table into a history of size X: if X is sufficiently large, then a correct value may be expecte. The turnover may then be compute by counting neighbors present in the most recent table that are not present in the olest one an by using the current HELLO elay as: r = nb new neighbors current HELLO elapse time. To aapt f HELLO, one also nees to efine some functions base on the turnover r. For instance, the amplitue at which f HELLO shoul be moifie (either increase or ecrease) shoul be etermine by the ifference between r an r opt : the higher the ifference, the more likely f HELLO an f opt are really ifferent from each other. To compute this amplitue, we propose to use the following function g(x): { ( r r opt ) 2 if r < 2 r g(x) = ropt opt, 1 otherwise. R(m)

6 Amplitue # new neighbors Theoretical values Experimental values Observe turnover R (m) Fig. 6. Function g(x) use to aapt f HELLO (r opt = ). Fig. 8. New neighbors per noe - t = 5s - S = 2m.s 1 - Increasing R # new neighbors Theoretical values Experimental values Observe turnover S (m.s 1 ) Spee Constant Optimal TAP Fig. 7. New neighbors per noe - R = t = 5s - Increasing S. Fig. 9. Observe turnover. This function is illustrate by Fig. 6, where r opt is fixe to in accorance with theoretical results (see Fig. 4). With this function, when r an r opt are only slightly ifferent, then f HELLO is only slightly moifie. Oppose to this case, the higher the ifference between r an r opt, the fastest f HELLO shoul converge to the optimal frequency. Of course, any other interesting function g(x) such that g(r opt ) = 0 may be use for this purpose since our protocol oes not epen on this particular one. Finally, to aapt the elay between two HELLO messages an thus the resulting turnover, we propose to use the following series: { } HELLO = HELLO + HELLO 4 g(r) if r r opt, HELLO HELLO 4 g(r) otherwise. Once again, any other function may be use to aapt the elay between HELLO messages. For instance, it may be possible to ajust the functions in orer to favor certain aspects, like the banwith usage. Evaluating what kin of functions may be use to favor such or such behavior is actually beyon the scope of the current paper. V. EXPERIMENTAL RESULTS Our experimental results were obtaine thanks to a homemae simulation tool, using the Unit Disk Graph moel. In our simulations, we use a Poisson point process of intensity λ = 100 A in a square area of size A = The results obtaine are within a 95% confience interval. For each iteration, a new network is generate. We use the functions escribe in Section IV-C with a history size X = 10. Regaring TAP, the targete turnover is fixe to. In these experiments, we o not consier the problem of etermining the lifetime of an entry of the neighborhoo table: an entry is remove as soon as the corresponing noe has not sent a HELLO at the right time. We chose to iscar all other protocols presente in Section III since they rely on very specific assumptions (e.g., slotte network, eicate harware). To evaluate our TAP protocol, we chose to compare it to two other schemes: Constant: f HELLO is fixe to 0.2 an never varies. Optimal: f HELLO is set to f opt (refer to Section IV-B) base on the current spee. We first provie results that emonstrate the correctness of the theoretical analysis performe in Section IV-B. We thus give the expecte average number of new real neighbors per noe for an observation perio t = 5s. The neighbors reference here are the real physical neighbors, an no neighborhoo table is use. On Fig. 7, R is fixe to 150m an S increases. On Fig. 8, S is fixe to 2m.s 1 an R increases. In both cases, one may notice that experimental an theoretical results perfectly match. On Fig. 9 the observe turnover for all selecte protocols is provie. As expecte, the turnover increases for the Constant scheme since the observation perios have a fixe uration ( HELLO is set to 5s) while the spee increases. A higher number of new neighbors is thus observe at each HELLO, an the turnover increases accoringly. The Optimal scheme ajusts f HELLO by using the exact value of the current spee, an provies a constant turnover. The observe turnover is close to, thus valiating the theoretical value compute in Section IV-B. Regaring TAP, it is interesting to note that it is effectively able to aim at a given ratio (set to here),

7 0 Delay between two HELLO (s) Fig. 10. Neighborhoo table accuracy (%) Constant Optimal TAP Spee Constant Optimal TAP Delay between two HELLO messages Fig. 11. Spee Accuracy of neighborhoo tables proviing a constant turnover. The observe value is slightly higher than expecte, but this may be correcte by using ifferent ajustment functions an/or by targeting at a slightly lower turnover. On Fig. 10, we give the observe value of HELLO for varying spee. Of course, the elay of the Constant scheme oes not vary since it oes not take the spee into account. The Optimal scheme computes f HELLO base on the real spee an shoul thus provie an optimal value of HELLO. Regaring TAP, the real spee value is not use, since it is not available. As explaine in Section IV, noes only observe the turnover an ajust the elay base on this observation. One can note that it is very effective. When the optimal turnover value of is targete, the elay is not the same as with the Optimal scheme because, as observe in Fig. 9, the real turnover is slightly higher than expecte. We finally give in Fig. 11 the accuracy of the neighborhoo tables, which is equal to the percentage of noes present in the table of a noe that are really physical neighbors of this noe: if f HELLO is too low, then tables are not up to ate an the accuracy rops. The Constant scheme oes not aapt f HELLO with the spee, an the accuracy thus quickly rops. Both the Optimal an TAP schemes are able to keep a correct accuracy of the tables because of the ajustment of HELLO observe in Fig. 10. The accuracy provie by TAP is slightly lower than with the Optimal scheme because HELLO is slightly higher than expecte. While this may be easily correcte by using ifferent ajustment functions, the provie accuracy is still sufficient for most applications. VI. CONCLUSION AND OPEN ISSUES We presente TAP, an aaptive HELLO protocol for mobile a hoc an sensor networks that simply estimates the neighborhoo turnover an ajusts the HELLO frequency base on this observation, to aim at a given optimal frequency. Besies the fact that our protocol is simple to implement, it is especially well-tailore to stanar mobile a hoc an sensor networks since it oes not rely on any specific harware to achieve the ajustment. We theoretically compute the optimal turnover base on given assumptions, an experimentally showe that the TAP protocol provies a goo accuracy when aiming at that optimal turnover uner these assumptions. There are some remaining open issues that we i not consier in this paper. One of them is about the timeout that shoul be use to remove eprecate neighbors from the table. We inee focuse on the frequency of HELLO messages an i not consier the problem of etermining the optimal lifetime of a table entry. This problem is important since consiering eprecate entries may lea to serious problems. Using a constant lifetime is not a goo solution since it shoul epen on the spee of the noes, just as the HELLO frequency. Another issue that we i not aress is about networks with heterogeneous spee or riven by more realistic mobility moels. A better physical layer moel (e.g., the lognormal shaowing moel [9]) might also be consiere since HELLO messages may then get lost before being receive. We woul like to further stuy the consequences of these more realistic assumptions an aapt our TAP protocol consequently. ACKNOWLEDGMENTS This work was partially finance by the European Commission uner the Framework 6 IST Project Wirelessly Accessible Sensor Populations (WASP). REFERENCES [1] I. Chakeres an E. Beling-Royer. The utility of hello messages for etermining link connectivity. In WPMC, [2] B. Clark, C. Colbourn, an D. Johnson. Unit isk graphs. Discrete Mathematics, 86(1 3): , [3] T. Clausen, P. Jacquet, A. Laouiti, P. Mühlethaler, A. Qayyum, an L. Viennot. OLSR - Optimize Link State Routing Protocol, October RFC [4] V. Giruka an M. Singhal. Hello protocols for a hoc networks : Overhea an accuracy trae-offs. In WoWMoM, [5] C. Gomez, A. Cuevas, an J. Paraells. A two-state aaptive mechanism for link connectivity maintenance in AODV. In REALMAN, [6] M. McGlynn an S. Borbash. Birthay protocols for low energy eployment an flexible neighbor iscovery in a hoc networks. In Mobihoc, [7] J. Moy. OSPF - Open Shortest Path First, March RFC [8] C. Perkins, E. Beling-Royer, an S. Das. AODV - A hoc On-Deman Distance Vector Routing, July RFC [9] L. Quin an T. Kunz. On-eman routing in MANETs: The impact of a realistic physical layer moel. In A Hoc Now, [10] G. Sawchuk, G. Alonso, E. Kranakis, an P. Wimayer. Ranomize protocols for noe iscovery in a hoc multichannel networks. In A Hoc Now, [11] A. Troël. Prise en compte e la mobilité ans les interactions e mobilité entre terminaux à profils hétérogènes. PhD thesis, Université e Rennes 1, France, In french. [12] G. Wattenhofer, G. Alonso, E. Kranakis, an P. Wimayer. Ranomize protocols for noe iscovery in a hoc, single broacast channel networks. In IPDPS, 2003.