Jounal of Compute Science 8 (5): 752-760, 2012 ISSN 1549-3636 2012 Science Publications The Impact of Radio Popagation Models on Ad Hoc Netwoks Pefomances 1 Rhattoy, A. and 2 A. Zatni 1 Depatment of Compute, Modeling Systems and Telecommunications Reseach Goup, Moulay Ismail Univesity, Highe School of Technology, B.P. 3103, 50000, Toulal, Meknes, Moocco 2 Depatment of Compute, Optonics Laboatoy, Ibnou Zoh Univesity, Highe School of Technology, B. P. 33/S, 80000, Agadi, Moocco Abstact: Poblem statement: Wieless netwoks ae chaacteized by a dynamic topology tiggeed by the nodes mobility. Thus, the wieless multi-hops connection and the channel do not have deteminist behaviou such as: Intefeence o multiple paths. Moeove, the nodes invisibility makes the wieless channel difficult to detect. This wieless netwoks behaviou should be scutinized. Appoach: In ou study, we mainly focus on adio popagation models by obseving the evolution of the outing laye s pefomances in tems of the chaacteistics of the physical laye. Results: Fo this pupose, we fist examine and then display the simulation findings of the impact of diffeent adio popagation models on the pefomance of ad hoc netwoks. To fully undestand how these vaious adio models influence the netwoks pefomance, we have compaed the pefomances of seveal outing potocols (DSR, AODV and DSDV) fo each popagation model. In ode to each cedible esults, we focused on the notion of nodes speed and the numbe of connections by using the well known netwok simulato NS-2. Conclusion: To conclude, the simulation findings ae to be taken as a stong efeence on the thee outing potocols behaviou; howeve, it shouldn t be consideed as an exact epesentation of its behaviou and eal envionment because of seveal simulation constaints such as: the dimension of movement field of mobile nodes, the taffic type and the simulation timing. Key wods: MANET, ad-hoc netwoks, outing potocols, DSR, DSDV, AODV, fading, popagation model, economic impact INTRODUCTION Befoe using a wieless netwok o installing the stations of a cellula netwok, we have to detemine the adio waves tageted coveage. The tageted adio coveage has a cucial economic impact because it detemines the equipment to be utilized. In othe wods, the bigge the coveage is the fewe antennas ae equied to cove the egion o to each a gand aea. Besides, the adio coveage depends on seveal paametes such as the emission powe. Howeve, the envionment whee the waves spead and the utilized fequency also play a cucial ole. The adio popagation waves ae contolled by stict ules, mainly when thee ae obstacles between the tansmitte and the eceive (Zang and Rowe, 2007; Kaya et al., 2009). Among the changes a wave may undego, we can cite: eflection, diffaction, Fig. 1: The diffeent physical phenomena distubing adio signal popagation The est of this study is oganized as follows. We give the adio popagation models types. Then we discuss of outing potocols concepts in ad hoc netwoks. In addition, we declae the methodologies of diffusion and absoption (Fig. 1). Coesponding Autho: Rhattoy, A., Depatment of Compute, Modeling, Systems and Telecommunications Reseach Goup, Moulay Ismail Univesity, Highe School of Technology, Agouay Road, Km 5, B. P. 3103, 50000,Toulal, Meknes, Moocco 752
J. Compute Sci., 8 (5): 752-760, 2012 simulation. Finally, we investigate the impact of adio popagation models on the pefomances of outing potocols in ad hoc netwoks and we pesent ou conclusions. Radio popagation models: In a popagation model, we use a set of mathematical models which ae supposed to povide an inceasing pecision. Popagation adio models ae thee types: path loss, shadowing and fading. The fist type can be expessed as the powe loss duing the signal popagation in the fee space. The second type is chaacteized by fixed obstacles on the path of the adio signal popagation. The thid categoy is the fading which is composed of multiple popagation distances, the fast movements of tansmittes and eceives units and finally the eflectos (Eltahi, 2007). Fee space model: The fee space model assumes that in the ideal popagation condition between the tansmitte and the eceive, thee is only one clea Line Of Slight (LOS) path. The following equation calculate the eceived signal powe in a fee space Eq. 1: P G G λ (4 π) d L 2 t t = 2 2 P (d) (1) whee, P t is the powe tansmission (in watts), G t and G ae the antenna gains of the tansmitte and eceive espectively. L is the system loss facto. λ is the wave length and d is the distance between the tansmitte and the eceive (Singh and Kapang, 2011) whee d is small. Hence, in this model, we calculate d c as a coss-ove distance. When d<d c, we use the fist equation, but when d < d c, the second equation is used. At the coss-ove distance, Eq. 1 and 2 give simila esults. Consequently, d c can be calculated as Eq. 3: 4πh th dc = λ (3) Shadowing model: Both the fee space and the two-ay models pedict the eceived powe in tems of the distance. They also epesent a communication aea as an ideal cicle. In fact, the eceived powe at a given distance vaies andomly because of multi-path popagation effects, known as fading effects. Thus, the two afoementioned models pedict the mean eceived powe at distance d. The shadowing model is twofold (Singh and Kapang, 2011). The fist model is the path loss model epesented by P (d). It employs a close in distance d 0 as follows Eq. 4: P (d 0) d = P (d) d β 0 (4) β is called the path loss exponent and is often empiically detemined by filed measuement. Equation 3 implies that β = 2 in fee space popagation. The Table 1 gives typical values of β (Fall, 2001). Lange values of β coespond to moe obstuctions and thus faste decease in aveage eceived powe as distance becomes lage. Fom Eq. 4, we have: Two-ay gound model: The fee space model mentioned above states that thee is only one single diect path. In fact, the signal eaches the eceive though multiple paths (due to eflection, efaction and scatteing). The two-path model attempts to account fo this phenomenon. In othe wods, the model advocates that the signal attains the eceive via tue paths: a lineof-slight path and a path though which the eflected wave is eceived (Singh and Kapang, 2011). In the twopath model, the eceived powe is epesented by Eq. 2: 2 2 Pt G tgh t h P (d) = (2) 4 d L P (d) d = 10βlog P (d ) d 0 db 0 whee, h t and h ae the heights of the tansmitte and eceive espectively. Nonetheless, fo shot distances, the two-ay model does not give accuate esults because of in oscillation caused by the constuctive and destuctive combination of the two ays. The popagation model in the fee space is instead, still used shadowing model. 753 (5) The second pat of the shadowing model eflects the vaiations of eceived powe at cetain distance (Eq. 5). It is a log-nomal andom vaiable. The oveall model is epesented by Eq. 6: P (d) d = 10β log + Χ P (d ) d 0 db 0 db (6) whee, X db is Gaussian andom vaiable with zeo mean and standad deviation σ db σ db is called shadowing deviation and also obtained though measuement in the eal envionment. Table 2 displays some typical values of σ db. This equation is also labelled a log-nomal
Table 1: Some Typical values of path loss β Envionment β Outdoo Fee space 2 Shadowed uban aea 2.7-5 In building Line-of-sight 1.6-1.8 Obstucted 4-6 Table 2: Typical values of shadowing deviation σdb Envionment σ db (db) Outdoo 4-12 Office, had patition 7.00 Office, soft patition 9.60 Factoy, line-of-sight 3-60 Factoy, obstucted 6.80 Small-scale fading model: Rayleigh and ice: This fading model depicts the apid fluctuations of the eceived signal due to multipath fading. This fading phenomenon is geneated by the intefeence of at least two types of tansmitted signals to the eceive with slight time intevals (Amjad and Stocke, 2010). The outcome may vay accoding to fluctuations and to diffeent phases in tems of multiple factos such as: delay between waves, the intensity and the signal band width. Hence, the system pefomance may be attenuated by the fading. Howeve, thee ae seveal techniques that help stopping this fading. The signal fading wee monitoed accoding to a statistical law wheein the most fequently used distibution is Raleigh s (Cavalho et al., 2004). The tansmitted signal is, thus, conditioned by the following phenomena: eflection, scatteing and diffusion. Thanks to these thee phenomena, the tansmitted powe may each the hidden aeas despite the lack of diect visibility (NLOS) between the tansmitte and eceive. Consequently, the amount of the eceived signal has a density of Rayleigh Eq. 7: 2 2x x exp( ), pou 0 x f ( x) = P P 0, pou x < 0 J. Compute Sci., 8 (5): 752-760, 2012 (7) whee, P is the aveage eceived powe. In case whee thee is a diect path (LOS) between the tansmitte and eceive, the signal no longe obeys to Rayleigh's law but to Rice s. The pobability density of Rice is epesented by Eq. 8: 2 ( K + 1) x 2x(K + 1) exp K I 0 P P K(K + 1) f (x) = 2x, pou 0 x P 0, pou x < 0 Whee: K = The atio of the powe eceived in the diect line and in the path P = The aveage powe eceived I 0 (x) = The zeo-ode Bessel function de fined by Eq. 9: 1 2π I 0(x) = exp( x cos θ)dθ 2 π (9) 0 The density of Rice is educed to the density of Rayleigh in the case of an absence of a diect path which means that K = 0 and thus I 0 (x) =1. Nakagami model: This distibution encompasses seveal othe distibutions as paticula cases. To descibe Rayleigh distibution, we assumed that the tansmitted signals ae simila and thei phases ae appoximate. Nakagami model is moe ealistic in that it allows similaly to the signals to be appoximate. Since we have used the same labels as in Rayleigh and j i Rice cases, we have = e θ. The pobability density of Nakagami elated to is epesented by Eq. 10: m 2m 1 2 2m m P ( ) = exp, 0 m Γ( m) Ω Ω (8) Dynamic Souce Routing (DSR): Duing the discovey pocess of outing, a souce node geneates a oute-equest packet which needs a new oute to a cetain destination. The oute equest is connected 754 i (10) whee, Γ(m) is gamma function, Ω = ( 2 ) and m = {E ( 2 )} 2 /va ( 2 ) with the constaint m 1/2. Nakagami model is a geneal distibution of fading which is educed to Rayleigh s distibution fo m = 1 and to unilateal Gaussian model fo m = 1/2. Besides, it epesents petty much ice model and it is close to cetain conditions in the lognomal distibution. Ad hoc outing potocols: Ad hoc outing potocols ae based on fundamental pinciples of outing such as: Inundation (flooding), the distance Vecto, the outing to the souce and the state of the site. Accoding to the way outes ae ceated and maintained duing the data delivey, the outing potocols can be chaacteised into two categoies: poactive and eactive (Feeney, 1999). Among the tested potocols in this study, only DSDV is poactive and the othes (DSR and AODV) ae all eactive. Poactive potocols update oute infomation peiodically, wheeas eactive potocols establish outes only when needed. Hee is a summay of the outing potocols assessed in this study.
though the netwok until it eaches some nodes with a oute to destination. A eply packet containing all infomation of intemediate nodes is sent back to the souce. The sent packets contain a list of all nodes though which they have to tansit. This list can be huge in a netwok with a big diamete. The nodes do not need the outing table. Thee ae two DSR basic opeations: the oute discovey and the oute maintenance. In ode to cut down the expenses and the fequency of the oute discovey, evey single node keeps tack of the paths thanks to eply packets. These paths ae used until they become useless (Khati and Rajput, 2010). Ad-hoc On-Demand Distance Vecto potocol (AODV): AODV has a way fo oute equest close to that of DSR. Howeve, AODV does not pefom a outing to the souce. Evey single node on the path efes to a point towads its neighbou fom which it eceives a eply. When a tansit node needs boadcasts a oute equest to a neighbou, it also stoes the node identifie in the outing table fom which the fist eply is eceived. To check the links state, AODV uses contol messages (Hello) between diect neighbous. Besides, AODV utilizes a sequence numbe to avoid a ound tip and to ensue using the most ecent outes (Alfawae and Hua, 2007). DSDV potocol: The algoithm Dynamic destination Sequenced Distance Vecto (DSDV) (Gupta and Saket, 2011; Ramesh et al., 2010) has been constucted fo mobile netwoks. Each mobile station keeps a outing table which contains all possible destinations, numbe of hops to each the destination, Sequence Numbe (SN) associated with the node destination to distinguish the new outes of the old a ones and avoid the fomation of ound tip outing. The table updating is peiodically tansmitted acoss the netwok so as to sustain the infomation consistency and thus geneates an impotant taffic. MATERIALS AND METHODS Methodology: In this study, on one hand we study the impact of diffeent popagation models in ode to analyse the envionment effect on the ad hoc netwoks pefomance. On the othe hand, we have compaed seveal outing potocols pefomances (DSR, AODV and DSDV) accoding to evey popagation models. In ode to obtain valid esults, we have inseted the notion of the nodes speed and the numbe of connections. The assessment is twofold: Fist, we divesified the nodes speed. Second, we alteed the numbe of connections. J. Compute Sci., 8 (5): 752-760, 2012 Scenaio 1: So as to analyse the ad hoc outing potocols behaviou, we selected taffic souces with a constant output (CBR) elated to UDP potocol. The packet emission ate is settled at 8 packets pe second with a maximal speed vaiation of nodes. Ten speed values wee consideed: 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 m sec 1. The assessed potocols ae: AODV, DSR and DSDV. These thee ae available in 2.34 of ns-2. The popagation models unde study ae: the fee space, the two-ray gound, Rice s and Nakagami s models. The simulation span is of 200 sec. The data packet size is 512 octets. The mobile nodes utilize the andom waypoint mobility model (Geetha and Gopinath, 2008). The Mobil nodes move within a squae dimension aea 670 670 m. At the moment, we limit the numbe of souces in 10 and we analyse the impact of the nodes speed. Scenaio 2: The numbe of souces may be anothe paamete that can be alteed so as to look at the diffeent outing potocols pefomance. In this pat, we display the impact of the taffic load on the outing potocols. Fo this eason, we have vaied a numbe of connections. Six cases wee consideed: 5, 10, 15, 20, 25 and 30 connections. Fo the time being, let s limit the nodes maximal speed at 10 m sec 1 while the othe paametes ae simila to those in the fist case. Pefomance indicatos: Because of the length chosen in this study, we have selected just thee pefomance indicatos in ode to study the outing potocols pefomances. They ae outlined as follows: Packet delivey faction, end aveage to end delay and the thoughput. Packet Delivey Faction (PDF): This is the atio of total numbe of CBR packets successfully eceived by the destination nodes to the numbe of CBR packets sent by the souce nodes thoughout the simulation: CBR ecv 0 1 Pkt _ Delivey 0 = 100 n CBR This estimation gives us an idea of how successful the potocol is in deliveing packets to the application laye. A high value of PDF indicates that most of the packets ae being deliveed to the highe layes and it is a good indicato of the potocol pefomance. Aveage End-To-End Delay (AE2E Delay): This is defined as the aveage delay in tansmission of a packet between two nodes and is calculated as follows: 755 n 1 sent
J. Compute Sci., 8 (5): 752-760, 2012 Avg _ End _ to _ End _ delay = n ( CBR sent _ Time CBR ecv _ Time ) 1 n 1 CBR A highe value of end-to-end delay means that the netwok is congested and hence the outing potocol does not pefom well. It depends on the physical chaacteistics of a link and the delay of teatment. ecv because the two models ceate a vey dynamic topology in ou simulations. Since DSR elies heavily on stoed paths, it is moe inclined to utilize infomation about lost paths. Consequently, this geneates high packet outing faction and low packet delivey. Thoughput: The thoughput data eflects the effective netwok capacity. It is computed by dividing the message size with the time it took to aive at its destination. It is measued consideing the hops pefomed by each packet. RESULTS AND DISCUSSION Simulation findings: In this pat, we display the study findings about the impact of the nodes maximal speed and the taffic load on the outing potocols; accoding to the thee afoementioned pefomance indicatos: packets Delivey faction, Thoughput and aveage end to end delay. Scenaio 1: The esults coesponding to the PDF, AE2E Delay and thoughput ae shown in Fig. 2-4 espectively. Packet delivey faction: In Fig. 2, we notice that the packet delivey faction vaies slightly accoding to the speed incease. Consequently, the links ae elatively steady and weake with a weak speed. AODV and DSR offe moe packets than DSDV. Besides, when the nodes speed inceases, the packet delivey deceases a bit in case of DSDV. Hence, the main eason fo the packet loss is mobility, congestion and the wieless channel chaacteistics. Meanwhile, we notice that the fee-space and the two-ay gound delive moe packets than the othe models such as; fist Rice, second Rayleigh thid Nakagami and finally the shadowing. Rice s model pefomance opeates accoding to staight sight and employs the fee-space fo long distance pediction. Wheeas, the shadowing bad pefomance is due to the low intensity of the signal caused by the obstacles. This esults in the packet loss on weak links, displays wongly the links disconnection and leads to the inteuption and thus the die need to set up a new itineay. DSR eacts Fig. 2: AODV- PDF DSDV-PDF DSR-PDF badly to the use of shadowing and Nakagami models vesus Speed 756
J. Compute Sci., 8 (5): 752-760, 2012 packets will be deleted once they each thei boken links. In addition, the data packets in DSR undego exta delays duing the communication intefaces waiting because of the fequent etansmissions. This latency causes the packets death (thei deletion). Similaly to PDF, we notice that the fee-space and the two-ay gound endue less delay than the othe models, followed by fist Rice, second Rayleigh thid Nakagami and finally the shadowing model. The weak pefomance of shadowing and Nakagami stems fom the fact that when we obseve the slope indicating the un-mentioned collisions ate, we ealize that the phenomenon is accounted fo. The nodes mobility has an influence on evey single paamete; in othe wods, it influences mainly the end-to-end delay. Thoughput: As mentioned in pat PDF, the highe the eceived packets ate. As we expected, the thoughput deceases slightly when the speed inceases because it has to find the path fo moe outing taffic delivey. Theefoe, the channel will be less used fo the data tansfe to as to educe the useful thoughput. Like AODV, in case of DSDV, the thoughput deceases as the speed inceases (Fig. 4). Scenaio 2: The esults coesponding to the PDF, AE2E Delay and Thoughput ae shown in Fig. 5-7 espectively. Packet delivey faction: Figue 5, displays, diffeent outing potocols pefomances in tems of the numbe of connections. The chats also display that if the numbe of connections inceases, the delivey faction value tends to decease fo all models. Thus, thee is netwok congestion. In this scenaio, DSDV is less pefement than AODV and DSR because thei PDF ae ove 99% in so fa as it eaches 10 connections. Howeve, when we incease the numbe of connections in PDF, DSR should be compaed to AODV. Fig. 3: AODV-AE2E Delay DSDV-AE2E Delay DSR-AE2E Delay vesus Speed Aveage end-to-end delay: In Figue 6, as expected, the delay is highe fo non diect-sight popagation models (NLOS). Moeove, as thee ae moe deliveies, the aveage delay also inceases. Consequently, the packets have to wait moe in a stand by position. In tem of delays, we can obseve that DSDV and AODV ae moe efficient than DSR. We also notice that delays fo the two potocols incease apidly accoding to the numbe of connections because of the high taffic congestion in some aeas of the ad hoc netwoks. DSDV, this is accounted fo by its use of pioity Aveage end-to-end delay: Figue 3, displays that DSR has moe system timing than AODV and DSDV because in DSR, the intemediate nodes ae allowed to eply though stoed paths in thei memoies, which ae unfotunately, often invalid. Hence, the tansmitted data citeia whee in the potocol packet is given pioity. 757
J. Compute Sci., 8 (5): 752-760, 2012 Fig. 5: AODV-PDF DSDV- PDF DSR-PDF vesus speed numbe of connections Hence, a potocol packet is always teated pio to any data packet even if it aives late. On the othe hand DSDV does not distinguish between the potocol packets and the data ones duing the waiting phase. Fig. 4: AODV-Thoughput DSDV- Instead all packets ae teated accoding to thei aival Thoughput DSR-Thoughput vesus speed anking. 758
J. Compute Sci., 8 (5): 752-760, 2012 Fig. 6: AODV-AE2E Delay DSDV-AE2E Delay DSR-AE2E Delay vesus numbe of connections Thoughput: In Figue 7, we notice that the thoughput diminishes significantly with an incease of the taffic load. DSDV potocol is steadie than AODV fo the inceasing numbe of connections. 759 Fig. 7: AODV-Thoughput DSDV-Thoughput DSR-Thoughput vesus numbe of connections
CONCLUSION Conclusions and pespectives: In this aticle, we study the impact of diffeent adio popagation models on the pefomance of ad hoc netwoks. Accoding to the simulation findings, we may state that the choice of the popagation models has a geat impact on the outing potocol s pefomance. In this espect, we have identified both the deteminist and the statistic modelizations. The simulation findings have evealed that the diffeent popagation models have a consideable impact on the pefomance of the ad hoc mobile netwok. The latte deceases apidly when the fading models, mainly Ricean, Rayleigh, Shadowing and Nakagami have been taken into consideation. The main easons of thei deteioation ae the outcome of the big vaiation in the eceived intensity signal. Accoding to the esults to the outing potocols pefomance, we find out that thee is no pefeable potocol among the othes all scenaios and the assessing citeia. On the othe hand, no matte how the nodes speed is, the DSDV is moe efficiency in tems of the delay because of its poactive featues. Howeve, its activity shaing is vey weak, which influences the netwok stability and thus becomes weak; wheeas, the activity concentation is high. AODV and DSR have the best pefomances in tems of the delivey packet faction. DSR uses the cash memoy fo the oute discovey. This facto deceases the delay pefomances which may be due to the excessive use of cash memoy and the inability to delete the old outes. Nonetheless, it seems that the use of cash memoy enables DSR to maintain a weak oveload. To conclude, the simulation findings ae to be taken as a stong efeence on the thee outing potocols behaviou; howeve, it shouldn t be consideed as an exact epesentation of its behaviou and eal envionment because of seveal simulation constaints such as: the dimension of movement field of mobile nodes, the taffic type and the simulation timing. In the fothcoming studies, we will look at the outing potocols behavious in the multi-channel envionment and/o multi-netwoks in ode to detemine the key paametes that have an impact on the potocols choice. Besides, we will ty to develop new potocols o alte the existing ones. REFERENCES Amjad, K. and A.J. Stocke, 2010. Impact of slow and fast channel fading and mobility on the pefomance of AODV in ad-hoc netwoks. Poceedings of the Loughboough Antennas and Popagation Confeence (LAPC), Nov. 8-9, IEEE Xploe Pess, Loughboough, pp: 509-512. DOI: 10.1109/LAPC.2010.5666192 J. Compute Sci., 8 (5): 752-760, 2012 760 Alfawae, Z.M. and G.W. Hua, 2007. Utilization of AODV in wieless ad hoc netwoks. J. Comput. Sci., 3: 218-222. DOI: 10.3844/jcssp.2007.218.222 Cavalho, M.M. and J.J. Gacia-Luna-Aceves, 2004. Modeling single-hop wieless netwoks unde Rician fading channels. Poceedings of the IEEE Wieless Communications and Netwoking Confeence, Ma. 21-25, IEEE Xploe Pess, pp: 219-224. DOI: 10.1109/WCNC.2004.1311546 Eltahi, I.K., 2007. The impact of diffeent adio popagation models fo Mobile Ad hoc NETwoks (MANET) in uban aea envionment. Poceedings of The 2nd Intenational Confeence on Wieless Boadband and Ulta Wideband Communications, Aug. 27-30, IEEE Xploe Pess, Sydney, NSW, pp: 30-30. DOI: 10.1109/AUSWIRELESS.2007.80 Fall, K., 2001. The ns manual. National Institute of Infomatics. Feeney, L.M., 1999. A taxonomy fo outing potocols in mobile ad hoc netwoks. SICS Repot. Geetha, J and G. Gopinath, 2008. Pefomance Compaison of Two On-demand Routing Potocols fo ad-hoc netwoks based on andom way point mobility model. Am. J. Applied Sci., 5: 659-664. DOI: 10.3844/ajassp.2008.659.664 Gupta, S.K. and R.K. Saket, 2011. Pefomance metic compaison of AODV and DSDV outing potocols in manets using ns-2. IJRRAS, 7: 339-350. www.apapess.com/volumes/vol7issue3/ijrras _7_3_15.pdf Kaya, A.O., L.J. Geenstein and W. Tappe, 2009. Chaacteizing indoo wieless channels via ay tacing combined with stochastic modeling. IEEE Tans. Wieless Commun., 8: 4165-4175. DOI: 10.1109/TWC.2009.080785 Khati, P. and M. Rajput, 2010. Pefomance study of ad-hoc eactive outing potocols. J. Comput. Sci., 6: 1159-1163. DOI: 10.3844/jcssp.2010.1159.1163 Ramesh, V., P. Subbaiah, N.K. Rao and M.J. Raju, 2010. Pefomance compaison and analysis of DSDV and AODV fo MANET. Int. J. Comput. Sci. Eng., 2: 183-188. Singh, P.K. and L. Kapang, 2011. Compaative study of adio popagation and mobility models in vehicula adhoc netwok. Int. J. Comput. Appl., 16: 37-42. DOI: 10.5120/2031-2600 Zang, L.F. and G.B. Rowe, 2007. Impoved modelling fo mobile Ad-hoc netwoks. Elect. Lett., 43: 1156-1156. DOI: 10.1049/el:20071530