QoS-aware routing for heterogeneous layered unicast transmissions in wireless mesh networks with cooperative network coding

Transcription

1 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 RESEARCH Open Access QoS-aware routng for heterogeneous layered uncast transmssons n wreless mesh networks wth cooperatve network codng Saran Tarno 1,2, Wuttpong Kumwlasak 3*, Poompat Saengudomlert 4, Yusheng J 1,2 andc CJayKuo 5 Abstract A novel qualty-of-servce (QoS)-aware routng scheme s proposed to support heterogeneous layered uncast transmssons and mprove the wreless channel utlzaton through cooperatve network codng (CNC) n lossy wreless mesh networks. The proposed routng scheme conssts of two steps. In the frst step, the scheme uses an optmzaton formulaton to compute the optmal routes of all layered uncast flows. The constrants of ths optmzaton problem, such as the transmsson rate of each data layer and tolerable error rates n wreless transmssons, are derved for QoS guarantee. In the second step, the scheme decdes whether or not CNC wll be appled to dfferent uncast flows at ntermedate nodes. The decson crtera are determned by the network structure and the QoS guarantee. Specfcally, f CNC at any ntermedate node does not volate the QoS constrants of nvolved uncast flows, t wll be appled. Otherwse, dfferent uncast flows wll be separately transmtted to ther destnatons wthout CNC. Numercal results wth dfferent network topologes and QoS requrements are conducted to demonstrate that the proposed QoS-aware routng scheme offers better throughput and channel utlzaton than separate uncast transmssons wthout CNC. Keywords: Cooperatve network codng; Multple uncast transmssons; Qualty-of-servce guarantee; Lossy wreless network; Optmzaton formulaton 1 Introducton Effectve transmssons n wreless mesh networks can be acheved by explotng wreless broadcast and network codng [1]. When there s more than one uncast flow n the network, cooperatve network codng (CNC) [2] can be used to mprove the total network throughput and channel utlzaton. In general, CNC s appled to uncast flows at ntermedate nodes n a network. However, CNC may affect the relablty of data n each uncast flow, especally n lossy wreless mesh networks, snce the success of a uncast sesson now depends on another uncast sesson nvolved n CNC. Essentally, all CNC packets must be delvered correctly at the encodng and decodng nodes. It s challengng to acheve hgh network throughput, data qualty guarantee, and effcent channel utlzaton under unrelable wreless mesh envronments. *Correspondence: wuttpong.kum@kmutt.ac.th 3 Kng Mongkut s Unversty of Technology Thonbur, 126 Pracha Utht Road, Bang Mod, Thung Khru, Bangkok 114, Thaland Full lst of author nformaton s avalable at the end of the artcle For multmeda transmssons over heterogeneous wreless networks, data are often separated nto multple data layers. Dependng on the end-to-end transmsson capacty between a source and a destnaton, the number of data layers receved determnes the qualty perceved by the destnaton. In short, CNC requres that the nvolved uncast sessons have the same data rate. Wth separated data layers, CNC can be appled n some data layers even though the overall data rates (or equvalently the transmsson capactes) of the nvolved uncast sessons are not equal. Hence, layered codng can ncrease the applcablty of CNC n heterogeneous wreless networks. In ths work, we nvestgate a novel qualty-of-servce (QoS)-aware routng scheme n lossy wreless mesh networks. The proposed scheme supports heterogeneous layered uncast transmssons wth QoS guarantee and mprove channel utlzaton by applyng CNC based on the local structure of the network. The proposed routng scheme conssts of two steps. In the frst step, the scheme uses a lnear optmzaton formulaton to compute routes 214 Tarno et al.; lcensee Sprnger. Ths s an Open Access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted.

2 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 2 of 18 of all layered uncast flows. The constrants of ths optmzaton problem, such as the transmsson rate of each data layer and tolerable error rates n wreless transmssons, are derved to acheve QoS guarantee. In the second step, the proposed scheme decdes whether or not CNC wll be appled to dfferent uncast flows at ntermedate nodes to mprove channel utlzaton. The decson crtera are determned by the local network structure and the correspondng QoS guarantee. The rest of ths paper s organzed as follows. Related work s dscussed n Secton 2. The network model and assumptons made n ths research are descrbed n Secton 3. The optmzaton formulaton used to compute the optmal routng of layered data transmssons s derved n Secton 4. A set of equatons pertanng the relablty of CNC encoded flows s derved and the QoS-aware CNC decson s presented n Secton 5. The performance of the proposed QoS-aware routng scheme s evaluated n Secton 6 usng numercal experments under random network topologes and dfferent traffc condtons. Concludng remarks are gven n Secton 7. 2 Related work Network codng was proposed for wred networks by Ahlswede et al. [3]. The authors derved the max-flow mn-cut theorem to demonstrate the beneft of network codng by allowng each destnaton of a multcast sesson to receve data up to the multcast capacty. Snce then, network codng has been extended to several other networks, ncludng wreless networks. The man beneft of applyng network codng s the throughput mprovement acheved by effcent sharng of transmsson resources. The physcal propertes of wreless networks are dfferent from those of wred networks. Unrelable physcal channels, lmted battery energy of moble devces, contenton of channel usages, and lack of centralzed control are ssues to be consdered. The term cooperatve network codng (CNC) s used to emphasze the cooperaton between dfferent nodes n a network. In the context of wreless broadcastng, a transmtted packet can be receved by all recevers n the transmsson range, and the COPE-type network codng was proposed by Katt et al. [4] to explot ths property. In partcular, COPE s presented as a new forwardng archtecture that sgnfcantly mproves the throughput of wreless networks. Instead of recevng and forwardng ncomng packets, each ntermedate node encodes several ncomng packets usng the XOR ( ) operaton and then forwards each coded packet to the next-hop node. The next-hop node can decode each coded packet f all the other nvolved coded packets have been receved, possbly through wreless broadcastng. Over all, CNC can help mprove both throughput and energy effcency n wreless networks. Packet routng ncorporatng network codng for wreless networks usng centralzed control has been studed extensvely. Network codng-aware routng was studed by Sengupta et al. [5,6], who demonstrated that network codng-aware routng yelds better throughput than network codng-oblvous routng. A smlar work on CNCaware routng n multrate networks, whch extends COPE by explotng spatal dversty, was proposed n [2]. A network codng-aware routng protocol n lossy wreless networks ncludng a path dscoverng process was proposed by We et al. [7]. Ths method offers throughput mprovement va the structure selecton of CNC. All aforementoned authors formulated optmzaton problems to obtan ther routng solutons. However, they do not consder QoS guarantee for data transmssons. The bound on the throughput gan of network codng and broadcastng n wreless networks was studed n [8]. The authors showed analytcally that the beneft was upper bounded by a constant for both the protocol model and the physcal model of wreless transmssons. L and L [9] nvestgated the beneft of network codng n the routng of multple ndependent uncast transmssons. They ponted out that the codng advantage s not fntely bounded n drected networks. In undrected networks, they showed that the potental for network codng to ncrease achevable throughput s equvalent to ts potental to ncrease bandwdth effcency. Traskov et al. [1] studed network codng for multple uncast sessons usng a lnear optmzaton formulaton. They proposed code constructon technques for certan connecton ponts that are feasble wth a network codng technque called the poson-antdote concept. However, QoS guarantee and layered transmssons were not taken nto consderaton n these studes. Due to the lmted transmsson range of a wreless node, t s typcal for a source node to transmt data to a destnaton node by gong through several ntermedate nodes. Layered vdeo transmsson n wreless networks usng relay nodes was proposed by Alay et al. [11]. Layered vdeo transmsson employs successve refnement of nformaton or scalable codng was consdered n [12]. Vdeo streamng usng network codng over wreless networks was proposed by Seferoglu and Markopoulou [13]. The proposed vdeo-aware opportunstc network codng scheme consders the decodablty of network codes by multple recevers as well as the relatve mportance and delay of vdeo packets. However, the QoS guarantee ssue has not yet been examned n depth n these papers. Mahapatra et al. [14] proposed a QoS- and energyaware routng scheme for real-tme traffc n wreless sensor networks. The scheme employs an adaptve prortzed medum access control (MAC) to provde a dfferentated servce model for real-tme packets. However, network codng was not consdered n [14]. More recently,

3 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 3 of 18 Supttayapornpong et al. [15] proposed a framework of layered data multcastng wth QoS guarantee, whch ncludes network code assgnment to each node n the network. In addton, a practcal algorthm whch calculates the optmal network code length provdng QoS guarantee for wreless multcast was proposed n [16]. However, ther framework dd not address the ssue of network contenton due to the coexstence of multple uncast vdeo streams. Greco et al. [17] proposed a framework for relable vdeo streamng n lossy wreless networks usng expandng wndow network codng (EWNC), multple descrpton codng (MDC), and a novel rate-dstorton optmsed (RDO) schedulng algorthm. However, they assumed that multple sources transmt the same vdeo to a sngle recever. In addton, ther framework cannot be appled to the streamng of layered vdeos. Oh and Km [18] proposed a practcal onlne schedulng algorthm for moble vdeo streamng to multple clents. In ther work, an access pont (AP) constructs and broadcasts the best network code, whch s based on the packets of I-frames wth hgh peak sgnal-to-nose rato (PSNR) durng a group of pcture (GoP), to all clents. Ther framework well addressed a problem of sngle-hop vdeo transmssons from an access pont to moble users n lossy wreless networks. However, they dd not consder multhop transmssons n wreless mesh networks. Yang et al. [19,2] proposed a network codng-based multpath routng (NCMR) scheme for wreless sensor networks. They used random lnear network codng to mprove the relablty of the data transmsson on braded multple paths. Ther approach was proven to be effcent n terms of energy consumpton, whch can be shown by a reduced number of transmssons n wreless sensor networks. Nevertheless, the QoS requrement and transmsson rate were not prmarly consdered n ther works. 3 System model and problem descrpton 3.1 Network model We model a wreless mesh network as a drected graph G(N, E),whereN and E are the sets of nodes and bdrectonal lnks n the network, respectvely. There are several uncast sessons n the network. Each sesson s defned by a unque source-destnaton par. Let s and d denote source and destnaton nodes of an arbtrary uncast sesson, respectvely. Table 1 summarzes the notatons used n ths paper. The lnk conveyng data from node a to node b s denoted by (a, b). In general, a wreless lnk connectng any par of nodes s bdrectonal. However, we can represent a bdrectonal lnk usng two drected lnks havng opposte flow drectons. For example, a bdrectonal lnk between node a and node b can be splt to two lnks, Table 1 Summary of notatons G(N, E) N E (a, b) t(l) r(l) T O (n) T I (n) Ɣ (s, d) c l p l Summary of notatons Drected graph that represents a wreless mesh network Set of nodes n the network Set of lnks n the network Lnk conveyng data from node a to node b Transmtter node of lnk l Recever node of lnk l Set of outgong lnks of node n Set of ncomng lnks of node n Set of all pars of source and destnaton nodes n the network Par of source node s and destnaton node d of an arbtrary uncast sesson Normalzed capacty of lnk l Probablty of packet loss of lnk l M (s,d) Number of the orgnal layers of data transmtted by (s, d) L (s,d) th layer of (s, d) r (s,d) Transmsson rate of th layer of (s, d) I (s,d) M Set of layer ndces of (s, d), where I (s,d) M = {, 1, 2,..., M (s,d) 1} t Normalzed transmsson rate M (s,d) Number of sublayers of (s, d), where M (s,d) = I (s,d) r(s,d) /t M M Maxmum number of sublayers that a source send to a destnaton n a network L (s,d) The th sublayer of (s, d) I M Set of sublayer ndces, where I M ={, 1, 2,..., M 1} P (s,d) f (s,d) l, R (s,d) x (s,d) q (s,d) J Z z l a γ Probablty of a successful packet transmsson for L of (s, d) called the relablty to 1 varable that ndcates whether or not lnk l s used to transmt a packet of L for (s, d) Set of lnks used to transmt packets of sublayer L from source s to destnaton d to 1 varable that ndcates whether or not packets of sublayer L are transmtted from source s to destnaton d Informaton value of L (s,d) used to prortze data sublayers QoS requrement of sublayer L (s,d) Set of ndces for all ndependent sets Set of parameters ndcatng the lnks that can be actvated at the same tme accordng to the th ndependent set Varable that ndcates whether or not lnk l can be actvatedn the th ndependent set Actvaton tme fracton of the th ndependent set n each tme slot Tunng parameter of the alternatve obectve functon, where <γ <1

4 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 4 of 18 namely (a, b) and (b, a), whch may have dfferent loss characterstcs. Alternatvely, for lnk l E, lett(l) and r(l) be the transmtter and recever nodes of lnk l, respectvely.for each node n N, lett O (n) = {l E n = t(l)} and T I (n) = {l E n = r(l)} be the sets of outgong and ncomng lnks of node n, respectvely.letɣ be the set of all source and destnaton pars n the network. In other words, (s, d) Ɣ denotes a uncast sesson. Each lnk has a normalzed postve ntegral capacty or transmsson rate denoted by c l.anormalzeduntcapacty can be translated nto bts per second. The probablty of a packet loss of lnk l s denoted by p l,where p l 1. Each (s, d) Ɣ transmts M (s,d) orgnal layers of data, where L (s,d) s the th layer wth transmsson rate r (s,d).let the set of layer ndces of each (s, d) be I M (s,d),where I M (s,d) ={, 1, 2,..., M (s,d) 1}. To generalze the layered scheme, we decompose each orgnal layer L (s,d) nto several sublayers wth the same transmsson rate based on r (s,d).lett be equal to one normalzed unt. Then, (s, d) has M (s,d) sublayers, where M (s,d) = I M (s,d) r (s,d). t Let M represent the maxmum number of sublayers that a source sends to a destnaton n the network,.e., M = max (s,d) Ɣ (M(s,d) ). Therefore, each (s, d) has up to M sublayers, where L (s,d) s the th sublayer wth the same common transmsson rate t, so that network codng can be appled across heterogeneous uncast sessons. Let the set of sublayer ndces for all (s, d) be I M,where I M ={, 1, 2,..., M 1}. 3.2 QoS guarantee Defnton 1. The QoS guarantee for (s, d) Ɣ and I M s a lower bound of the probablty that source s can transmt a packet of sublayer L (s,d) to destnaton d successfully. The probablty of a successful packet transmsson for L (s,d), called the relablty and denoted by P (s,d),canbe expressed as P (s,d) = l E (1 p l ) f (s,d) l,, (1) where f (s,d) l, ndcates whether or not lnk l E s used.iftsused,f (s,d) l, = 1. to transmt a packet of L (s,d) Otherwse, f (s,d) l, =. 4 Optmal path selecton for layered uncast In ths secton, we descrbe a method for selectng an optmal set of paths to transmt layered data for all uncast sessons. The selecton s constraned by the QoS guarantee of each data layer and by wreless lnk schedulng. The defnton of an optmal set of paths s gven below. Defnton 2. Apathfor(s, d) Ɣ and I M s a set of lnks, denoted by R (s,d), used to transmt packets of sublayer L (s,d). An optmal set of paths s such that R (s,d), (s, d) Ɣ, I M, maxmze the obectve functon under a set of constrants. We dscuss the obectve functon as well as the set of constrants n the followng subsectons. 4.1 Obectve functon Let x (s,d) be the varable ndcatng whether or not packets of sublayer L (s,d) are transmtted wth QoS guarantee. If the sublayer s transmtted wth QoS guarantee, x (s,d) = 1. Otherwse, x (s,d) =. Moreover, to prortze data sublayers, we defne the nformaton value of each sublayer as,where,when <. Thsmeans that, the lower a data sublayer, the hgher ts prorty. The throughput of sublayer L (s,d) s the product of the relablty P (s,d) and normalzed transmsson rate t. One of our obectves s to maxmze the total throughput whle takng the relablty nto account. The nformaton value of the sublayer L (s,d),, s used to provde prortes among dfferent sublayers. Sublayers from the same orgnal layer wll have the same nformaton value. Specfcally, = M, wherethesublayerl (s,d) s from the th layer. Consequently, = f both L (s,d) and L (s,d) are from the same orgnal layer. The concept of nformaton value s demonstrated n Fgure 1. Furthermore, we attempt to reduce the channel use by mnmzng the path length for each R (s,d) snce a shorter path can result n a smaller number of transmssons used for each flow, leadng to more effcent channel utlzaton and shorter delay n wreless networks. Based on the above dscusson, we frst select the followng obectve functon: x (s,d) log (P (s,d) t). (2) (s,d) Ɣ I M We use the logarthmc throughput n (2) snce a sum of logarthmc utlty functons ensures proportonal farness. To avod nonlnear optmzaton whch demands

5 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 5 of 18 The proof of Theorem 1 can be found n the Appendx. Fgure 1 An example of defnng the nformaton value of each sublayer based on ts orgnal layer. To show the concept used for defnng the same prorty of the sublayers belongng to the same layer. hgher computatonal complexty, we can maxmze the followng equvalent functon {log P (s,d) + x (s,d) log t}, (3) (s,d) Ɣ I M whch can be solved by lnear optmzaton. The equvalence between these two obectve functons s stated and proved as Theorem 1. The obectve functon n (3) can be rewrtten as {log (1 p l ) f (s,d) l, + x (s,d) log t}. (4) (s,d) Ɣ I M l E Thus, our obectve functon takes the followng fnal form: { p l f (s,d) l, + x (s,d) log t}, (5) (s,d) Ɣ I M l E where p l = log (1 p l ). Relevant propertes based on the obectve functon n (5) are summarzed n Theorem 1. Theorem 1. The obectve functon n (5) has the followng propertes: 1. Maxmzng the obectve functon {log P (s,d) (s,d) Ɣ (s,d) Ɣ I M I M + x (s,d) log t} (6) s equvalent to maxmzng the obectve functon x (s,d) log (P (s,d) t). (7) 2. In an optmal set of paths for each uncast sesson, for any two paths n ths set, a path havng a hgher relablty transmts packets of ether the same or hgher nformaton value. 3. Gven a lossy network, the obectve functon yelds a set of paths that has the mnmum number of channel uses n the case of equal lnk loss probabltes. 4.2 Flow conservaton constrant The consdered wreless mesh network s modeled as a network wth nformaton flows. Consder nformaton flows for each (s, d) Ɣ of the th sublayer, where I M. The total flow nto a partcular ntermedate node s equal to the total flow out of the node. The flow of sublayer L (s,d) from source node s to destnaton node d s equal to sublayer rate t. Thus, the constrant on nformaton flow conservaton can be expressed mathematcally as l T O (n) tf (s,d) l, l T I (n) tf (s,d) l, = tx (s,d), n = s tx (s,d), n = d, otherwse (8) for all I M, (s, d) Ɣ, andn N. Notethat, when x (s,d) =, the total flow out of a source or nto a destnaton must be zero. 4.3 Relablty constrant The QoS requrement of sublayer L (s,d) s denoted by q (s,d), where q (s,d) 1. Based on (1), the constrant on packet transmssons of sublayer L (s,d) wth QoS guarantee can be expressed as P (s,d) = l E (1 p l ) f (s,d) l, q (s,d) (9) for all I M and (s, d) Ɣ. By takng the logarthm on both sdes of (9), we obtan f (s,d) l, p l q (s,d), (1) l E where q (s,d) = log q (s,d). Ths constrant demands each path selected by the optmal routng to acheve the QoS requrement based on the relablty consderaton. The choce of the QoS requrement of each data layer, q (s,d), s based on ts prorty and type of applcaton and s obtaned from experences of end users. For example, n voce over IP (VoIP) traffc, the packet loss rate should not exceed 5% to not affect the qualty sgnfcantly. When lnk qualtes of a wreless mesh network are n hostle condtons, the orgnal QoS requrements may not be feasble because the proposed optmzaton framework cannot fnd feasble transmttng paths guaranteeng the orgnal QoS requrements of those data layers. Ths nfeasblty s, however, common to communcaton networks. The problem can typcally be handled through the process of call admsson control (CAC), whch we assume to exst but whose detals are beyond the scope of our nvestgaton. The ILP problem can be used for network resource allocaton n conuncton wth CAC.

6 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 6 of Wreless lnk schedulng constrant Due to the broadcast nature of wreless communcatons, a transmsson of a partcular node can affect transmssons of other nodes n ts coverage range. Snce wreless channels are shared among multple nodes, a node placed n the transmsson and coverage ranges of other nodes may be nterfered by smultaneous communcatons. In ths work, we assume that the wreless nterference can be managed by an approprate channel plannng [21,22]. A recever node cannot smultaneously receve more than one packet whereas a transmtter node can send no more than one packet at a gven tme. Therefore, a wreless lnk schedulng technque s needed to coordnate wreless broadcastng. A broadcast transmsson schedulng technque usng the ndependent set concept was proposed by [2]. An ndependent set conssts of a set of lnks where no two lnks share a common end node. In our network model, any par of lnks n an ndependent set must share nether a common transmtter node nor a common recever node. It s also assumed that broadcastng s acheved usng omndrectonal antenna, where the transmsson of each packet goes nto all drectons. The number of all possble ndependent sets n a gven network can be qute large snce t grows exponentally wth the number of lnks. Instead of consderng all ndependent sets, t suffces to consder a famly of ndependent sets whose unon can cover all lnks of the network. The problem of choosng such ndependent sets for a network can be formulated as a set coverng problem (SCP) [23] whose soluton can be solved by usng ether nteger lnear optmzaton or greedy algorthm. To gve an example as shown n Fgure 2, nstead of consderng all feasble ndependent setsnthenetwork,wecanconsderthefollowngndependent sets: {(1,2), (4,5), (3,6)}, {(1,2), (5,4), (3,6)}, {(1,2), (4,5), (6,3)}, {(1,2), (3,4)}, {(2,1), (3,4)}, {(2,3), (4,5)}, {(3,2), (4,5)}, {(1,2), (4,3)}, {(2,3), (5,1)}, and {(2,3), (1,5)}. Fgure 2 An exemplary wreless network. To show a set of drected lnks n a wreless network. Let Z be a set of parameters ndcatng the lnks that can be actvatedatthe sametme accordng to the th ndependent set. In partcular, Z ={z l } l E.Ifz l = 1, lnk l can be actvated; otherwse, lnk l cannot be actvated n the th ndependent set. The set of ndces for all Z s denoted by J. For example, Z for ndependent set {(1,2), (4,5), (3,6)} of the network shown n Fgure 2 s Z ={z (1,2), z (2,3), z (3,4), z (4,5), z (5,1), z (1,5), z (5,4), z (4,3), z (3,2), z (2,1), z (3,6), z (6,3) } ={1,,, 1,,,,,,, 1, }. (11) To acheve tme sharng accordng to lnk capactes, each selected ndependent set Z wll be actvated for a tme fracton a n each transmsson tme slot. The value of a s a 1for J, and J a = 1. Then, the wreless lnk schedulng constrants can be expressed mathematcally as f (s,d) l, c l z l a (12) (s,d) Ɣ I M J for all l E,and a = 1. (13) J 4.5 Problem formulaton: a summary Based on the above dscusson, we can formulate the optmal path selecton problem as a lnear optmzaton usng the obectve functon n (5) wth constrants of the flow conservaton n (8), the relablty n (9), and the wreless lnk schedulng n (12) and (13). The overall problem s summarzed n the followng: Maxmze { p l f (s,d) l, (s,d) Ɣ I M l E subect to tf (s,d) l, tx (s,d) tf (s,d), n = s l, = tx l T O (n) l T I (n) (s,d), n = d, otherwse (14b) I M, (s, d) Ɣ, n N, l E (s,d) Ɣ p l f (s,d) l, f (s,d) l, I M a = 1, J x (s,d) + x (s,d) log t} (14a) q (s,d), I M, (s, d) Ɣ, (14c) J a c l z l, l E, (14d) (14e) x (s,d) +1, I M 1, (s, d) Ɣ, (14f)

7 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 7 of 18 f (s,d) l, {, 1}, I M, (s, d) Ɣ, l E, (14g) x (s,d) {, 1}, I M, (s, d) Ɣ, (14h) a 1, J, (14) where I M 1 ={, 1,..., M 2}. Specfcally, we can explan each constrant as follows. Constrant (14b) s the flow conservaton constrant. Constrant (14c) s the relablty constrant. Constrants (14d) and (14e) are the wreless lnk schedulng constrants. Constrant (14f) s the layered data constrant. A transmsson path of a hgher sublayer wll be chosen only f a transmsson path of a lower sublayer has been selected. Constrants (14g), (14h), and (14) are the feasble values of f (s,d) l,, x (s,d),anda,respectvely. Searchng for a set of paths that maxmze the throughput of each layered uncast sesson requres hgh computatonal complexty because all feasble lnks must be consdered. To reduce the complexty of the problem, the obectve functon n (14a) s modfed as { } (s,d) Ɣ I M x (s,d) log t γ f (s,d) l, l E, (15) where γ s a tunng parameter between zero and one. The obectve functon n (15) gves a suboptmal soluton wth respect to the orgnal obectve functon n (14a). The obectve functon n (15) may not satsfy the second property of the orgnal obectve functon snce t does not take nto account the successful transmsson probablty of each lnk. However, the thrd property of the orgnal obectve functon stll holds,.e., the obectve functon n (15) provdes shortest paths n terms of hop dstances satsfyng both the transmsson rate and QoS requrement of each sublayer, whch can be proven by usng the smlar approach to the thrd property of Theorem 1. The constraned lnear optmzaton s solved to obtan an optmal set of paths R (s,d), (s, d) Ɣ, I M,asdefned n Defnton 2. An optmal soluton to the problem can be obtaned by varous mathematcal programmng tools. We select ConMP [24], whch s a C-API lbrary that supports most of the functonalty of Con Lnear Programmng (CLP), Con Branch-and-Cut (CBC), and Cut Generaton Lbrary (CGL) proects, to be the solver for lnear programmng. Ths s the frst step of the proposed QoS-aware routng scheme. These obtaned optmal paths arenputstothesecondstepoftheproposedqos-aware routng scheme as descrbed n the next secton. 5 QoS-aware CNC for layered uncasts The CNC establshment (CNCE) protocol s presented n ths secton and s used to decde whether or not CNC wll be performed on dfferent uncast pars at ntermedate nodes. The decson crteron s derved based on the QoS requrement of transmtted layered data. 5.1 Three basc local structures We consder three local structures for the applcaton of CNC, called the A-B, Y, and X structures, as shown n Fgure 3. The dashed and regular arrows shown n Fgure 3 represent the overhearng and drect transmssons, respectvely. These three local structures were partly used n [2,6,7]. They serve as the bass n typcal networks. For the A-B structure, CNC s employed at node C, whch combnes each par of packets receved from node A and node B, and then broadcasts the combned packet back to those nodes. Transmsson delay and energy consumpton n a shared network can be reduced at the cost of lower relablty of transmtted data. Ths s because to receve the transmtted data correctly at nodes A and B, all data packets nvolved n the network codng operaton must be successfully receved by node C, whle the network coded packets at node C must be successfully receved by nodes A and B. For the Y structure, there are two uncast flows: (1) from node A to node B and (2) from node B to node D. CNC Fgure 3 Three basc local structures for the CNCE protocol. (a) The A-B structure, (b) the Y structure, and (c) the X structure. The dashed and regular arrows represent the overhearng and drect transmssons, respectvely. To show the basc local structures used n the CNCE protocol. The dashed and regular arrows represent the overhearng and drect transmssons, respectvely.

8 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 8 of 18 s conducted at node C. In partcular, node D receves a packet transmtted by node A va opportunstc lstenng. Node C encodes each par of packets receved from node A and node B, and then broadcasts the network coded packet to nodes B and D smultaneously. For the X structure, there are two uncast flows: (1) from node A to node B and (2) from node E to node D. NetworkcodngsoperatedatnodeC. The coded data packet s then broadcast to nodes D and B. Transmsson delays and energy consumptons of these uncast flows are reduced snce the number of channel uses s reduced due to CNC. However, the relablty n transmtted data deterorates due to the dependency on requred packets n data decodng at destnaton nodes. These local structures are potentally embedded n general random topologes. We provde numercal results n terms of the transmsson relablty for general random topologes that perform CNC usng these three local structures n Secton Codng rules and opportuntes In ths subsecton, we dscuss the codng rules and opportuntes of CNC. Consder k packets ρ, ρ 1, ρ 2,, ρ (k 1) that are ndependent of one another and are on ther own flows traversng a common ntermedate node. The packets ρ, ρ 1, ρ 2,, ρ (k 1) leave a common ntermedate node and travel to nodes n, n 1, n 2,, n (k 1), respectvely. At the ntermedate node, nterflow codng usng the XOR ( ) operaton forms the coded packet ρ = ρ ρ 1 ρ 2 ρ (k 1). Next, the coded packet ρ s broadcast to nodes n, n 1, n 2,, n (k 1). The coded packet s vald and can be decoded at each n only f n has receved packets ρ for all {, 1, 2,, k 1} and =. These codng rules are demonstrated n Fgure 4. The next node n can have all mentoned packets ρ wth the followng two condtons: 1. Packet ρ belongs to a flow that has traveled through n,wheren keeps the packet n ts memory for a perod of tme for the purpose of CNC. Ths stuaton, known as the nonopportunstc lstenng CNC operaton, s applcable to the A-B structure 2. Node n receves packet ρ by overhearng the packet from a transmsson of ts adacent node. For the network codng operaton, node n keeps the packet for later decodng of an encoded packet. The operaton, called the opportunstc lstenng CNC operaton, s used by the X structure. The Y structure conducts both nonopportunstc and opportunstc lstenng CNC operatons. In what follows, we adopt these condtons as the codng rules and opportuntes for the CNC establshment. Note that the proposed codng rules may not be optmal n terms of the number of channel uses n some network topologes. Other COPE structures, whch consst of more than two nformaton flows and accordngly establsh more complex encodng/decodng structures than ours, have dfferent codng rules and potentally provde more reducton n the number of channel uses. However, these complex COPE structures are rarely seen n practcal networks snce they requre overlappng transmsson ranges of more nodes to form ther structures compared to the basc local structures n our work. 5.3 Relablty computaton In ths secton, the effects of performng CNC n lossy wreless networks on the relablty of layered data transmssons are nvestgated. A termnal node n each CNC structure can reproduce ts desred packet f t has the coded packet and all the other nvolved noncoded packets. In addton, to encode a packet successfully for a uncast flow that passes node A and then node B, an ntermedate node needs all requred noncoded packets from other Fgure 4 Codng rules wth XOR ( ) operaton. To show the codng rules appled to our routng scheme.

9 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 9 of 18 uncasts travellng along lnks that do not belong to path R (A,B). Statement 1. For a flow on path R (A,B) that s assocated wth the CNC structure, the partcpatng lnks to the flow on path R (A,B) are the lnks that are not on R (A,B) and carry ether a noncoded packet to be used for encodng at an ntermedate node or a noncoded packet to be used for decodng a coded packet at termnal node B. A partcpatng lnk can be a lnk on the flow of another path cooperatng wth the flow on path R (A,B) or a lnk used n opportunstc lstenng. We examne the partcpatng lnks of the basc CNC structures n the followng. For the A-B structure, the partcpatng lnk to the flow on path R (A,B) s e BC snce node C needs a noncoded packet from node B to generate the coded packet, whch s obtaned by performng the XOR operaton of a packet from node A and a packet from node B. Smlarly, we can derve the partcpatng lnk to the flow on path R (B,A). For the Y structure, the partcpatng lnk to the flow on path R (A,B) s e BC snce node C needs a packet from node B to generate the coded packet. On the other hand, the partcpatng lnks to the flow on path are e AC and e AD snce both nodes C and D need packets from node A to generate and decode the coded packet, respectvely. Note that node D can receve a packet from node A through opportunstc lstenng. For the X structure, e EC and e EB are the partcpatng lnks to the flow on path R (A,B) snce node C needs a R (B,D) packetfromnodee on e EC,whlenodeB needs a packetfromnodee on e EB to generate the coded packet and to decode the coded packet, respectvely. Smlarly, one can derve the partcpatng lnks to the flow on path R (E,D), whch are e AC and e AD. Statement 2. Let ξ be the set of partcpatng lnks to the flow travelng along subpath R (A,B) of R (s,d) wth CNC performed, the relablty of the flow on R (s,d) can be expressed as P (s,d) = (1 p l ) (1 p l ). (16) l ξ l R (s,d) Note that the probablty of a successful packet transmsson along path R (s,d) has prevously been computed n (1). When CNC s appled, the relabltes of the partcpatng lnks affect the decodablty of transmtted data at a termnal node. The expresson n (16) reckons the probablty of a successful packet transmsson takng all relabltes of lnks n R (s,d) and all partcpatng lnks nto account. We use the A-B structure as an example. When the nvolved transmsson lnks are lossy, the successful transmsson probablty of sublayer L (s,d) from node A to node B and from node B to node A wth CNC at node C can be expressed as P (A,B) = (1 p eac )(1 p ecb )(1 p ebc ), (17) and P (B,A) = (1 p ebc )(1 p eca )(1 p eac ). (18) For the extended A-B structure that has two ntermedate nodes,.e., nodes C 1 and C 2, as shown n Fgure 5, we can generalze (17) to P (A,B) = (1 p l ) (1 p lcn ), (19) l R (A,B) where node C n s the node that performs CNC and l Cn s the ncomng lnk of node C n n the drecton opposte to the outgong lnk of node C n n R (A,B). For the Y structure that has fve transmsson lnks as shown n Fgure 3b, the relabltes of uncast flows travelng from node A to node B and from node B to node D wth CNC at node C can be expressed as P (A,B) = (1 p eac )(1 p ecb )(1 p ebc ), (2) and P (B,D) = (1 p ebc )(1 p ecd )(1 p eac )(1 p ead ), (21) respectvely. They can be generalzed as P (A,B) = (1 p l ) (1 p ebc ), (22) l R (A,B) Fgure 5 An extended A-B structure whch has more than one ntermedate node. To show an extended A-B structure whch s a specal case of the A-B structure havng more than one ntermedate node. The node that performs network codes can be selected from one of these ntermedate nodes.

10 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 1 of 18 and P (B,D) = l R (B,D) (1 p l ) (1 p eac )(1 p ead ), (23) where e AC s the ncomng lnk to node C on R (A,B), e BC s the ncomng lnk to node C on R (B,D),ande AD s the ncomng lnk to node D from any node upstream of node C on R (A,B). For the X structure that has sx lnks as shown n Fgure 3c, the relabltes of uncast flows travelng from node A to node B and from node E to node D wth CNC at node C are expressed as P (A,B) = (1 p eac )(1 p ecb )(1 p eec )(1 p eeb ), (24) and P (E,D) = (1 p eec )(1 p ecd )(1 p eac )(1 p ead ). (25) We can generalze (24) and (25) for two uncast flows that on the X structure as P (A,B) = (1 p l ) (1 p eec )(1 p eeb ), (26) and l R (A,B) P (E,D) = l R (E,D) (1 p l ) (1 p eac )(1 p ead ), (27) where e AC and e EC are the ncomng lnks to node C on R (A,B) and R (E,D), e AD s the ncomng lnk to node D from any node upstream of A on R (A,B),ande EB s the ncomng lnk to node B from any node upstream of E on R (E,D). 5.4 CNCE protocol Dfferent uncast flows can be combned to reduce the use of network resources when there are bottlenecks n the network. Our goal s to apply CNC as much as possble whle guaranteeng the QoS of uncast flows of dfferent data sublayers. However, f combnng uncast flows for CNC leads to a volaton of the QoS requrement, CNC wll not be performed and uncast flows wll be separately transmtted. The search for CNC structures s executed by the central controller. The optmal paths obtaned from Secton 4 are nvestgated over all lnks to fnd A-B, Y, and X structures. The central controller detects each CNC structure by examnng whether a group of lnks match wth the consdered CNC structure. If a group of lnks match the underlyng CNC structure, these lnks must convey two uncast flows havng the same transmsson rate. The CNCE protocol can be executed step by step as follows: Stage 1: CNCE for the A-B structure Step 1: Fnd all A-B structures n R (s,d) for all I M and for all (s, d) Ɣ. Step 2: For each A-B structure dentfed n step 1, we fnd two uncast flows from two pars of (s, d) Ɣ that go through ths A-B structure. Step 3: For each ntermedate node, denoted by C n,where n = 1, 2,, and s the number of ntermedate nodes n the A-B structure, we use (19) to compute the relablty of applyng CNC at ths node. Select an ntermedate node C n that satsfes the QoS requrements of two uncast flows obtaned n step 2. If there s more than one ntermedate node that can satsfy the QoS requrements wth CNC, choose the node wth the best QoS. At the selected node, perform CNC on these two uncast flows. Otherwse, CNC wll not be performed, and these two uncast flows wll be transmtted separately. Stage 2: CNCE for the Y structure Step 4: In R (s,d) for all I M and for all (s, d) Ɣ, fnd all Y structures that have lnks not n the A-B structures dentfed n step 1. Step 5: For each Y structure n step 4, use (22) and (23) to compute the relabltes of two uncast flows. If the uncast flows transverse through the prevous A-B structure, the relabltes of (22) or (23) wll be modfed by multplyng the successful transmsson probablty of the lnk l Cn from the A-B structure. Ths modfcaton s needed snce the relablty of the current CNC n the Y structure reles on the relablty of the CNC n the A-B structure. Step 6: If the computed relabltes from step 5 of the Y structure satsfy the QoS requrements of these two uncast flows, perform CNC on two uncast flows. Otherwse, these two uncast flows wll be transmtted separately. Stage 3: CNCE for the X structure Step 7: In R (s,d) for all I M and for all (s, d) Ɣ,fndall XstructuresthathavelnksnotntheA-Bstructureand the Y structure as dentfed n steps 1 and 4. Step 8: For each X structure n step 7, use (26) and (27) to compute the relabltes of two uncast flows. If the uncast flows travel through the prevous A-B structure, the relabltes of (26) or (27) wll be modfed by multplyng the successful transmsson probablty of the lnk l Cn from the A-B structure. If the uncast flows travel through the prevous Y structure, the relabltes of (26) or (27) wll be modfed by multplyng (1 p ebc ) or (1 p eac )(1 p ead ) n the Y structure, dependng on the uncast flows. If the uncast flow travels through the A-B as well as the Y structures, both modfcatons are adopted. Step 9: If the computed relabltes from step 8 of the X structure satsfy QoS requrements of these two uncast

11 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 11 of 18 flows, perform CNC on the two uncast flows. Otherwse, they wll be separately transmtted. The computed relabltes at the end of step 9 yeld the fnal relablty of sublayer L (s,d). We can nfer from ths relablty that all L (s,d) have the QoS guarantees snce ther end-to-end successful transmsson probablty are equal to or greater than ther QoS requrements. 6 Expermental results In ths secton, we compare the performance of the followng three routng schemes: Shortest path routng (SP-R), whch was consdered n [2,6,7,1], QoS-aware layered uncast routng (QoSSP-R) as presented n Secton 4, QoS-aware layered uncast routng wth an alternatve obectve functon (15) (QoS-R), the tunng parameter s set to.1 (.e., γ =.1), and ther enhanced versons by ncorporatng our CNCE algorthm, whch s presented n Secton 5.4. Thus, we can evaluate how CNC affects these routng schemes. 6.1 Expermental setup We smulate the three routng schemes, SP-R, QoS-R, and QoSSP-R, and ther modfed schemes, SP-R w/ CNCE, QoS-R w/ CNCE, and QoSSP-R w/ CNCE, on random network topologes. We use the graph lbrary [25], whch s a free software package to generate and smulate undrected and drected graphs of complex network research. The node postons are placed randomly n a square whose sde length s 4 m. The transmsson range of each node s set to 1 m. The transmsson rate s set dependng on the receved power threshold and the correspondng maxmal dstance based on the IEEE 82.11a standard [2]. We set the transmsson rate from 6, 12, 18, 24, 36, 48, up to 54Mbps.Fortherate6Mbps,wesetthemaxmaldstance of 1 m. Then, we calculate hgher transmsson rates for shorter dstances correspondng to the path loss model P r = αp t /d 4,whereP r, P t, α, andd represent the receved power, the transmtted power, the path loss coeffcent used n the smulaton, and the dstance measured from the transmtter to the recever, respectvely. A normalzed unt of lnk capacty s set to 512 kbps. The relatonshp between the transmsson data rate and the receved power s shown n Table 2. Whle more accurate path loss models can be derved from complex analytcal models or from measurements where system specfcatons such as the locatons of access ponts must be known, a smplfed path loss model s used Table 2 Dstance thresholds for dfferent transmsson data rates Data rate Normalzed rate Receved power Dstance (Mbps) (unt) (dbm) (m) because t can suffcently capture the essence of sgnal propagaton for the purpose of data delverng as well as nterference consderaton. Note that the proposed CNCE algorthm can also be appled when other path loss models are assumed. We perform numercal experments by adustng one of the followng three parameters: Successful data transmsson probabltes of lnks Node denstes Traffc demands Assume that there are no packet retransmssons. We evaluate the performance of each routng scheme by usng three metrcs: (1) total throughput of a network, (2) number of channel uses, and (3) throughput per channel use. The total throughput of a network s a sum of transmsson rates of all sublayers L (s,d) that satsfy ther QoS requrements. In our experments, a snk node dscards the sublayers that cannot satsfy ther QoS requrements as well as ther dependences. The number of channel uses s a sum of lnks of all the paths used to transmt all layered uncast flows n each network. It reflects the wreless channel utlzaton of each routng scheme. Fnally, the throughput per channel use s the rato between the total throughput of a network and the number of channel uses. Ths metrc measures the effcency of wreless channels n data transmsson. A source-destnaton (s-d) par transmts one base layer and two enhancement layers. We set t equal to one normalzed unt whch s 512 kbps. The transmsson rates of the base layer, the frst enhancement layer, and the second enhancement layer are equal to 2, 1, and 1 unts, respectvely. We set the QoS requrements, whch are successful transmsson probabltes, to.9,.8, and.7 for the base layer, the frst enhancement layer, and the second enhancement layer, respectvely. Therefore, each s-d par transmts four sublayers, L (s,d), L (s,d) 1, L (s,d) 2,andL (s,d) 3.The nformaton values of L (s,d), L (s,d) 1, L (s,d) 2,andL (s,d) 3 are set to 4, 4, 3, and 2, respectvely. The routng soluton of each

12 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 12 of 18 routng scheme s obtaned from the Python programmng language [26] together wth the PulP package [27] and the ConMP solver [24]. 6.2 Effects of lnk transmsson probabltes Ten source-destnaton (s-d) pars are randomly chosen n 5 randomly selected networks wth 15 nodes. The successful data transmsson probablty of each lnk s randomly generated, where Z 1 p l 1andZ {.89,.9,.91,.92,.93,.94,.95,.96}. Note that the x-axs of all the result plots specfes the value of Z. Fgure 6 shows the throughputs of the consdered routng schemes wth CNCE algorthm as a functon of the successful packet transmsson probablty. From the results, QoSSP-R w/ CNCE gves the hghest throughput among all routng schemes. In addton, QoSSP-R w/ CNCE gves sgnfcantly better results than SP-R at all cases of successful packet transmsson probabltes. The throughput gan s more sgnfcant at low successful packet transmsson probabltes because SP-R may select paths wthout guaranteeng QoS requrements. The throughput gan of QoSSP-R w/ CNCE over ts suboptmal counterpart, QoS-R w/ CNCE, s modest. However, QoSSP-R w/ CNCE acheves a throughput gan over the QoS-R w/ CNCE snce QoSSP-R w/ CNCE selects paths wth the hghest end-to-end transmsson relablty, whereas QoS-R w/ CNCE merely chooses paths that satsfy the QoS requrements. Obvously, transmsson paths satsfyng the QoS requrements may not gve the hghest relablty. The throughput of QoSSP-R w/ CNCE s close to that of QoS-R w/ CNCE. We can conclude from the results that QoS-R w/ CNCE could be an effectve alternatve to QoSSP-R w/ CNCE f maxmzng the throughput s our obectve. Next, Fgure 7 evaluates the performances of routng schemes n terms of the number of channel uses. The numbers of channel uses of QoSSP-R and QoS-R are sgnfcantly less than that of SP-R at all lnk qualtes. The number of channel uses from SP-R s the hghest at all lnk qualtes although ts achevable throughput ncreases as a functon of the successful transmsson probablty. In other words, SP-R has the lowest effcency of channel utlzaton, especally at low lnk qualtes. QoS-R has a lower number of channel uses than QoSSP-R both wth and wthout CNCE algorthm. QoSSP-R selects paths wth the hghest transmsson relablty regardless of the number of lnks used to transmt btstreams whereas QoS-R chooses the shortest paths that satsfy the QoS requrements. The mportance of CNCE algorthm s also scrutnzed wth the consdered routng schemes. Frst, there s not much dfference n terms of the number of channel uses between SP-R and SP-R w/ CNCE. When SP-R s a routng scheme, the selected transmsson paths of SP-R generally have low relabltes. Applyng CNCE algorthm wll further deterorate transmsson relabltes and QoS guarantees. Therefore, CNC structures are rarely formed to enhance channel utlzaton n ths envronment. However, the gan from usng CNCE algorthm can be seen n both QoSSP-R and QoS-R. The number of channel uses of both routng schemes decreases due to CNCE algorthm. In addton, the CNCE algorthm can decrease the number of channel uses for QoSSP-R more than for QoS-R. Ths comes from the fact that QoSSP-R selects the optmal paths wth hgher relabltes than QoS-R. Therefore, Throughput (unt) QoS Successful data transmsson probablty of each lnk Fgure 6 Comparson of the throughput for varous lnk qualtes n the networks havng 15 nodes. To compare the throughput for dfferent routng schemes as a functon of lnk qualtes n the smulated networks havng 15 nodes. Channel use QoS 3 2 QoS Successful data transmsson probablty of each lnk Fgure 7 Comparson of the number of channel uses for varous lnk qualtes n the networks havng 15 nodes. To compare the number of channel uses for dfferent routng schemes as a functon of lnk qualtes n the smulated networks havng 15 nodes.

13 Tarno et al. EURASIP Journal on Wreless Communcatons and Networkng 214, 214:81 Page 13 of 18 the CNCE algorthm has a better chance to establsh more CNC structures wthout breakng QoS requrements. Fgure 8 shows the throughput per channel use of all routng schemes. QoS-R w/ CNCE acheves the best throughput per channel use among all routng schemes. BothQoSSP-Rw/CNCEandQoS-Rw/CNCEsgnfcantly acheve a better throughput per channel use than SP-R wth and wthout CNCE algorthm n all network envronments. Fgures 9, 1, and 11 exhbt the throughput, number of channel uses, and throughput per channel use of all routng schemes, when the number of nodes n the smulated network s equal to 2. From the results, the performances of all routng schemes show the same propertesasthoseforthecaseof15nodes. We can draw a concluson from our experments that QoS-R should be used n transmssons wth QoS guarantees. QoS-R gves almost the same throughput as QoSS-R, whereas t provdes better channel utlzatons n all network envronments. SP-R s not sutable to be used n wreless networks wth poor lnk qualtes snce t cannot provde both QoS guarantees and hgh channel utlzatons. 6.3 Effects of node denstes The nfluence of node denstes over all routng schemes s studed n ths secton wth 5 randomly selected networks. The number of nodes n the network s vared from 15 to 2 nodes. The successful transmsson probablty s random and unform n the range of.9 1 p l 1. Fgure 12 shows the throughputs of SP-R w/ CNCE, QoSSP-R w/ CNCE, and QoS-R w/ CNCE. There s no effect of the node densty on the achevable Throughput/channel use (unt/tme) QoS QoS Successful data transmsson probablty of each lnk Fgure 8 Comparson of the throughput per channel use for varous lnk qualtes n the networks havng 15 nodes. To compare the throughput per channel use for dfferent routng schemes as a functon of lnk qualtes n the smulated networks havng 15 nodes. Throughput (unt) QoS Successful data transmsson probablty of each lnk Fgure 9 Comparson of the throughput for varous lnk qualtes n the networks havng 2 nodes. To compare the the throughput for dfferent routng schemes as a functon of lnk qualtes n the smulated networks havng 2 nodes. throughput. Both QoSSP-R w/ CNCE and QoS-R w/ CNCE can acheve a throughput gan over SP-R w/ CNCE at all smulated node denstes. The gans are more sgnfcant when we ncrease the number of nodes. Fgure 13 llustrates the number of channel uses of routng schemes when we vary the node densty. We found that the number of channel uses ncreases wth the number of nodes n each network. In other words, the effcency of channel utlzaton decreases because of the wreless lnk schedulng constrant. Transmtted packets have hgher collson probabltes when nodes are denser. As a result, transmtted packets use more transmsson channels from a source to a destnaton to avod collson based on the defnton Channel use QoS 3 2 QoS Successful data transmsson probablty of each lnk Fgure 1 Comparson of the number of channel uses for varous lnk qualtes n the networks havng 2 nodes. To compare the number of channel uses for dfferent routng schemes as a functon of lnk qualtes n the smulated networks havng 2 nodes.