The Impact of Random Waypoint Mobility on Infrastructure Wireless Networks

Transcription

1 The Imact of Random Wayoint Mobility on Infrastructure Wireless Networks Dennis Pong and Tim Moors School of Electrical Engineering and Telecommunications The University of New South Wales, NSW 5 Australia dennis@student.unsw.edu.au and t.moors@unsw.edu.au Abstract In this aer we reort the imact of the Random Wayoint model on infrastructure wireless networks that utilise multi-rate scheme. The Wayoint model causes a higher concentration of nodes near the centre of the mobility area. As a consequence of this, we show that a wireless network could aear to achieve higher caacity, and that base stations near the centre of the mobility area will exerience higher frequencies of transmission rate change. These aberrations could affect simulation results that should be interreted with care. 1. Introduction Mobility models lay an imortant role in the evaluation of wireless network rotocols. The connectivity and caacity of a network often deends on the nodes mobility behaviour. The Random Wayoint model is one of the widely used models for ad-hoc and infrastructure wireless simulations and has been imlemented in many network simulators including ns-. The Wayoint model is used in simulation studies for infrastructure wireless networks such as the IEEE.11, IEEE.16 and cellular networks [1, ]. However, revious research [3, 6] shows this model suffers from the border effect which causes nodes to have a higher robability of being located near the centre of the mobility region. This aer highlights the two erformance asects affected by this uneven node distribution in an infrastructure network - the caacity (total throughut of a cell of with base station) and the transmission rate change overhead (the number of rate fallbacks and ugrades er unit time). The imact of the Wayoint model on network erformance in relation to toology settings and in articular, the size of the mobility area and the location of the base station will be investigated. In the first art of the aer, we demonstrate the aarent increase in cell caacity with mobile nodes which moves according to the Wayoint model in comarison to stationary nodes which are uniformly distributed. In the second art of this aer, we illustrate how rate change overhead varies deending on the base station s location Random Wayoint Mobility In this model, the starting and ending ositions of a node movement, called wayoints, are uniformly distributed in a secified domain. The mobility is characterised by a node moving from one wayoint to another in a straight line with constant velocity. The analyses in this aer assumed a nonsto motion such that the ause time at each wayoint is zero. We consider a two dimensional circulaobility domain which defines the region of node movements. Within this domain, the area encomassing a base station is idenfied as the coverage area of radius r c, determined by the maximum transmission range of the base station. The size of the mobility area is reresented by radius such that >r c. The location of the coverage area is denoted by d, which is the distance between the centres of the mobility and coverage areas. Mobility area Mobility centre d a 4 a 3 a base station Coverage area r = a c 1 Figure 1. Concetual model of a multi-rate wireless infrastructure network.. Transmission Rate Distribution The rimary focus of this study is the long term signal change caused by satial movements of the nodes. The dis-

2 tance between the base station and the mobile node is often the main determinant of the signal strength at the receiver and hence the adoted transmission rate. If a node selects the best transmission rate according to its distance from the base station, the region in which a articular rate is used can be reresented by a series of annuli around the base station (figure 1). This abstract model is similar to the omnidirectional antenna model imlemented in the ns- simulator. This model allows the analysis of how the transmission rates used by the nodes are distributed. We highlight the following findings from this research which are discussed in more details in [4]: ffl The size of the mobility area ( ) relative to the coverage area (r c ) determines the transmission rate distribution. For ß r c, the transmission rate distributions are different for nodes moving in Wayoint model and nodes distributed uniformly in the coverage area. Whereas for > 3r c, the rate distributions aroach the same value for both cases. ffl The location of the coverage area (d), as determined by the base station s location, has minimal effect on the transmission rate distribution, even when the coverage area is close to the boundary of the mobility area. 3. IEEE.11a Wireless LAN Caacity To understand the extent of how the above findings would affect the caacity of a wireless network, the analysis uses the IEEE.11a Physical layer (PHY) and the Distributed Co-ordination Function (DCF) in the MAC layer. The standard rovides transmission modes (modes 1, 3, 5 are mandatory) for different levels of robustness and transmission ranges. The tyical transmission ranges of a standard.11a equiment [7] are used (table 1). The number of transmission modes are reduced from to 4, by relabelling modes 1, 3, 5, 7 to i = 1,, 3, 4, in order to simlify the analysis. Mode i Rate (Mbs) Range (a i, in metres) Table 1. Tyical transmission range of.11a with omni-directional antenna in an outdoor environment [7]. The caacity analysis is based on a slotted model under saturation condition roosed by Bianchi []. For each time slot, the transmission robability (fi) is a function of the collision robability for a transmitted frame (), the minimum contention window size (W ), the number of nodes in contention (n) and the maximum backoff stage (s). (1 ) fi = (1 )(W +1)+W (1 () s ) Throughut = (1) =1 (1 fi ) n 1 () P sp te[frame] (1 P t)tidle +P tp se[t s]+pt(1 P s)e[tc] (3) P t = P(at least one transmission in a slot) = 1 (1 fi ) n (4) P s = P(successful transmission in a transmitted slot) nfi (1 fi )n 1 = (5) P t The frame size is assumed to be of constant 15 bytes so that E[frame] = 15. Using the basic access scheme (without RTS/CTS), the duration values of an idle slot T idle, a successful transmission T s (i) and a collided transmission T c (i) for transmission mode i are calculated as follows. T idle = 9μs T s (i) = (T reamble + T sig )+d 16+6+(E[frame]+) N e DBPS(i) T sig + SIFS + d N DBP S;basic (i) sig + DIFS T c (i) = (T reamble + T sig )+d 16+6+(E[frame]+) N DBP S(i) et sig +DIFS T reamble, T sig, N DBPS, SIFS and DIFS are.11a PHY related arameters. Their values can be found in the IEEE.11a standard [9]. The exected successful and collision durations are: E[T s ] = E[T c ] = i=1 P (AijA)T s (i) (6) i1=1 i=1 P (Ai1 ja)p (A i ja) max(t c (i 1 );T c (i )) (7) P (AijA) is the robability of a node transmitting with mode i given it is located inside the coverage area A. Readers can refer to the aendix for the derivation of P (AijA). Several aroximations are used to make the analysis tractable. Firstly, the use of EIFS after an erroneous frame is not considered. Secondly, the equation of collision duration E[T c ] only considers collisions involving two nodes. The robabilities of collision involving three or more nodes are much lower and its imact on E[T c ] is negligible (figure ).

3 nodes nodes 3 nodes 4 nodes nodes nodes 3 nodes nodes Probability P(N c ) nodes 4 nodes RTS/CTS No RTS/CTS 1 nodes 4 nodes 1 nodes nodes.5 3 nodes 4 nodes Number of frames colliding in a slot (N c ) Ratio of mobility area radius to coverage area radius (r /r ) m c Figure. The robabilities involving three oore nodes in a collision is under 5% which has negligible effect on collision duration. Figure 3. A decrease in mobility area changes node distribution leading to an increase in network throughut. 16 Wayoint mobility Uniformly distributed stationary nodes Numerical Results The results illustrate how sensitive the WLAN caacity is to the network toology settings denoted by ;r c and d. The same transmission ranges (a 1 ;:::;a M from table 1) are used throughout the analysis. We first locate the base station (or Access Point) at the centre of the mobility area (d =) and vary the mobility area s radius ( ). The base station is then laced at various distances (d) from the centre of the mobility area to study how the caacity is affected. Note that fewer nodes may fall inside the coverage as mobility area increases. To allow a fair comarison, we assume the number of nodes (n) in a coverage area remains constant. Using equations (1) - (7), the caacity of a coverage area is calculated. It is shown in figure 3 that the caacity can increase by u to 45% as the mobility area aroaches the size of the coverage area. This henomenon is due to the higher robability of nodes being located near the centre of the mobility area and thus higher roortion of nodes selecting the high transmission rates. We observe that the caacity increase is significant only when ß r c. We confirmed the numerical results with simulations in ns- for = r c =9m, as shown in figure 4. Figure 5 shows the network caacity as d varies from to ( -r c ). Due to circular symmetry, it is sufficient to consider one-dimensional changes with d. For various values of, the caacity changes are small (by less than %). There is a noticeable increase in caacity as the coverage area moves towards the border of the mobility region. However, the magnitude of increase remains small Time (seconds) Figure 4. Simulation results from ns- confirmed with numerical results showing a higher WLAN caacity for nodes moving in Wayoint mobility comared to uniformly distributed stationary nodes, with = rc RTS/CTS No RTS/CTS = 5m r = m m = 15m r = 1m m = 5m = m = 15m = 1m Distance between centres of coverage and mobility areas (metres) Figure 5. Total throughut with 3 nodes as d varies. The location of the coverage area has minimal effect on caacity as mobility area remains fixed.

4 4. Transmission Rate Change with Wayoint Mobility In this section we investigate the frequency of transmission rate change for communications between the base station and mobile nodes. Changes in transmission rates often incur further imlications on scheduling scheme, admission control and resource rovisioning in roviding the required quality of service. We are interested in the frequency of rate change in terms of and d. A higher switching rate introduces higher overheads for traffic scheduling and affects the ability of a node to maintain stable service quality. To aroximate the overhead of rate change under the same simlified concetual model, we utilise the mathematical model, develoed by Hyytiä et al. [1], which was originally roosed for calculating the handover rate for a cellular network. We modify the model for the multi-rate scenario by allowing the use of arbitrary values for transmission range and mobility area (i.e. a i and ). We assume a node, based on the distance from the sender/receiver, will switch to a lower (higher) bit rate whenever it moves out of (into) the range of the best available transmission mode. Adated from [1], the number of rate changes er second for a node with Wayoint motion is given by: fl = i=1 Z ß Z ß ( 1 a i (rm C x )sinffi v r m x cos (ffi + ff fi) dffdffi) () Z C v = ßE[ 1 rm Z ß v ] r(rm r ) r cos ffidffidr x = d +drcosff + r ; fi = tan 1 rsinff d + rcosff E[ v 1 ] is the exected value of the inverse velocity v 1, a i is the range of transmission mode i. The summation in eqn () sums u the rate change for each transmission rate. An observation is that fl is roortional to the mean node seed. Therefore the traffic scheduler will exerience higher number of rate changes with more mobile users. To verify the theoretical results obtained, simulations are erformed with the node seed drawn from a random distribution in the range (,1)ms 1. The analysis focuses on one node in a coverage area. However, it can easily be scaled to more nodes by multilying fl in eqn () by the number of nodes in the mobility area. Rate changes foultile coverage areas can be calculated by the summation of fl for each coverage area. 5 wayoints are simulated for each scenario Results Figure 6 shows the situation when d varies for a mobility area of 19m and a coverage area of 9m. A higher rate change overhead is exerienced by the base station if it is located near the centre of the mobility area (d ß ). There may also be a higher frequency of failed transmissions with adatation schemes such as Automatic Rate Fallback, which relies on the absence of acknowledgements to signal a fallback in transmission rate. The higher scheduling overheads and failed transmissions will translate to a lower caacity for base stations near the centre of the mobility area. We observe in figure 7 that the number of rate changes increases momentarily and then follow a decreasing trend as mobility area increases from 9m to 19m. The temorary increase is due to the fact that nodes are not allowed to go outside the coverage area when = r c.as increases, nodes crossing from coverage area to no coverage (or vice versa) add to the number of rate changes. As continues to increase, more nodes are out of the coverage area and fewer rate changes are recorded during this time. Mean number of rate changes er second Simulation Theoretical Distance from centre of mobility (d) in metres Figure 6. The average number of rate changes decreases as the coverage area moves towards the border of the mobility area. ( = 19m, r c = 9m). Mean number of rate changes er second Ratio of mobility to coverage area radius ( /r c ) Theoretical Simulation Figure 7. The number of rate change eaked at =rc ß 1:5 and decreases as increases.

5 Probability distribution = 9m = 49m = 69m = 9m = 19m = 19m where f (r) is the robability density function for the Wayoint model node distribution [5]. a i : a 1 ;:::;a M are radii of the concentric circles around a base station determined by the maximum range of each transmission mode i. d is the distance between the centres of mobility and coverage area. is the radius of the mobility area Number of rate changes er wayoint movement Figure. Probability distribution of rate changes er wayoint movement. For >rc, the robability of high rate change eovement is significantly higher than the case for = r c. 5. Conclusion This aer aims to rovide better understanding of the fundamental roerties of the Wayoint model when alied to a multi-rate infrastructure wireless network. The non-uniform node distribution, caused by the border effect, can roduce unwanted artifacts on caacity and transmission rate changes. It is imortant for readers to be aware of these effects when conducting simulations with the Wayoint model. 6. Aendix The conditional robability of a node located in annulus Ai, given it is inside the coverage area A is derived as follows: P (AijA) = >< >: P (A i) P (A i+1) P (A) P (A i) P (A) : i =1;:::;M 1 : i = M where P (A) = P (A 1 ). P (A i ) is the robability of a node in a circular area A i formed by the transmission range of mode i. d<a i : P (A i ) = Z Z r rf(r) dr d 1 r1 = ß, r = dcos + a i d sin 1 = ß, r 1 = (9) Acknowledgement Dennis Pong and this work are suorted by SingTel Otus Ltd. and the Australian Research Council. Tim Moors is artially suorted by the National ICT Australia. References [1] S.T. Sheu, J. Chen, H.W. Tseng, H.T. Chiang, A Safe Multile Access-Rates Transmission (SMART) Scheme for IEEE.11 Wireless Networks, Proc. Int l Conf. on Advanced Information Networking and Alications 3, [] D.A. Joseh, B.S. Manoj, C.S.R. Murthy, Interoerability of Wi-Fi Hotsots and Cellular Networks, The nd ACM Int l Worksho on Wireless Mobile As. and Services on WLAN Hotsots 4, [3] C. Bettstetter, H. Hartenstein, X. Pérez-Costa, Stochastic Proerties of the Random Wayoint Mobility Model, Wireless Networks: Secial Issue on Modeling and Analysis of Mobile Networks, Vol.1, Setember 4, [4] D. Pong, T. Moors, The Imact of Mobility Models on Wireless Network Performance, Technical Reort, The University of New South Wales, February 5. (htt://uluru.ee.unsw.edu.au/ dennis/ublications/) [5] C. Bettstetter, C. Wagner, The Satial Node Distribution of the Random Wayoint Mobility Model, Proc. German Worksho on Mobile Ad Hoc Networks (WMAN), [6] G. Resta, P. Santi, An Analysis of the Node Satial Distribution of the Random Wayoint Mobility Model for Ad Hoc Networks, Proc. nd ACM Int l Worksho on Princiles of Mobile Comuting, [7] Cisco Aironet 13AG Series.11a/b/g Access Point Data Sheet, Cisco Systems 4. [] G. Bianchi, Performance Analysis of the IEEE.11 Distributed Coordination Function, IEEE JSAC, Vol.1, No.3, Mar., [9] IEEE Std.11a-1999: High-seed Physical Layer in the 5 GHz Band. [1] E. Hyytiä, J. Virtamo, Random Wayoint Mobility Model in Cellular Networks. (htt:// d a i : 1 ai = sin d, r = d cos + a i d sin 1 ai 1 = sin d, r 1 = d cos a i d sin f (r) = r 4 m ß r + r m ß