Number of Paths and Neighbours Effect on Multipath Routing in Mobile Ad Hoc Networks

Transcription

1 Numbe of Paths and Neighbous Effect on Multipath Routing in Mobile Ad Hoc Netwoks Oday Jeew School of Infomation Systems and Accounting Univesity of Canbea Canbea ACT 2617, Austalia Masoud Mohammadian School of Infomation Systems and Accounting Univesity of Canbea Canbea ACT 2617, Austalia Kim Blackmoe The Austalian National Univesity Canbea ACT 0200, Austalia In this pape the numbe of paths in a multipath outing potocol and distibution of neighbou nodes in the discoveed outes ae studied fo netwoks with fequent topology changes. Specifically, we conside how the placement of neighbou nodes, which ae used by the souce node to each a destination in a multipath outing potocol, affects total netwok powe consumption. We develop an analytical model, veified by simulation, which shows that, while the netwok pefomance is affected by souce node speed and oute length, it also depends on the geometic aangement of neighbou nodes aound the souce node. The esults eveal that total netwok powe consumption is minimized when the moving souce node has six well distibuted neighbou nodes, and one path to the destination via each neighbou node. 1. INTRODUCTION In mobile ad hoc netwoks, nodes move feely in abitay diections and speeds that lead to fequent links failue and new outing paths need to be discoveed. The cached outes become outdated, and hence invalid, and finding altenative outes consumes netwok esouces. Multipath outing (Radi et al. 2012; Vaidya et al. 2008) appeas to be a pomising technique fo ad hoc outing potocols to solve this poblem. Howeve, thee has not been geneal analysis of the optimal utilization of multipath outing. Fo instance, the netwok powe consumption may educe if the souce moving node obtains many paths to each destination by educing the numbe of oute discovey, howeve, that inceases the numbe of oute eplies equied to establish the outes which inceases the netwok powe consumption. Theefoe, the numbe of paths is a significate facto that effect netwok pefomance and equied to be caeful conside. Most of the poposed multipath outing potocols allow the destination node to select the paths based on the degee of disjointedness among paths found, howeve the necessity of this assumption is debatable (Rookhosh et al. 2008; Zafa et al. 2007) and does not conside the distibution of neighbou nodes aound the souce node. Fo instance, if a moving souce node has multiple paths to a destination via neighbous located vey close to each othe, the links with these neighbous disconnected quickly when the souce node moves in an opposite diection to these neighbous and hence the souce loses the benefit of having altenative paths to its destination. An on-demand multipath outing scheme is pesented by Liu and Liu as a multipath extension of Dynamic Souce Routing (DSR) (Liu and Liu 2010). They poposed the destination node selects disjoint paths with minimum end to end delay accoding to the accumulated delay calculated by the intemedin nodes. Oma et. at. (Oma et al. 2011) consideed the esidual enegy of the nodes in the selection of paths. They poposed on-demand multipath potocol that the souce node selects disjoint paths with the maximum esidual enegy. Howeve, they did not conside the neighbou nodes and the numbe of paths. Tsiigos and Haas (Tsiigos and Haas 2004a) and (Tsiigos and Haas 2004b) consideed load balancing by distibuting data load ove multiple paths. c The Authos. Published by BCS Leaning and Development Ltd. 1 Poceedings of the 2 nd BCS Intenational IT Confeence 2014

2 Numbe of Paths and Neighbous Effect on Multipath Routing in Mobile Ad Hoc Netwoks Jeew Blackmoe It was found that the pobability of successful communication of packets inceases with the numbe of used paths. Howeve, the analysis does not conside the powe consumption induced by acquiing multiple paths. Pham and Peeau (Pham and Peeau 2003) compaed the ovehead of eactive multipath outing with single path outing when all nodes in the netwok ae mobile. They showed that the ovehead inceases significantly when the numbe of multiple paths exceeds thee. Howeve, this esult did not conside the aangement of neighbou nodes in the discoveed outes. The main contibutions of this pape ae the following: (i) We conside a multipath outing scheme, whee the destination stoes all the copies of outes which aived, in ode to detemine which equests to espond to based on the distibution of the neighbous of the souce node. (ii) We exploe how the numbe and spead of neighbou nodes used by the souce node to each the destination in a multipath outing potocol affects the total netwok powe consumption. (iii) poposing an analytical model to calculate the netwok powe consumption when the souce node moves in abitay diections and speeds. We assume each oute stats with a diffeent neighbou node that well distibuted aound the souce node, as then a link failue with a neighbou in one oute does not effect the othes. Diffeent citeia ae suggested to detemine the numbe of altenative outes used by the potocol (Nasipui et al. 2001). We will late show that the best esults ae achieved with about six outes. The emainde of this pape is oganized as follows. In Section 2 we set up the mathematical famewok fo powe consumption. In Section 3 we intoduce the geomety of the souce node and its neighbous. In Section 4 we develop expessions fo expected powe consumption fo a multipath outing potocol. In Section 5 we pesent a compaison of theoetical and simulation esults, with conclusions in Section TOTAL POWER CONSUMPTION We will efe to total powe consumption as the powe consumed by the netwok nodes in ode fo the souce node to obtain single/multiple outes, in addition to the powe equied to fowad datapackets to a destination. In this eseach we ae inteested in minimizing total powe consumption by selecting the numbe of multipath outes needed to send data fom souce to destination. Accodingly, we assume that all the nodes consume the same amount of powe fo sending a data-packet, P d, and outing packets (oute equest, oute eply) ae tansmitted at default powe, P. In multipath outing the souce node obtains multiple outes to the destination using a single oute discovey pocess. The souce node, n s, selects a valid oute (of length (h d + 1)) fom its cache, then (h d +1)P d is the powe consumed by sending a datapacket to n d. If all the outes to n d ae expied, a new oute discovey pocess must by caied out. We assume that the oute discovey pocess eveals a path though each of the K neighbous, and that the numbe of hops fom neighbou i to n d is h i. The powe consumed fo flooding the oute equest is (n 1)P, whee n is the total numbe of nodes in the netwok, plus the oute eplies along each of the K paths. Let t a be the time of aival of a new packet destined fo n d, and T be the oute expiy time fo the lagest suviving oute. The total powe consumed is given by (h d + 1)P d t a < T PC = (n 1)P + Σ K i=1 (h i + 1)P (1) +(h d + 1)P d t a > T In ode to detemine the time T when outes beak, we need to make easonable assumptions about the aangement and movement of the nodes. Fo simplification we assume that oute beakages only occu due to souce node movement. Ou chosen netwok topology is discussed in the following section. 3. TOPOLOGY SCENARIO We assume that each node is equipped with an omnidiectional antenna and that signal attenuation is due only to path loss elated to distance tansmitted. We assume that the tansmission anges of all nodes ae identical and equal to. We assume that the velocities of the neighbou nodes ae slow enough to be consideed stationay and that n s moves with a constant speed, v, in a andom diection, θ s. The scenaio could also be extended such that the speeds of the neighbouing nodes ae combined with the speed of n s, and v is the elative speed. This scenaio fits well with the andom waypoint mobility model. All node-to-node communications ae assumed to be bi-diectional. We assume that the souce node has a set of well distibuted neighbous. This can be achieved in a dense netwok using, fo example, topology contol, whee a set of neighbou nodes is selected by dividing a disk cented at the souce node into a numbe of cones by lines. The angle of the maximum cone is no moe than α and one neighbou node is selected fo evey cone (Wu and Dai 2006; Podui et al. 2009). 2

3 Numbe of Paths and Neighbous Effect on Multipath Routing in Mobile Ad Hoc Netwoks Jeew Blackmoe /(v sin(π/3)) is achieved when d o,i = / tan(π/3). Then the PDF and CDF of the link esidual time is given by 2v 2 i sin 2 (π/k) f Ri ( i ) = (5) 2 v 2 i 2 sin2 (π/k) F Ri ( i ) = v 2 i 2 sin2 (π/k) (6) Figue 1: An example of fou neighbou nodes at equal angles and vaying distances spead aound the souce node, n s. n 1 and n 2 ae adjacent neighbous Link Residual Time The time fom when n s moves fom its initial position to the point whee the link with n i beaks is called the link esidual time, R i. The link esidual time is shotest if the souce node moves exactly between two neighbous. We assume this wost case scenaio as illustated in Fig 1. To detemine when the link between the souce node and the neaest neighbou beaks, we let the angle between n s and its neighbous be θ s θ i = θ s θ i+1 = π/k, whee θ s is the diection of movement of n s, and θ i and θ i+1 ae angles of adjacent neighbou nodes. The distance that n s has to tavel in diection θ s, befoe the link with its adjacent neighbous beaks is given by d i = d o,i cos(θ s θ i ) + 2 d 2 o,i sin2 (θ s θ i ) (2) If n s moves distance d i at velocity v then, R i = d i /v. Assume d o,i U[0, ), then the PDF and CDF of the link esidual time fo diffeent values of K ae as follows: Two Neighbous The link esidual time, is equal to /v and 0 espectively when d o,i is at its limiting values 0,. The PDF and CDF of the link esidual time is given by i v 2 f Ri ( i ) = (3) 2 i 2v2 2 i 2 F Ri ( i ) = 1 v2 (4) Thee Neighbous The link esidual time, is equal to /v fo d o,i equal to both 0 and. The maximum link esidual time R i = Fou o Moe Neighbous The link esidual time, is equal to /v fo d o,i = 0. The maximum link esidual time R i = 2 cos(π/k)/v is achieved when d o,i =. The PDF and CDF of the link esidual time is given by f Ri ( i ) = 1 v v 2 i sin 2 (π/k) cos(π/k) + 2 v 2 i 2 sin2 (π/k) (7) F Ri ( i ) = 1 ( ) v i cos(π/k) 2 v 2 i 2 sin2 (π/k) (8) 3.2. Packet Aival Time Packet aival times, t a, ae geneally modelled as having an exponential distibution, with paamete λ a appopiate to the given netwok. We use this model hee. The PDF and CDF of aival times is given by f a (t) = λ a e λ at F a (t) = 1 e λ at (9) (10) In this section we have pesented a statistical model of the topology scenaio. We will use this model to develop an analytical model of the expected powe consumption. 4. EXPECTED POWER CONSUMPTION We conside the expected powe consumed with the occuence of data-packets equests and new oute equests. The expected value of the powe consumption is equal to the cost of an individual data-packet equest, multiplied by the pobability that thee is an unexpied oute in the cache, in addition to the cost of an individual oute discovey pocess, multiplied by the pobability that the oute is necessay. The pobability of oute discovey is detemined by the topology scenaio and the caching stategy. Assume the souce node n s and destination n d ae initially sepaated by distance L d. The path length 3

4 Numbe of Paths and Neighbous Effect on Multipath Routing in Mobile Ad Hoc Netwoks Jeew Blackmoe is longest if the neighbou node that is selected to fowad data is located in the opposite diection to the destination, thus θ d θ i = π, as illustated in Fig. 2. Assume d o,i U[0, ), and similaly fo all hop lengths in each path then the expected length of each hop is 0.5, then the expected distance between the sending neighbou node and destination is L d + 0.5, and the expected numbe of hops fom the neighbou to the destination is h d = L d / Powe Consumption (watt) Powe Consumption of K Multipath, h d = 8 v/ = 0.12 v/ = 0.08 v/ = Paths (neighbous), K Figue 3: Netwok powe consumption as it vaies with souce node velocity, fom (13). Simulation esults ae depicted by makes while theoetical esults ae depicted by lines. and the values of R i,min and R i,max depend on the numbe of neighbou nodes, K. Thee is no closed fom solution to (13), so it must be calculated numeically. Figue 2: An example of a wost-case path length scenaio illustates the distance elationship between moving souce node, n s, active neighbou nodes, n 1, n 2, n 3 and n 4, and destination node, n d. The PDF of the maximum link esidual time, R max, of the two closest neighbous is detemined by finding the CDF fist, as follows F Rmax (t) = P {R max < t} = P {(R i1 < t) (R i2 < t)} = F 2 R i (t) (11) Taking the deivative of (11) it can be seen that the PDF of the maximum R i value is given by f Rmax (t) = 2F Ri (t)f Ri (t) (12) Combining (1) and (12), and using the PDF and CDF obtained in Section 3.1, we can detemine an expession fo the expected powe consumption, whee E{P C K paths} = Ri,max R i,min E{P C R 1, R 2 }f Rmax 2 (t) dt Ri,max = 2(h d + 1)P d (1 e λat )F Ri (t)f Ri (t)dt R i,min + 2((n 1)P + (h d + 1)P + (h d + 1)P d ) Ri,max R i,min e λ at F Ri (t)f Ri (t)dt (13) 5. RESULTS In this section we pesent and discuss esults of theoetical calculations and Monte-Calo simulations, conducted in Matlab, fo expected total powe consumption, discussed above. We assume a netwok with n = 400 nodes, each node in the netwok has a default powe level, P = 280mW, fo the tansmission ange, = 250m. The node uses P d = 140mW fo fowading of datapacket to the destination. The souce node sends data-packets to the destination at aival time t a seconds while it moves in a andom diection. It is assumed that the souce node moves at low, medium and high speed with 10, 20 and 30m/s, espectively. Fo each instance of the simulation, the souce node diection θ s U[0, 2π), and the neighbou node location, d o,i U[0, ) and θ i, ae geneated accoding to the scenaio in Fig. 1. The souce node geneates packets accoding to an exponential distibution with paamete λ a = 0.1. The packet aival time is compaed to the link esidual times, and the total powe consumption is counted. The expected powe consumption fo fixed path length h d is shown in Fig. 3. The esults show that the numbe of paths, K, has a significant effect on powe consumption. At low numbes of paths the powe-consumption cuves decease with K, since an incease in the numbe of paths deceases the numbe of oute discoveies by poviding altenative outes to the destination. Howeve, afte a cetain numbe of paths, the eduction in powe 4

5 Numbe of Paths and Neighbous Effect on Multipath Routing in Mobile Ad Hoc Netwoks Jeew Blackmoe Powe Consumption (Watt) Powe Consumption of K Multipath, v/ = Paths (neighbous), K h d = 20 h d = 10 h d = 5 Figue 4: Netwok powe consumption as it vaies with h d, fom (13). Simulation esults ae depicted by makes while theoetical esults ae depicted by lines. consumption due to poviding altenative paths is outweighed by the powe consumed by oute eplies fo each discoveed path. Theefoe, inceases to the numbe of paths past that point inceases powe consumption. We see fom the esults that the minimum netwok powe consumption can be achieved when the souce node has six multipath outes via neighbou nodes that ae equally angled aound the souce node. Fig. 4 shows the effect of the numbe of hops between the souce and destination on the netwok powe consumption at modeate speed of souce node. The esults show that powe consumption inceases with the numbe of hops, since that inceases the numbe of nodes that paticipate in communication between the souce and the destination. The esult also shows that selecting six paths via neighbou nodes equally spead aound the souce nodes minimizes the netwok powe consumption fo diffeent numbes of hops between the souce and the destination, unless the destination is close, in which case up to eight paths may be useful. 6. CONCLUSION In this pape the numbe of paths in a multipath outing potocol and the distibution of neighbou nodes in the discoveed outes ae studied when the souce node moves in abitay diections and speeds. We assume that the potocol identifies sepaate outes though all active neighbous of the souce node. An analytical model is developed and veified by simulation. The esults show that the total netwok powe consumption is dependent on the numbe of paths coesponding to the neighbous of the souce node. If the numbe of paths is too low, the powe consumption is inceased because of inceased need fo oute discovey, but if the numbe of paths is high, the netwok powe consumption is inceased because of an inceased numbe of oute eply packets. This becomes moe ponounced with inceasing mobility and geate souce-destination sepaation. We show that, in most cases, the total netwok powe consumption is minimized when the moving souce node has six well distibuted neighbou nodes. REFERENCES Shun Liu and Jian Liu. Delay-awae multipath souce outing potocol to poviding QoS suppot fo wieless ad hoc netwoks. In Poc. of Communication Technology Confeence, IEEE, pages , Asis Nasipui, Robet Castaneda, and Sami R. Das. Pefomance of multipath outing fo on-demand potocols in mobile ad hoc netwoks. Mobile Netwoks and Applications, 6(4): , August Smail Oma, Mekkakia Zoulikha, and Benad Cousin. Enegy efficiency in ad hoc wieless netwoks with node-disjoint path outing. In Poc. of Systems, Signal Pocessing and thei Applications Confeence, IEEE, pages , Pete P. Pham and Sylvie Peeau. Pefomance analysis of eactive shotest path and multi-path outing mechanism with load balance. In Poc. of INFOCOM 2003 Confeence, IEEE, volume 1, pages , Sameea Podui, Sundeep Pattem, Bhaska Kishnamachai, and Gauav S. Sukhatme. Using local geomety fo tunable topology contol in senso netwoks. IEEE Tansactions on Mobile Computing, 8(2): , Febuay Majan Radi, Behnam Dezfouli, Kamalulnizam Abu Baka, and Maley Lee. Multipath outing in wieless senso netwoks: Suvey and eseach challenges. Sensos, (12): , Fahimeh Rookhosh, Abolfazl Tooghi Haghighat, and Saeed Nickmanesh. Disjoint categoies in low delay and on-demand multipath dynamic souce outing adhoc netwoks. In Poc. of Distibuted Famewok and Applications Confeence, pages , Aistotelis Tsiigos and Zygmunt J. Haas. Analysis of multipath outing-pat I: the effect on the packet delivey atio. IEEE Tansactions on Wieless Communications, 3(1): , Januay 2004a. Aistotelis Tsiigos and Zygmunt J. Haas. Analysis of multipath outing, pat 2: mitigation of the effects 5

6 Numbe of Paths and Neighbous Effect on Multipath Routing in Mobile Ad Hoc Netwoks Jeew Blackmoe of fequently changing netwok topologies. IEEE Tansactions on Wieless Communications, 3(2): , Mach 2004b. Binod Vaidya, Dong-You Choi, Jong-An Pak, and Seung Jo Han. Multipath outing scheme fo wieless multihop netwok. In Poc. of ICCSA (2) Confeence, pages , Jie Wu and Fei Dai. Mobility-sensitive topology contol in mobile ad hoc netwoks. IEEE Tansactions on Paallel and Distibuted Systems, 17(6): , June Haseeb Zafa, David Hale, Ivan Andonovic, and Mahmood Ashaf. Patial-disjoint multipath outing fo wieless ad-hoc netwoks. In Poc. of Local Compute Netwoks (LCN 2007) Confeence, IEEE, pages ,