Ad Hoc Networks. Optimal physical carrier sense in wireless networks

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1 Ad Hoc Networks 9 (2) 6 27 Contents lsts avalable at ScenceDrect Ad Hoc Networks journal homepage: Optmal physcal carrer sense n wreless networks Kyung-Joon Park a, *,, Jhyuk Cho b, Jennfer C. Hou a,2, Yh-Chun Hu b, Hyuk Lm c,d a Department of Computer Scence, Unversty of Illnos, 2 N. Goodwn Avenue, Urbana, IL 68, USA b Department of Electrcal and Computer Engneerng, Unversty of Illnos, 46 W. Green Street, Urbana, IL 68, USA c Department of Informaton and Communcatons, GIST, Republc of Korea d Department of Nanobo Materals and Electroncs, GIST, Republc of Korea artcle nfo abstract Artcle hstory: Receved 2 January 2 Receved n revsed form 23 March 2 Accepted 23 Aprl 2 Avalable onlne 28 Aprl 2 Keywords: Carrer Sense Multple Access Spatal reuse Hdden node problem Exposed node problem We nvestgate the problem of maxmzng Medum Access Control (MAC) throughput n Carrer Sense Multple Access (CSMA) wreless networks. By explctly ncorporatng the carrer sense threshold and the transmt power nto our analyss, we derve an analytcal relaton between MAC throughput and system parameters. In homogeneous networks, we derve the optmal carrer sense range at a gven node densty as a functon of the rato between the transmt power and the carrer sense threshold. The obtaned optmal carrer sense range s smaller than that for coverng the entre nterference range, whch s n sharp contrast to what has been consdered to be optmal n prevous studes. Only when the node densty goes to nfnty, the optmal carrer sense range converges to that for exactly coverng the nterference range, thereby elmnatng all the hdden nodes. For nonhomogeneous networks, any dstrbuted algorthm for tunng the carrer sense threshold, n whch each node tres to maxmze ts own throughput wthout coordnaton, may sgnfcantly degrade MAC throughput. In order to properly desgn a dstrbuted algorthm, each node not only consders ts own throughput, but also needs to take account of ts adverse mpact on others. Our analyss s verfed by smulaton studes under varous network scenaros. Ó 2 Elsever B.V. All rghts reserved.. Introducton * Correspondng author. Tel.: E-mal addresses: kjp@snu.ac.kr (K.-J. Park), jcho43@llnos.edu (J. Cho), yhchun@llnos.edu (Y.-C. Hu), hlm@gst.ac.kr (H. Lm). K.-J. Park was wth the Department of Computer Scence, Unversty of Illnos at Urbana-Champagn at the tme of ths work. He s now wth Seoul Natonal Unversty, Seoul, Korea. 2 J. C. Hou was wth the Department of Computer Scence, Unversty of Illnos at Urbana-Champagn at the tme of ths work. She s now deceased. Mult-hop wreless networks, e.g., wreless mesh networks, have emerged as a promsng, cost-effectve technology for next-generaton wreless networkng []. Ther man advantage s the capablty of buldng networks wthout a pre-nstalled nfrastructure. Instead of coordnatng the rado channel by a central entty, a dstrbuted access mechansm s deployed at each node to arbtrate access to the channel. Caused by ths convenence, most deployed mult-hop wreless networks are employng Carrer Sense Multple Access (CSMA). Here, our man focus s on CSMA wreless networks. A crtcal performance metrc n CSMA wreless networks s network capacty,.e., the average number of data bts that can be transported smultaneously n the network. Ths metrc heavly depends on the level of spatal reuse characterzed by carrer sense. For example, IEEE 82. Dstrbuted Coordnaton Functon (DCF) [2] has employed two types of carrer sense: mandatory physcal carrer sense that montors the sgnal strength of the channel, and optonal vrtual carrer sense that uses the Request-To-Send/Clear-To-Send (RTS/CTS) handshake to reserve the medum pror to transmsson. In ths paper, we manly focus on physcal carrer sense and wll dscuss the effect of RTS/CTS as an extenson. For physcal carrer sense, before each transmsson, a sender lstens to the channel and determnes whether or not the channel s /$ - see front matter Ó 2 Elsever B.V. All rghts reserved. do:.6/j.adhoc.2.4.6

2 K.-J. Park et al. / Ad Hoc Networks 9 (2) busy by comparng the receved sgnal strength wth the carrer sense threshold. If the sgnal strength s below the carrer sense threshold, the sender consders the channel to be dle and starts ts transmsson. Otherwse, the sender consders the channel to be busy and defers ts transmsson. Snce the receved sgnal strength s proportonal to the transmt power of the correspondng sender, both the carrer sense threshold and the transmt power are major control knobs for physcal carrer sense. There have been a number of studes that focus on the mpact of physcal carrer sense on network capacty. (We wll gve a detaled summary of exstng work n Secton 2.) Most research efforts [3 5], however, have concentrated ether on the relaton between physcal carrer sense and Shannon capacty,.e., the achevable channel rate under the addtve whte Gaussan nose channel model (nstead of Medum Access Control (MAC) throughput,.e., the average rate of successful message delvery n the MAC layer) or on the dervaton of a smple condton for elmnatng all the hdden nodes (wthout consderng suffcent detals of how physcal carrer sense operates) [6,7]. What has not been fully nvestgated s the analytcal relaton between physcal carrer sense and the MAC throughput. Hereafter, we nterchangeably use network MAC throughput (aggregate MAC throughput over every node) and network capacty to denote MAC-level throughput under the saturaton condton [8]. In ths paper, we are nterested n seekng solutons to the followng questons: What s the analytcal relaton between network capacty and system parameters such as the carrer sense threshold and the transmt power? Is elmnatng all the hdden nodes really optmal n terms of network capacty? If not, what s the optmal condton? As n the case of usng Shannon capacty [3 5] to characterze network capacty, can we stll quantfy network capacty as a functon of the rato of the carrer sense threshold to the transmt power? Furthermore, s there any advantage of deployng nonhomogeneous networks (where the system parameters can be adjusted ndependently by each node) over homogeneous networks (where system parameters are set to the same values for every node)? We am to answer the above questons n an analytcal framework. Specfcally, our contrbutons are as follows: By explctly ncorporatng the carrer sense threshold and the transmt power nto our analyss, we establsh an analytcal relaton between network capacty and the level of spatal reuse characterzed by physcal carrer sense. Although there have been consderable research efforts on modelng the performance of CSMA wreless networks [8 ], none of them have explctly ncorporated the carrer sense threshold and the transmt power n ther models. In the case of homogeneous networks, we show that network capacty depends on the rato of the transmt power to the carrer sense threshold. By usng the noton of the carrer sense range, we derve the optmal carrer sense range as an explct functon of system parameters such as node densty, channel access probablty, and duraton of each channel state. We dentfy that the optmal carrer sense range s smaller than the value for exactly coverng the entre nterference range of the recever, whch mples that the hdden nodes wll not be totally elmnated. Ths result s n sharp contrast to what has been consdered to be optmal n prevous studes. Only when the node densty goes to nfnty, the optmal carrer sense range converges to that for exactly coverng the entre nterference range, thereby elmnatng all the hdden nodes. Ths analyss quantfes the ntutve tradeoff between the hdden node problem and the exposed node problem. In the case of nonhomogeneous networks, the carrer sense threshold and the transmt power should be consdered ndependently n order to determne network capacty. The problem of maxmzng network capacty n a fully dstrbuted manner s shown to be a non-cooperatve game [2]. Any selfsh dstrbuted algorthm n whch every node tunes ts own parameters for maxmzng ts own throughput, wthout coordnaton wth other nodes, wll fal to maxmze network capacty and may result n a poor system performance. Consequently, each node needs to consder not only ts own throughput, but also needs to ntroduce a certan form of penalty as a prce for the adverse mpact on others. The remander of the paper s organzed as follows: In Secton 2, we gve a detaled summary of related work and hghlght the dfference between pror work and ours. In Secton 3, we ntroduce the propagaton and nterference models used n our analyss. Then, by focusng on physcal carrer sense, we characterze the MAC throughput. In Secton 4, we derve an analytcal relaton between network capacty and system parameters. Based on the relaton, we fnd the optmal carrer sense range, whch maxmzes network capacty. Then, we dscuss several related ssues such as the effect of RTS/CTS on network capacty and multple data rates. We present smulaton results n Secton 5, and conclude the paper n Secton 6 wth a lst of research avenues for future work. 2. Related work We categorze related work nto the followng three cases. 2.. Performance analyss of IEEE 82. DCF There have been consderable studes on the performance of IEEE 82. DCF both n sngle-cell scenaros [8 ] and mult-hop networks []. In[8], Banch modeled the behavor of the bnary back-off counter at one tagged node as a two-dmensonal Markov chan, and derved a fxed-pont model for IEEE 82. DCF. Calì et al. [9] derved a throughput bound by approxmatng IEEE 82. DCF wth a p-persstent model. Kumar et al. [] generalzed the fxed-pont analyss of Banch s model. Recently, Medepall and Tobag [] extended Banch s work, and provded an analytcal model that captures several mportant performance metrcs such as throughput, delay, and farness. In all of these prevous studes, the mpact of the carrer sense threshold and the transmt power has not been fully nvestgated.

3 8 K.-J. Park et al. / Ad Hoc Networks 9 (2) Studes on physcal carrer sense for mprovng the level of spatal reuse Recently, a number of studes have been carred out to study how physcal carrer sense affects spatal reuse [6,7]. Gven a predetermned transmsson rate, Zhu et al. [6] derved condtons for the carrer sense threshold n order to cover the entre nterference range. Zhu et al. also proposed n [7] a dynamc algorthm for adjustng the carrer sense threshold. There have been also a number of studes on the relaton between physcal carrer sense and Shannon capacty [3 5]. Yang and Vadya [4] are perhaps the frst to address the mpact of physcal carrer sense on Shannon capacty of wreless ad hoc networks whle takng nto account the MAC layer overhead. Zha and Fang [5] nvestgated the mpact of physcal carrer sense n mult-rate and mult-hop scenaros. Km et al. [3] showed that wth a schedulng-based MAC, spatal reuse only depends on the rato of the transmt power to the carrer sense threshold. In addton, an mplementaton-orented study was presented n [3]. Recently, Zhu et al. [4] derved an mplct relaton for obtanng the optmal carrer sense range n homogeneous networks. A more comprehensve study on optmzng CSMA networks has been performed n [5]. In addton, a non-cooperatve game-theoretc approach for control of the carrer sense threshold has been proposed n [6]. However, none of these studes have derved an explct functonal relaton for the optmal physcal carrer sense. Once we obtan a functonal relaton between the optmal carrer sense threshold and system parameters (node densty, channel access probablty, duraton of each channel state, etc.), we can explot ths relaton to further mprove the network performance Transmt power control The ssue of transmt power control has been extensvely studed n the context of topology mantenance [7 9], where the man objectve was to preserve network connectvty whle mtgatng MAC-level nterference and reducng power consumpton. The problem of how to control the carrer sense threshold n topologycontrolled wreless networks has been nvestgated n [2]. Use of transmt power control for maxmzng capacty has been consdered, for example, n [2], n whch Monks et al. proposed a power control protocol, called Power Controlled Multple Access (PCMA), where the recever advertses ts nterference margn that t can tolerate on an out-of-band channel and the transmtter selects ts power n order not to dsrupt any ongong transmssons. Recently, the problem of jont optmzaton of transmt power and carrer sense has been also proposed n [22]. 3. Network model In ths secton, we ntroduce the network model used n our analyss. 3.. Wreless channel model and related notons Consder a wreless network consstng of a set of N nodes, ndexed from to N, denoted by N. For a gven node 2 N, let rðþ 2N denote the correspondng recever of node. Let P denote the transmt power of node, g the antenna gan, and h the path loss exponent (whch typcally ranges between 2 and 4), then the receved power s denoted by P rðþ ¼ gp d h ;rðþ, where d,j denotes the dstance between node and node j. As a necessary condton for the recever r() to correctly decode the symbols, P r() should be larger than or equal to the receve threshold of r(), denoted by c r(),.e., P rðþ P c rðþ : ðþ By (), the transmsson range d T (,r()), whch s the maxmum of d,r() satsfyng (), can be obtaned as d T ð; rðþþ ¼ ðgp =c rðþ Þ h. In addton to (), the receved power P r() should be large enough so that the nterference from other nodes does not prevent the recever from correctly decodng the symbols. Ths condton can be usually expressed wth the sgnal to nose nterference rato (SINR) as follows: SINR ¼ P rðþ N rðþ þ P j gp jd h j;rðþ P b rðþ ; where N r() s the ambent nose and b r() s called the SINR threshold of the recever r(). Now the nterference set of recever r(), denoted by I r(), s defned as the set of nodes whose smultaneous transmsson wth node, taken one at a tme, wll cause collson at r(). Wth neglgble nose N r(), I r() can be expressed as n I rðþ ¼ jjp rðþ = gp j d h j;rðþ < b rðþ o ¼fjjd j;rðþ < d I ð; jþg; where d I ð; jþ :¼ ðp j b =P Þ h d;rðþ s termed as the nterference range. Wth () and the noton of I r(), we assume that a transmsson between node and the correspondng recever r() s successful f r() s nsde the transmsson range of and no node n I r() s smultaneously transmttng,.e., d ;rðþ < d T ð; rðþþ and d j;rðþ P d I ð; jþ; ð2þ for every node j that s smultaneously transmttng. Note that the condton (2) corresponds to the well-known protocol model [23]. Let x denote the carrer sense threshold of node. If the sensed sgnal level at node s larger (smaller) than x, the channel wll be consdered busy (dle) by node. For a gven node, let C denote the carrer sense set of node, whch s defned as n C ¼ jjgp j d h ;j P x o ¼fjjd ;j 6 d C ð; jþg; where d C ð; jþ :¼ ðgp j =x Þ h s the carrer sense range. Hence, node wll be slenced f any node n C s transmttng. In a smlar manner, let L denote the slence set of node, whch s defned as n o L ¼ jjgp d h ;j P x j ¼fjjd ;j 6 d L ð; jþg; ð4þ ð3þ

4 K.-J. Park et al. / Ad Hoc Networks 9 (2) where d L ð; jþ :¼ ðgp =x j Þ h s the slenced range. Thus, every node j 2 L wll be slenced when node transmts. Note that C = L only n a homogeneous network under a symmetrc topology, and C L n general. Fnally, H denote the set of hdden nodes of node. Then, we have H ¼ H [ H þ, where H ¼ I rðþ n C and H þ ¼ I rðþ n L, whch can be descrbed as follows: The transmsson attempt of node wll fal ether f there s any ongong transmsson n H, or f any nodes n H þ transmt durng the transmsson of node. Ths s the well-known hdden node problem. One may partally resolve the hdden node problem by expandng the slence set L. However, a large L may degrade network performance by ncurrng unnecessary deferrng of transmssons as follows: Let E := L ni r(). Then, whle node s transmttng, nodes n E wll be unnecessarly deferrng ther transmsson even though they do not nterfere wth node. Ths phenomenon s called the exposed node problem. Thus, how to balance these two problems s a crtcal ssue for mprovng the overall network performance. In the followng, we derve an analytcal relaton for maxmzng network capacty by balancng these two problems Characterzaton of CSMA MAC throughput We focus on the behavor of an ndvdual node and characterze ts per-node throughput. In order to derve the throughput of a gven node, we need to fnd an explct relaton among the followng three varables: the attempt probablty that node transmts n any vrtual slot, 3 the condtonal collson probablty of node gven that a transmsson attempt s made, and the vrtual slot tme of node Dervaton of attempt probablty The attempt probablty under the exponental back-off mechansm has been derved n [8]. Specfcally, the attempt probablty s that node transmts n a randomly chosen vrtual slot can be expressed as follows: 2ð 2q s ¼ Þ ð 2q ÞðCW m þ Þþq CW m ð ð2q Þ m Þ ; ð5þ where q s the condtonal collson probablty gven that a transmsson attempt s made, m ¼ log 2 wth CW m CW M CWm and CW M beng the mnmum and the maxmum contenton wndow szes, respectvely. Note that, f we assume an ndependent contenton wndow sze wth an average value of CW, s n (5) s further smplfed as s ¼ 2=ðCW þ Þ [8] Dervaton of vrtual slot tme The expressons for the condtonal collson probablty and the vrtual slot wll be dfferent from those n [8]. We frst derve the vrtual slot tme. Let v denote the expected vrtual slot tme. In order to characterze v, we need to model the channel behavor from the vewpont of node 3 We follow Banch s noton and defne a vrtual slot as the nterval between the occurrences of two specfc events. It may be much longer than the physcal slot sze r.. By consderng the channel status together wth the node actvtes, we have a total of four channel states seen by node. Successful transmsson by node : If node receves an ACK frame wthn an nterval of Short Interframe Space (SIFS) after the data frame s transmtted, t determnes that the transmsson s successful. Note that node cannot detect whether or not transmssons by other nodes are successful, because a frame s determned to be successfully receved f and only f the sender receves the correspondng ACK frame. Collson ncurred by node : If node does not receve an ACK wthn an nterval of SIFS after the data frame s transmtted, t determnes that a collson occurs. Idle channel: If the receved sgnal strength falls below the carrer sense threshold x, the channel s consdered to be dle. Busy channel: If the receved sgnal strength exceeds the carrer sense threshold x, the channel s consdered to be busy. Ths busy channel results from transmssons of other nodes. Note that we do not dstngush whether ths transmsson s successful or not. Let the average duraton of each state be denoted by t S, t C, t I, and t B. Then, t S = T H + T P + T ACK + SIFS + DIFS, where T H, T P, and T ACK are, respectvely, the tme requred to transmt the header, the payload, and the acknowledgement. In addton, DIFS stands for the DCF Interframe Space [2]. Smlarly, t C = T H + T P + SIFS + DIFS, t I = r, where r s the physcal slot tme, and t B s approxmated by t B =(t S + t c )/ 2. 4 Node makes a transmsson attempt wth probablty s, and each attempt s successful wth probablty q. Thus, the probablty of successful transmsson s s ( q ). Also, the probablty of collson s s q. The channel s dle when no node n C [ {} transmts. Thus, the probablty of dle channel s ð s Þ Q j2c ð s j Þ. Fnally, the channel s busy when node s n the back-off stage and at least one node n C transmts. Hence, the probablty of busy channel s ð s Þ Q j2c ð s j Þ. By gatherng everythng together, the vrtual slot tme v can be expressed as v ¼ s ð q Þt S þ s q t C þð s Þ Y ð s j Þt I j2c þð s Þ Y! ð s j Þ t B : j2c ð6þ Dervaton of condtonal collson probablty What s left to be derved s the condtonal collson probablty q. The transmsson of node wll result n collson f () at least one node n I r() transmts smultaneously at the begnnng of the transmsson of node, or () at least one node n H transmts before or durng the transmsson of node. Frst, let g denote the probablty of transmsson attempt of node. If we assume that g j, 4 Ths approxmaton does not ntroduce sgnfcant error n our analyss snce t S t c t I.

5 2 K.-J. Park et al. / Ad Hoc Networks 9 (2) 6 27 j s ndependent of transmsson attempt of node, then we have that the probablty of node fndng no ongong transmsson n H becomes Q j2h ð g j Þ. Now, n order to account for the hdden nodes n H þ, let the vulnerable perod, denoted by V, be defned as the tme nterval durng whch the transmsson between node and node r() wll fal f any node n H attempts to transmt. Then, V = T H + T P, where T H and T P are, respectvely, the tme requred to transmt the header and the payload. Hence, the expected number of transmsson attempt n duraton of V s V/v. Now, the condtonal collson probablty q can then be expressed as q ¼ Y ð g j Þ Y Y ð s j Þ ð s k Þv V k: ð7þ j2i rðþ j2h k2h þ In (7), from the defnton of s, we further have g s, whch mples that the hdden node effect from H þ domnates q over that from H. Hence, we have the followng approxmaton for q. q Y Y ð s j Þ ð s k Þv V k: ð8þ j2i rðþ k2h þ Dervaton of per-node throughput Let T denote the throughput of node. Then, T can be expressed as T ¼ Ls ð q Þ Ls Q j2i rðþ ð s j Þ Q k2h ð s ¼ þ k Þv V k ; ð9þ v v where L s the payload sze. Compared to the sngle-cell model n [8], the throughput model (9) s much more complcated n that physcal carrer sense s consdered through H þ and v s ncluded n the exponent. By a careful observaton of (9), we can dentfy a tradeoff between the level of spatal reuse and the hdden node problem as follows: as the carrer sense threshold/transmt power s ncreased/decreased to allow more spatal reuse, the vrtual slot tme v wll be decreased, whch wll ncrease T. Meanwhle, the hdden node problem becomes more severe, and the collson probablty q wll be ncreased, whch n turn wll decrease T. Consequently, there exsts a tradeoff between the level of spatal reuse and the hdden node problem. It s of crtcal mportance to quantfy ths tradeoff n order to fnd the optmal operatng condton. 4. Throughput analyss In ths secton, we derve optmal operatng condton of the carrer sense threshold and the transmt power for maxmzng network capacty. 4.. Analyss n homogeneous networks 4... Interdependence among varables and dfferentaton of the node throughput Under the assumpton of a homogeneous network, we omt the node ndex and use x and P to denote the carrer sense threshold and the transmt power, respectvely. Furthermore, snce C = L by (3) and (4), let X :¼ ðgp=xþ h X (=d C (,j)=d L (,j)), whch corresponds to the common carrer sense range for every node. From (6), (8) and (9), t can be easly shown that the node throughput T depends only on X. Thus, T s fully determned by P/x wthout need for consderng x and P ndependently. Let T s be the network capacty, whch s expressed as T S ¼ XN ¼ T : ðþ In order to fnd the optmal value of X for maxmzng T S n (), we dfferentate T S wth respect to X: dt S dx ¼ XN ¼ dt dx : τ s v s Fg.. Descrpton of a logcal nterdependence among varables of node on ts throughput n a homogeneous network. ðþ It turns out that t s not so smple to calculate the total dervatve of T S wth respect to X n () due to the complcated nterdependence among s, q, v, and T. We tackle the problem by makng use of the chan rule [24]. The frst step for carryng out the operaton s to specfy the nterdependence among s, q, v, and T. After a careful observaton on (5), (6), (8) and (9), we pck the nterdependence as n Fg.. 5 From Fg., let s =: f (X), v ¼: g ðx; s ; q ¼: h ðx; fs j g j2irðþ ; fv k g k2h þþ, and T =: F(s,v,q ). fs j g j2c Þ, The dfferentaton of T wth respect to X can be expressed as dt dx dx dx dx dx þ df j j dx þ df j j2i j dx þ k2h þ k df k dx 3 þ k df l A5: ð2þ l2c l dx We have explct formulas for h and F from (8) and (9), respectvely. Thus, we can obtan all the terms related to 5 It should be noted that the dagram n Fg. s not ntended to show the physcal relaton, but to ntroduce a logcal relaton for the mathematcal purpose. Furthermore, t s not the unque way for descrbng the logcal nterdependence. In order to dfferentate T wth respect to X, we need to choose one specfc nterdependence among many possble alternatves. Dependences that do not appear explctly n Fg. are consdered mplct. The nterested reader s referred to [24] for further detal. q T

6 K.-J. Park et al. / Ad Hoc Networks 9 (2) h and F n (2). However, explct expressons for f and g are stll lackng. Consequently, we stll have dffculty n dervng an explct expresson for dt /dx n (2). It should be noted that the dffculty does not come from the specfc choce of the nterdependence among many alternatves, but results from the ntrnsc nature of the problem we are dealng wth. As a matter of fact, for a gven value of X, (5), (6) and (8) represent a nonlnear system for s s, q, and v s, whch s extremely dffcult to solve n an analytcal manner. Even n the sngle-cell scenaro where two unknowns s and q consttute a nonlnear system, only a numercal soluton based on fxed-pont analyss s avalable n general [8]. In order to resolve ths problem, we mpose an assumpton on the attempt probablty s. Let CW and CW denote the contenton wndow sze used by node and ts average, respectvely. As we mentoned n the prevous secton, f we assume that CW s ndependent of X, the attempt probablty s s gven as s ¼ 2=ðCW þ Þ. Hence, (2) can be smplfed as 2 3 dt k 5; k2h þ where v = g (X), q ¼ h ðx; v ; fv j g j2h þþ, T = F(v,q ). Now we are ready to derve an explct relaton between network capacty and system parameters Optmal condton for a homogeneous network wth a symmetrc topology Consder a homogeneous network wth a symmetrc topology, n whch d = d, d I (,j)=d I, and s = s for all ; j 2 N. Proposton gves an approxmate soluton for the optmal carrer sense range, denoted by X *, whch maxmzes network capacty. Proposton. For a homogeneous network wth a symmetrc topology, let X * = argmax X T S. Also, let q denote the node densty of the nterference set I r(), defned as q ¼ I rðþ =ðpd 2 I Þ. If q, then the optmal carrer sense rage X * s qffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff X ðd þ Q q Þ 2 þ R 2 q ðq q þ R q Þ; where D = d + d I, Q q = C q /B q, R q = B q /(2KA q ), and A q ¼ h pffffffffffffffffffffffffffffffffff q ðp 2aÞj 2 þ 4j 2 2, B q ¼ 2pd I ðt B t I Þ log s q ð sþ pd2 I qþ, C q ¼ B q d I þð sþ½t B ðt B t I Þð sþ pd2 I q Š, K = svlog(/( s)), j ¼ d I =d ¼ b h, a = arccos(/2j). If q =, T S s constant for all feasble X 6 D. Proof. In a homogeneous network wth a symmetrc topology, T s are the same for 8 2 N. Thus, from (), t s suffcent to fnd X * such that X * = argmax X T. Let q denote the node densty of the nterference set I r(), defned as q ¼ I rðþ =ðpd 2 I Þ. Then, I rðþ ¼ pd 2 I q ¼ pb 2 h d2 q. Under the assumpton of a homogeneous network wth a symmetrc topology, together wth the fact that I r() and s are ndependent of X, (3) becomes dt dx ¼ T sv logð v 2 H v @X In (4), the number of hdden nodes H þ s gven as ( H þ ðxþ ¼ q½ /X2 þ dx sn / þ wd 2 I Š; f X 6 D; ; otherwse: ð5þ d2 þd 2 I X2 2dd I h where / ¼ mn p; arccos X2 þd 2 d 2 I, w ¼ mn p; p 2dX arccos, and D = d + d I. Snce there exsts a constant such that T, v P > n the feasble regon of X, n order to determne whether T s ncreasng or decreasng, from (4), t s suffcent to consder f ðxþ ¼ H ; where K = svlog( s). If q =,f(x) = and T wll be constant wth respect tox. When q, we consder the followng two subcases. () When X > DWe have H þ ¼ þ =@X ¼ from (5). Also, t s straghtforward to verfy P from (6). Thus, f(x)= /@X 6 and T s a non-ncreasng functon of X. () When X 6 DIn order to get an explct expresson for X *, we ntroduce the followng approxmatons for H þ and v. ( H þ ðxþ A qðx DÞ 2 ; f X 6 D; ; otherwse; h pffffffffffffffffffffffffffffffffff where A q ¼ H þ j R¼dI =d 2 ¼ q ðp 2aÞj 2 þ 4j 2 2, a = arccos(/2j), j = d I /d. Also, v (X) B q X + C q, where B q ¼ dv dx j X¼d I ¼ sðt S t C Þ dq dx j X¼d I þ 2pd I ðt B t I Þ log qð sþ pd2 I qþ ; s and C q ¼ B q d I þ v j X¼dI. By further ntroducng dq dx j X¼d I 2dlog A s q ð sþ I rðþþ VH þ j X¼dI v j X¼dI ; we have B q 2 log ð sþ s pd2 I q h pd I ðt B t I Þð sþq þ dsðt S t C ÞA q ð sþv V d 2 Aq I 2pd I ðt B t I Þ log qð sþ s pd2 I qþ ; and C q = B q d I + v I, where v I s t j S þ j t B þð sþt B ðt B t I Þð sþ pd2 I qþ ð sþ½t B ðt B t I Þð sþ pd2 I q Š: Now, wth omttng the subscrpt q for smplcty, f ðxþ ABKX 2 ð2ack þ B 2 ÞX BC þ AKDðBD þ 2CÞ:

7 22 K.-J. Park et al. / Ad Hoc Networks 9 (2) 6 27 The dscrmnant of f(x) s D =4A 2 (BD + C) 2 K 2 + B 4 >. Thus, f(x) = has two dstnct real roots, denoted by X *, and X *,2 (X *, > X *,2 ). Then, X ; ; X ;2 ¼ p D ffffff ð2ack þ B 2 Þ : 2ABK Snce df X¼X df X¼X < and >, the maxmum of T dx ; dx ;2 s attaned at X *,. From () and (), X * = X *, when q. h Corollary gves how X * n Proposton changes wth respect to the node densty q. Corollary. For a homogeneous network wth a symmetrc topology, there exsts q such that X * s an ncreasng functon of the node densty q f q P q. Furthermore, as the node densty ncreases, the optmal carrer sense range X * converges to D (=d + d I ), whch covers the entre nterference range,.e., lm q" X * = D(=d + d I ). Proof. Let f(q):=d + Q q and g(q): = R q. Then, " # " f df ¼ f 2 þ g 2 dq g dg pffffffffffffffffffffffffffffff f 2 þ g 2 dq : From Proposton, we have lm q" Q q = and lm q" R q =. Hence, lm q" f(q)=and lm q" g(q) =. Consequently, p f = ffffffffffffffffffffffffffffff qffffffffffffffffffffffffffffffffffffffffffff f 2 þ g 2 ¼ = þðg=fþ 2 # as?. In a smlar manner, g= ffffffffffffffffffffffffffffff qffffffffffffffffffffffffffffffffffffffffffff f 2 þ g 2 ¼ ðg=fþ= þðg=fþ 2 " p as q?. Thus, together wth the fact that df/dq > and dg/ dq <, there exsts q > for q P q. Furthermore, t s straghtforward from Proposton that lm q" X * = D because lm q" Q q = and lm q" R q =. h Fg. 2 depcts, n a qualtatve manner, the relaton between the optmal carrer sense range X * and the node densty q. When the node densty s not so hgh, X * wll be X, whch s smaller than d + d I.Asqncreases, X * wll get close to d + d I as X 2. It should be noted that X = d + d I corresponds to the case of exactly coverng the entre nterference range, thus elmnatng all the hdden nodes. Also, note that X * can become negatve for small values of q from T as ρ ncreases + X X 2 d d I Fg. 2. The optmal carrer sense range X * as a functon of the node densty q. X Proposton. In practce, the carrer sense threshold should be smaller than the receve threshold, whch mples that X should be at least larger than d. The practcal meanng of X * smaller than d n Proposton s that there are vrtually no nterferng neghbor nodes and we can reduce the carrer sense range to the mnmum feasble value, wthout much concern about the nterference or the hdden node problem Optmal condton for a homogeneous network wth a random topology Now we consder a homogeneous network wth a random topology n Proposton 2. Proposton 2. In a homogeneous network wth a random topology, let X ¼ arg max X T and q ¼ I rðþ =ðpd 2 I Þ for node. qffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff If q, X ðd þ Q q Þ 2 þ R 2 q ðq q þ R q Þ, where all the constants are the same as those n Proposton, except d nstead of d. If q =,T s constant for all feasble X 6 D. for k 2 H þ Proof. For tractablty, assume that v k v (whch holds true f q q j for j 2 C.) Then, the rest of the proof wll follow the same lne of Proposton. h By Proposton 2, we know that X s are dfferent among nodes because d s and q s are dfferent. Thus, no sngle value of X can maxmze the throughput of every node at the same tme. However, f nformaton on d s and q s s avalable, one smple approxmaton of X ¼ arg max X P2N T s X P N 2N X from Proposton Nonhomogeneous network We consder a nonhomogeneous network where each system parameter can be arbtrarly adjusted for each node. In a nonhomogeneous network, x s and P s should be consdered as ndependent parameters n order to properly descrbe T. The problem of maxmzng network capacty can be formulated as follows. " # max x;p T S X 2N T ðx; PÞ ; ð6þ where x =(x,...,x N ) and P =(P,...,P N ). Snce the search space n (6) contans that of a homogeneous network (whch has a restrcton of x = = x N and P = = P N ), t s obvous that network capacty of a nonhomogeneous network can be at least not smaller than that of a homogeneous network, f properly tuned. A crtcal ssue n practce s how to desgn an algorthm for tunng x and P n a dstrbuted manner. We show that any dstrbuted algorthm that maxmzes the throughput of each node wthout coordnatng wth other nodes wll fal to maxmze the overall network capacty. Intutvely, the throughput of each node wll ncrease as ts carrer sense threshold/transmt power ncreases gven that those of other nodes are fxed. Hence, wthout consderaton of other nodes, each node wll ncrease ts carrer sense threshold and transmt power as much as possble, whch wll sgnfcantly degrade the overall network performance. Proposton 3 valdates ths ntuton.

8 K.-J. Park et al. / Ad Hoc Networks 9 (2) Proposton 3. Any dstrbuted algorthm that maxmzes the throughput of each node by tunng ts own carrer sense threshold and transmt power wthout coordnaton wth other nodes wll fal to maxmze network capacty. Proof. If node ncreases x wth x and P fxed where x =(x,...,x,x +,...,x N ), then v wll be decreased because C s reduced n (6), wth q unchanged. Thus, T wll be ncreased. In a smlar manner, f node ncreases P wth x and P fxed where P =(P,...,P,P +,...,P N ), then q wll be decreased because H þ s reduced n (8), wth v unchanged. Thus, T wll be P : ð7þ Any dstrbuted algorthm n whch every node maxmzes ts own throughput wthout coordnatng wth other nodes can be formulated as max T ðx; PÞ; for 2 N: ð8þ x ;P From (7), the optmal soluton of (8) s ðx ; P Þ¼ðx ; P Þ where x and P are maxmum feasble values of x and P. Thus, y ¼ððx ; P Þ;...; ðx N ; P N ÞÞ s the equlbrum of (8). h From Proposton 3, f every node works n a selfsh manner, the operatng pont wll converge to the trval equlbrum that s obvously not optmal from the system vewpont. Ths phenomenon results from the fact that T not only depends on x and P, but also depends on x and P. Although Proposton 3 s ntutve, ts mplcaton on the desgn of a dstrbuted algorthm s qute sgnfcant. In fact, the problem of maxmzng network capacty n a fully dstrbuted manner corresponds to a non-cooperatve game [2]. Consequently, each node not only need to consder ts own throughput T (as proft), but also need to ntroduce a certan penalty G (as prce) for ts adverse mpact on other nodes. In ths manner, (8) should be modfed as max½t ðx; PÞ G ðx ; P ÞŠ; for 2 N; ð9þ x ;P where G s a prcng functon of node, whch s nondecreasng and convex n x and P. In fact, one approach for solvng (9) has recently been proposed n [6]. It wll be an nterestng avenue of future work to compare the performance of dfferent knds of a prcng functon G Dscusson on remanng ssues Now we pont out several mportant ssues whch are worthy of further nvestgaton. Frst, we have not consdered data rate adjustment accordng to the sgnal qualty (such as the auto-rate functon avalable n most IEEE 82.a/b/g chpsets). There are 4 data rates (, 2, 5.5, Mb/s) avalable n 82.b and 8 data rates (6, 9, 2, 8, 24, 36, 48, 54 Mb/s) avalable n 82.a/g. Usually the hgher the SINR value, the hgher the data rate at whch the transmsson can sustan. For a gven value of SINR, one may then choose the hghest possble data rate (whch allows correct decodng for that gven SINR value) n order to maxmze system throughput. Snce a hgher data rate can be sustaned wth a larger SINR threshold, the data rate sustaned s a functon of the carrer sense threshold and the transmt power. Ths ssue has been studed n [3] wthout consderaton of the MAC specfcs. It wll be nterestng to nvestgate the mpact of multple data rates on network MAC throughput. Second, the effect of the RTS/ CTS handshake mechansm has not been consdered n our analyss. We beleve that the RTS/CTS mechansm has a mnmal mpact on our dervaton, and lkely t wll only reduce the duraton of collson state t C. A more thorough nvestgaton s underway to valdate our ntuton. 5. Smulaton study In ths secton, we carry out a smulaton study to valdate the derved relaton between network capacty and Normalzed optmal carrer sense range x Average contenton wndow sze node densty n nterference range Average contenton wndow sze x 4 Node densty n nterference range (a) Normalzed optmal carrer sense range (b) Contour plot of normalzed optmal carrer sense range Fg. 3. Optmal carrer sense range as a functon of node densty and contenton wndow sze.

9 24 K.-J. Park et al. / Ad Hoc Networks 9 (2) 6 27 system parameters. In partcular, we corroborate the model presented n Secton 3.2 as well as Propostons and 2. Frst, we look nto the relaton between network capacty and system parameters such as the contenton wndow sze and the node densty. Fg. 3 shows the numercal result on the normalzed optmal carrer sense range,.e., (X * d)/d I as a functon of the node densty q and the average contenton wndow sze CW when d = m and j =3. Note that only non-negatve values of (X * d)/d I are shown n Fg. 3 by plottng max((x * d)/d I,). For a fxed value of CW, we can dentfy from Fg. 3 that (X * d)/d I ncreases (except when q ) and converges to one as q ncreases. For a gven value of q, (X * d)/d I decreases as CW ncreases. Ths behavor s due to the fact that the attempt probablty s decreases wth CW. As a result, the effectve node densty also decreases. Fg. 3 shows that (X * d)/d I becomes negatve for large values of W, whch mples that there are no nearby nterferng nodes. Now, we further study how the node densty and the SINR threshold mpact on the optmal carrer sense range Table Parameters used n ns-2 smulatons. Propagaton Two-ray RTS/CTS Dsabled CW sze 5 slots Nose floor 96 dbm Data rate (6,2,24) Mb/s SINR thresh (2.5,5.,5.8) db va ns-2 smulatons. The smulaton study s carred out by usng the 82. Ext model [25] newly ncluded n ns- 2 snce verson Frst, we adopt a symmetrc crcular topology, n whch there are two concentrc crcles wth a radus of 5 m and 25 m. N senders and N recevers are evenly located, respectvely, on the outer and nner crcle. The correspondng recever to each sender s on the same dameter, and thus the dstance between a sender and a recever, d, s m. The parameter values used n the smulaton study are lsted n Table. Smulatons are performed for N = 4, 8, 6 wth the data rate r = 6, 2, 24 Mb/s n Fg. 4. The maxmum pont n each curve s marked wth a crcle. The dotted vertcal lnes n Fg. 4a c, whch are 25.8 m, 32.4 m, and 49.8 m, respectvely, denote the ponts of X = d + d I, whch covers the entre nterference range. In the meantme, our analyss gves the followng optmal values, respectvely for each fgure n Fg. 4: (8.2, 8.9, 5.4), (.28, 9.33, 3.96), (42.32, 49.63, 49.8), and (5.4, 3.96, 49.8). The analytcal results become more accurate as the node densty ncreases, whch can be also nferred from Fg. 3a. In addton, the regon of small non-zero values when the node densty s near zero n Fg. 3a, whch corresponds to the approxmaton error, s responsble for the decreasng trend of the analytcal values for N =4. Here, several observaton can be made. Frst, the optmal carrer sense range s smaller than d + d I n general. Furthermore, as the node densty ncreases, the optmal Average node throughput (Mb/s) d + d I 4 flows 8 flows 6 flows Carrer sense range (m) Carrer sense range (m) (a) Node throughput vs. carrer sense range when r = 6Mb/s (b) Node throughput vs. carrer sense range when r = 2 Mb/s Average node throughput (Mb/s) flows 8 flows 6 flows d + d I Average node throughput (Mb/s) d+ d I 4 flows 8 flows 6 flows Carrer sense range (m) Carrer sense range (m) (c) Node throughput vs. carrer sense rangewhenr = 24 Mb/s (d) Node throughput vs. carrer sense range when N = 6 Fg. 4. Average node throughput as a functon of the carrer sense range under a crcular topology. Average node throughput (Mb/s) Mbps 2Mbps 24Mbps

10 K.-J. Park et al. / Ad Hoc Networks 9 (2) Average node throughput (Mb/s) d + d I d +.8 flows 5 flows 2 flows Carrer sense range (m) Carrer sense range (m) (a) Node throughput vs. carrer sense range when r = 2 Mb/s (b) Node throughput vs. carrer sense range when r = 24 Mb/s Fg. 5. Average node throughput as a functon of the carrer sense range under a random topology. Average node throughput (Mb/s) flows 5 flows 2 flows d I pont converges to d + d I, whch verfes the result n Corollary. We further show n Fg. 4d how the node throughput changes wth respect to change n the data rate, whch valdates that the nterference range expands as the data rate ncreases because of ncrease n the SINR threshold. Now, as a more realstc scenaro, we consder the followng random topology. In the crcular area wth the radus of 25 m, total of N transmsson pars are randomly located wth d =m. Fg. 5 shows the average node throughput as a functon of the carrer sense range for varous data rates. The analytcal values obtaned from Proposton for Fg. 5a and b are, respectvely, (24.39,3.47,3.95) and (49.78,49.8,49.8). It can be verfed n Fg. 5 that these analytcal values match the trend of smulaton results. Overall, we can summarze that, nstead of coverng the entre nterference range, t s benefcal to ncrease the carrer sense threshold, or equvalently, decrease the carrer sense range. In partcular, the typcal value of the carrer sense threshold used n the IEEE 82. WLAN may be too conservatve for network capacty and need to be carefully examned. 6. Concluson and future work In ths paper, we have nvestgated the ssue of maxmzng network capacty of CSMA wreless networks. In partcular, we have explctly ncorporated the carrer sense threshold and the transmt power nto the analyss. In a homogeneous network, we have found that the optmal carrer sense range s smaller than the value for exactly coverng the entre nterference range. In a nonhomogeneous network, the problem of maxmzng network capacty n a fully dstrbuted manner has been shown to be a noncooperatve game. We have dentfed several future research avenues. Frst, our model can be extended to ncorporate the effects of multple data rates and the RTS/CTS handshake mechansm. Furthermore, based on the nsght shed from the analyss, an effcent dstrbuted algorthm can be developed for tunng the carrer sense threshold and the transmt power. One key step for desgnng such dstrbuted algorthms s to properly defne the prcng functon n (9). Snce there have been extensve studes on power control n the context of topology mantenance, we may leverage exstng power control algorthms to develop a framework for jont control of the transmt power and the carrer sense threshold. References [] J.C. Hou, K.-J. Park, T.-S. Km, L.-C. Kung, Medum access control and routng protocols for wreless mesh network, n: E. Hossan, K.K. Leung (Eds.), Wreless Mesh Networks: Archtectures and Protocols, Sprnger, 27. October. [2] IEEE, Wreless LAN Medum Access Control (MAC) and Physcal Layer (PHY) Specfcatons, IEEE Standard 82., 999. [3] T.-S. Km, H. Lm, J.C. Hou, Improvng spatal reuse through tunng transmt power, carrer sense threshold, and data rate n multhop wreless networks, n: Proceedngs of ACM MobCom, 26. [4] X. Yang, N.H. Vadya, On the physcal carrer sense n wreless ad hoc networks, n: Proceedngs of IEEE INFOCOM, 25. [5] H. Zha, Y. Fang, Physcal carrer sensng and spatal reuse n multrate and multhop wreless ad hoc networks, n: Proceedngs of IEEE INFOCOM, 26. [6] J. Zhu, X. Guo, L. Yang, W.S. Conner, Leveragng spatal reuse n 82. mesh networks wth enhanced physcal carrer sensng, n: Proceedngs of IEEE ICC, 24. [7] J. Zhu, X. Guo, L. Yang, W.S. Conner, S. Roy, M.M. Hazra, Adaptng physcal carrer sensng to maxmze spatal reuse n 82. mesh networks, Wley Wreless Communcatons and Moble Computng 4 (24) [8] G. Banch, Performance analyss of the IEEE 82. dstrbuted coordnaton functon, IEEE Journal on Selected Areas n Communcatons 8 (3) (2). [9] F. Calì, M. Cont, E. Gregor, Dynamc tunng of the IEEE 82. protocol to acheve a theoretcal throughput lmt, IEEE/ACM Transactons on Networkng 8 (6) (2) [] A. Kumar, E. Altman, D. Morand, M. Goyal, New nsghts from a fxed pont analyss of sngle cell IEEE 82. WLANs, n: Proceedngs of IEEE INFOCOM, 25. [] K. Medepall, F.A. Tobag, Towards performance modelng of IEEE 82. based wreless networks: a unfed framework and ts applcatons, n: Proceedngs of IEEE INFOCOM, 26. [2] T. Basßar, G.J. Olsder, Dynamc noncooperatve game theory, SIAM Seres n Classcs n Appled Mathematcs (999). January. [3] J. Zhu, B. Metzler, X. Guo, Y. Lu, Adaptve CSMA for scalable network capacty n hgh-densty WLAN: a hardware prototypng approach, n: Proceedngs of IEEE INFOCOM, 26. [4] Y. Zhu, Q. Zhang, Z. Nu, J. Zhu, On optmal physcal carrer sensng: theoretcal analyss and protocol, n: Proceedngs of IEEE INFOCOM Mnconferences, 27. [5] H. Ma, R. Vjayakumar, S. Roy, J. Zhu, Optmzng 82. wreless mesh networks based on physcal carrer sensng, IEEE/ACM Transactons on Networkng 7 (5) (29)

11 26 K.-J. Park et al. / Ad Hoc Networks 9 (2) 6 27 [6] K.-J. Park, J.C. Hou, T. Basßar, H. Km, Noncooperatve carrer sense game n wreless networks, IEEE Transactons on Wreless Communcatons 8 () (29) [7] N. L, J.C. Hou, L. Sha, Desgn and analyss of a MST-based dstrbuted topology control algorthm for wreless ad-hoc networks, IEEE Transactons on Wreless Communcatons 4 (3) (25) [8] R. Ramanathan, R. Rosales-Han, Topology control of multhop wreless networks usng transmt power adjustment, n: Proceedngs of IEEE INFOCOM, 2. [9] R. Wattenhofer, L. L, P. Bahl, Y.-M. Wang, Dstrbuted topology control for power effcent operaton n multhop wreless ad hoc networks, n: Proceedngs of IEEE INFOCOM, 2. [2] K.-J. Park, L. Km, J.C. Hou, Adaptve physcal carrer sense n topology-controlled wreless networks, IEEE Transactons on Moble Computng 9 () (2) [2] J. Monks, V. Bharghavan, W.-M. Hwu, A power controlled multple access protocol for wreless packet networks, n: Proceedngs of IEEE INFOCOM, 2. [22] H. Ma, J. Zhu, S. Roy, S.Y. Shn, Jont transmt power and physcal carrer sensng adaptaton based on loss dfferentaton for hgh densty IEEE 82. WLAN, Computer Networks 52 (9) (28) [23] P. Gupta, P.R. Kumar, The capacty of wreless networks, IEEE Transactons on Informaton Theory 46 (2) (2) [24] R.C. Buck, Advanced Calculus, Waveland Press Inc., 23. [25] Q. Chen, F. Schmdt-Esenlohr, D. Jang, M. Torrent-Moreno, L. Delgross, H. Hartensten, Overhaul of IEEE 82. modelng and smulaton n ns-2, n: Proceedngs of ACM MSWM, 27. Kyung-Joon Park receved hs B.S., M.S., and Ph.D. degrees all from the School of Electrcal Engneerng and Computer Scence (EECS), Seoul Natonal Unversty (SNU), Seoul, Korea n 998, 2, and 25, respectvely. He s currently a research assstant professor n the School of EECS at SNU. He has been a postdoctoral research assocate n the Department of Computer Scence, Unversty of Illnos at Urbana-Champagn (UIUC) from 26 to 2. He worked for Samsung Electroncs, Suwon, Korea as a senor engneer n 25 26, and was a vstng graduate student, supported by the Bran Korea 2 Program, n the Department of Electrcal and Computer Engneerng at UIUC n He has current research nterests n characterzaton and desgn of medcal-grade protocols for wreless healthcare systems, analyss of malcous and selfsh behavor for wreless network securty, and desgn and analyss of self-adjustng protocols for wreless envronments. He s the Gold Prze Wnner of the 4th Insde Edge Internatonal Thess Competton from Samsung Electro-Mechancs n 28. He has receved a Dstngushed Paper Prze at the OPNET Conference n 25. He s also a wnner of the Human-Tech Thess Prze from Samsung Electroncs n 23, 24, and 25. Jhyuk Cho receved the B.S. and M.S. degrees from Seoul Natonal Unversty, Seoul, Korea n 998 and 2, respectvely. He s a Ph.D. canddate at the Department of Electrcal and Computer Engneerng of the Unversty of Illnos at Urbana-Champagn (UIUC). He was a research engneer at Electroncs and Telecommuncatons Research Insttute (ETRI), Korea from 2 to 23. He was also a senor researcher at LG Electroncs Insttute of Technology, Korea from 23 to 26. Hs research nterests nclude wreless network protocols and network securty. Jennfer C. Hou was born on September 26, 964 n Tape, Tawan. She receved her B.S.E. degree n Electrcal Engneerng from Natonal Tawan Unversty, Tawan, ROC n 987, M.S.E degrees n Electrcal Engneerng and Computer Scence (EECS) and n Industral and Operatons Engneerng (I & OE) from the Unversty of Mchgan, Ann Arbor, MI n 989 and n 99, and Ph.D. degree n EECS also from the Unversty of Mchgan, Ann Arbor, MI n 993. She was an assstant professor n Electrcal and Computer Engneerng at the Unversty of Wsconsn, Madson, WI from 993 to 996, and an assstant/assocate professor n Electrcal Engneerng at Oho State Unversty, Columbus, OH from 996 to 2. She joned the Unversty of Illnos Computer Scence faculty n 2. She was a prncpal researcher n networked systems and served as the drector of the Illnos Network Desgn and Expermentaton (INDEX) research group. She has supervsed several federally and ndustry funded projects n the areas of network modelng and smulaton, network measurement and dagnostcs, and both the theoretcal and protocol desgn aspects of wreless sensor networks. She has publshed (wth her former advsor, students, and colleagues) over 6 papers n archved journals, book chapters, and peerrevewed conferences. Her work on topology control and performance lmts n wreless networks has been wdely cted. Dr. Hou has been nvolved n organzng several nternatonal conferences sponsored by professonal organzatons such as ACM Mobcom, IEEE INFOCOM, IEEE MASS, and IEEE RTAS, as well as edtor n archval journals and magaznes such as IEEE Trans. on Computers, IEEE Trans. on Wreless Communcatons, IEEE Trans. on Moble Computng, IEEE Trans. on Parallel and Dstrbuted Systems, IEEE Wreless Communcaton Magazne, Elsever Computer Networks, and ACM Trans. on Sensor Networks. Dr. Hou was a recpent of an ACM Recognton of Servce Award n 24 and 27, a Csco Unversty Research Award from Csco, Inc., 22, a Lumley Research Award from Oho State Unversty n 2, a NSF CAREER award from the Network and Communcatons Research Infrastructure, Natonal Scence Foundaton n and a Women n Scence Intatve Award from The Unversty of Wsconsn-Madson n She was elected as an IEEE Fellow and an ACM Dstngushed Scentst n 27. Dr. Hou passed away on December 2, 27 n Houston, Texas at the age of 43. Yh-Chun Hu receved hs B.S. Magna Cum Laude n 997 n Computer Scence and Mathematcs from the Unversty of Washngton. He receved hs Ph.D. n 23 from the Computer Scence Department at Carnege Mellon Unversty. He was a Postdoctoral Researcher at the Unversty of Calforna, Berkeley. He s currently an assstant professor n the Department of Electrcal and Computer Engneerng at the Unversty of Illnos at Urbana-Champagn. Hs general research nterests are n securty and systems, wth emphass on the areas of secure systems and moble communcatons. He has publshed papers n the areas of secure Internet routng, DDoSreslent forwardng, secure routng n wreless ad hoc networks, securty and anonymty n peer-to-peer networks, effcent cryptographc mechansms for routng securty, and the desgn and evaluaton of mult-hop wreless network routng protocols, ncludng Qualty-of-Servce mechansms for ad hoc networks.

12 K.-J. Park et al. / Ad Hoc Networks 9 (2) Hyuk Lm receved hs B.S., M.S., and Ph.D. degrees all from the School of Electrcal Engneerng and Computer Scence, Seoul Natonal Unversty, Seoul, Korea n 996, 998, and 23, respectvely. He s currently an assstant professor n the Department of Informaton and Communcatons, and the Department of Nanobo Materals and Electroncs, Gwangju Insttute of Scence and Technology (GIST), Gwangju, Republc of Korea. He was a postdoctoral research assocate n the Department of Computer Scence, Unversty of Illnos at Urbana-Champagn n Hs research nterests nclude analytcal modelng and emprcal evaluaton of computer networkng systems, network protocol desgn and performance analyss for wreless networks, measurement and dagnostcs for wred/ wreless networks, and locaton-aware applcatons n ubqutous sensor networks.