Delay Variation Optimized Traffic Allocation Based on Network Calculus for Multi-path Routing in Wireless Mesh Networks

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1 Appl. Math. Inf. Sc. 7, No. 2L, ) 467 Appled Mathematcs & Informaton Scences An Internatonal Journal Delay Varaton Optmzed Traffc Allocaton Based on Network Calculus for Mult-path Routng n Wreless Mesh Networks Feng Zeng 1, Lan Yao 2 and Zhgang Chen 1 1 School of Software, Central South Unversty, Changsha , Chna 2 College of Mathematcs and Econometrc, Hunan Unversty, Changsha , Chna Receved: 7 Oct. 2012, Revsed: 24 Dec. 2012, Accepted: 26 Dec Publshed onlne: 1 Jun Abstract: Ths paper studes the traffc allocaton n mult-path routng n consderaton of the strct requrement for delay varaton n the real-tme applcatons. Frstly, the queung delay s analyzed based on network calculus and the upper bounds of end-to-end delay and ts varaton n all paths are deduced. Then the transfer rate of data flowng nto each path should be used as constrant for satsfyng end-to-end delay requrement, and the Maxmum Allowed Rate MAR) for each path s calculated. Based on MAR, a traffc allocaton algorthm named as TADVO s proposed for delay varaton optmzaton, n whch the traffc s allocated proportonal to MAR of each path. Fnally, TADVO s ntegrated nto AOMDV. The smulaton shows that the new protocol outperforms the other two n terms of delay and delay varaton. Keywords: Wreless mesh network, mult-path routng, traffc allocaton, network calculus Wreless Mesh Network WMN) s an emergng technology for future broadband wreless access. In the archtecture of WMNs, the mddle layer s wreless backbone, whch conssts of mesh routers and gateways. As the communcaton brdges between the wreless backbone and the Internet, the gateways are always performance bottlenecks [1]. In order to provde the guaranty of the qualty of servce QoS) to mesh clents, the performance of wreless backbone s concerned. Ths paper focuses on the optmzaton of delay varaton n multpath transmsson n wreless backbone. The wreless backbone s smlar to an ad hoc network n nature, but wth statc nodes, no energy constrants, and relatve stable topology. Some routng protocols n ad hoc can be used n wreless backbone drectly wth lttle modfcaton. However, the performance of these protocols s much worse than what expected. In recent years, a lot of research works have been done wth attenton to the characterstcs of WMNs, and new routng protocols such as [2,3,4,5] are presented. These protocols can be classfed nto sngle-path and multpath routng protocols. Sngle-path routng protocol s smple to mplement and easy to manage and confgure. However, excessve traffc on a partcular path may lead to the formaton of hot spots of network traffc, resultng n the decrease of network performance and QoS. In multpath routng, multple paths are establshed and used to transmt data streams, and network traffc s dstrbuted among multple paths. Therefore, the throughput and traffc balance on the network can be mproved, wth lower packet loss rate and end-to-end delay. In general, contrastng to sngle-path routng, a better QoS can be obtaned wth the use of mult-path routng [6]. Therefore, the mult-path routng s a better soluton for real-tme data transmsson. In the research, some researchers have proposed the mult-path routng protocols [3, 5] for the WMNs, and the research work mostly focuses on how to dscover multple paths, how to select the transmt paths, and how to manten the paths. However, the problem of traffc allocaton and dstrbuton n mult-path routng should not be gnored, whch have an mportant mpact on the QoS. For real-tme applcatons, the end-to-end delay s strctly constraned. Moreover, when multple paths are used for data transmsson, the varaton of end-to-end delay among all paths should satsfy the requrement of Correspondng author e-mal: fengzeng@csu.edu.cn

2 468 Feng Zeng et al: Delay Varaton Optmzed Traffc Allocaton Based on Network Calculus... dfferent applcatons such as audo, vdeo, and network games. In ths paper, we emphasze on the traffc allocaton problem n mult-path routng. We propose the traffc allocaton algorthm for delay varaton optmzaton based on network calculus. sender Path 1 D 1 D 2 Path 2 recever 1 Related Works From the above analyss, gateways often become the bottleneck of network performance n WMNs. To mprove end-to-end QoS, gateways should dstrbute the traffc among multple paths nstead of routng all traffc along one path, whch can balance the network traffc and effcently avod the traffc aggregaton n hot spots. Therefore, mult-path routng n WMNs has become a hot research area [7]. Many mult-path routng protocols are proposed n the past research, and these protocols manly focus on the mechansm of routng dscovery, paths selecton, and routng mantenance. Long Le [8] presented a mult-path routng desgn for WMNs, and the key dea was a QoS-aware algorthm for mult-path computaton that took channel load and nterference on wreless lnks nto consderaton. Bed and Gupta [9] proposed a geographc mult-path routng protocol whch used vrtual coordnate for packet transmsson. The hop-count metrc n the protocol can recognze congeston and locaton of ts mmedate neghbors. Qu, Ren, and Wang [10] proposed a node-dsjont mult-path routng protocol, whch was based on AOMDV, and added the routng sequence number,.e., somethng lke the source routng sequence n DSR. The new mult-path routng algorthm had less computatonal complexty and routng overhead than AOMDV. L [11] had studed the cooperaton problem among mesh routers n mult-path routng, and proposed a reputaton-based system n mult-path routng to stmulate each node n dfferent paths to forward packets from others. Hu and hs partners [12] has studed how to mantan forwardng paths n the routng, and proposed a mult-path routng protocol MGMP wth multple gateways supported. Smulaton result showed that MGMP outperforms HWMP, AODV, and OLSR. The prevous research work mamly emphasze on the constructon of routng paths, the ncrease of network throughput, and the decrease of routng overhead. However, n real-tme applcatons, we need take the end-to-end delay nto consderaton. Rong and the co-authors [13] had studed the mult-path routng for vdeo delvery over wreless mesh networks. To meet the strct delay requrements, they developed an optmzed algorthm for packet schedulng to shorten packet delay of vdeo communcaton n mult-path routng. Unfortunately, the delay varaton among the multple paths was not studed n ther work. For the end-to-end delay n a sngle path, the delay varaton among the transmsson paths has an mportant mpact on QoS n the vdeo systems. Fg. 1 Traffc Allocaton for Two Paths Routng. In mult-path routng, the traffc allocaton algorthm s senstve to the path delay and ts varaton, as shown n Fg. 1. In the fgure, there are two paths between the sender and recever, wth path 1 havng the better transmsson capablty than path 2. It s assumed that two back-to-back packets travel through path 1 and path 2 from the sender to recever wth the experenced delay as D 1 and D 2, respectvely. To real-tme applcatons, the necessary QoS requres that 1) D 1 and D 2 cannot exceed the delay upper bound, and 2) D 1 D 2, the varaton of D 1 and D 2, should be as small as possble. Addton to end-to-end bandwdth of two paths, the strategy of traffc allocaton s related to D 1 and D 2. Due to less transmsson capacty of path 2, a lttle more traffc assgned to path 2 wll result n the sharp ncrease of D 2. However, path 1 can carry much more traffc than path 2 wth lttle mpact on D 1. Therefore, traffc allocaton between path 1 and path 2 should be taken nto account n two-path routng as shown n Fg. 1. Ths paper focuses on the traffc allocaton among the multple routng paths, and proposes the allocaton algorthm for the reducton of the delay varaton among the paths, whle end-to-end delay of each path satsfes the requrement. 2 Problem Descrpton In mult-path routng, there exst many routng paths between the source and the destnaton, and the source node should share the forwardng traffc of all paths for parallel transmsson. Ths paper studes the strategy of traffc allocaton, takng nto account the end-to-end delay of each path and delay varaton among all paths. Defnton 1: Delay Constrant To any packet P, f t leaves the source node at the tme T s, and reaches the destnaton at the tme T r, the transmsson delay s D = T r T s. In real-tme system, D should be bounded by, whch s related to the system. Defnton 2: Delay Varaton Assume that there be m paths between the source and destnaton, m packets are sent from the source node at the same tme through the m paths, respectvely, and the

3 Appl. Math. Inf. Sc. 7, No. 2L, ) / transmsson delays of each packet are D 1, D 2,..., and D m. The delay varaton of these m paths s defned as: V m = MAX 1 < j m D D j. In vdeo transmsson applcatons, to ensure the clarty of the vdeo mage, we should reduce V m as much as possble, whle the transmsson delay of each path satsfes the requrement of real-tme system. Ths paper, by adjustng the allocaton scheme of the traffc, optmzes the delay varaton V m, therefore, the problem studed n ths paper can be descrbed as a lnear programmng problem. mnv m s.t. D 1 m). It s a NP-Hard problem to get the optmal soluton for the above LP problem. In the next secton, based on network calculus, a further analyss s carred out on the delay and ts varaton n mult-path routng, and a traffc allocaton algorthm s proposed for reducton of the delay varaton among the routng paths. 3 Analyss of Delay and Its Varaton In ths secton, delay and ts varant n mult-path routng are analyzed based on network calculus, and the drecton for delay varant optmzaton s gven. 3.1 Network Calculus Network Calculus NC) s an effcent framework or theory for performance evaluaton of QoS-based queung networks. The prevous work shows that t s a useful tool for the analyss of performance bounds such as delay, jtter, backlog, and so on. Recently, NC s also used for lnk-layer modelng and TCP performance mprovement n wreless network. In NC, arrval curves and servce curves are used to express the propertes of network flows, and deduce the performance bounds. In the followng paragraphs, the basc knowledge of NC for performance analyss s gven. For more detal about NC theory, readers can refer to [14]. In the network, from the vewpont of QoS, every node should take the control of the nput traffc, and provde the QoS wth guaranteed servce for the nput data flows. Smlar to the leaky bucket controller shown n Fg. 2, for any tme t, the data n the bucket denoted as xt) should not exceed a constant σ, whch s the maxmum capacty of the leaky bucket. Therefore, for a gven output rate ρ, the nput traffc Rt) must be constraned. For any nput traffc Rt), f xt) s always below the maxmum capacty σ for any tme t, t s Fg. 2 Leaky Bucket Controller. consdered that R satsfes the controller of σ, ρ) leaky bucket. Defnton 3: Cumulatve Functon The cumulatve functon Rt) s defned as the number of bts on the flow n the tme nterval [0,t], and R0) = 0. Functon R s always wde-sense ncreasng. Defnton 4: Arrval Curve Gven a wde-sense ncreasng functon α for t 0, f a flow R ts cumulatve functon) satsfes one of two equvalent condtons: 1) Rt) Rs) αt s) and 2) R R α for all s t, t s sad that α s the arrval curve of the flow R. In the second condton, stands for the operaton of mn-plus convoluton. Defnton 5: Mn-Plus Convoluton Let f and g be two wde-sense ncreasng functons. The mn-plus convoluton between f and g s: f g)t) = nf [ f t s) + gs)]. 0 s t Theorem 1: If a flow R s under the control of σ, ρ) leaky bucket, Rt) s constraned by the arrval curve αt) = σ + ρt. In consderaton of QoS, the queung delay of any packet n a node s lmted, and supposed to be bounded by T. That s to say that any packet has the maxmum queung delay of T. To a node, for any tme t, t s assumed that the nput and output traffc are denoted by Rt) and R t), respectvely. For any s T, R and R must satsfy R s) Rs T ). 1) From the above nequalty, we can fnd that, for a gven nput functon R, the nodes should provde needed processng capacty to ensure that packets queung delay satsfes the QoS requrement, and the output functon R s related to the processng capacty of the node. In NC, the processng capacty of a node s expressed as the servce curve. Defnton 6: Servce Curve

4 470 Feng Zeng et al: Delay Varaton Optmzed Traffc Allocaton Based on Network Calculus... Fg. 3 Mult-path Transmsson. Fg. 4 Concatenaton of Servce Curves. To a wde-sense functon βt) wth β0) = 0, consderng a system S and a flow through S wth the nput functon R and output functon R, f the nequalty 2) s satsfed, t s sad that S offers a servce curve β to the flow. R R β 2) In a communcaton network, a flow often goes through many nodes. Therefore, t should be consdered that the nodes as a whole provde a servce curve for the flow. Theorem 2: Concatenaton of Nodes Assume a flow Rt) traverse n nodes, whch offers the servce curves β 1 t), β 2 t),......, β n t), respectvely. Then, the path defned by the concatenaton of these nodes offers the followng servce curve β to the flow. β = β 1 β 2 β n 3) Based on the arrval and servce curve, the queung delay bounded n a node for any packet can be calculated. Theorem 3: Delay Bound Assume a flow Rt), constraned by arrval curve αt), traverse a system S that offers a servce curve βt). For any tme t, the delay dt) satsfes the nequalty 4), n whch the hα,β) s the horzontal devaton between αt) and βt). dt) sup{nf{d 0;αt) βt + d)}} t 0 = hα,β) 3.2 Delay Varaton Analyss n Mult-Path Routng There are multple paths between the source and the destnaton n mult-path routng and network traffc s dstrbuted on those paths. The m paths are used to dstrbute the nput flow R between gateway g and mesh router d as shown n Fg. 3, and R s constraned by the arrval curve αt) = σ + ρt, n whch s the nstantaneous burst of traffc, and ρ s the long-term average rate for data transmsson. In mult-path routng, the flow would be dvded nto m sub-flows wth the nput functons R 1 t), R 2 t),......, 4) and R m t). For the th path, the nput functon s R, and Rt) = R 1 t) + R 2 t) + + R m t). In consderaton of end-to-end delay, the nput functon R should be constraned. Assume R be under the control of leaky bucket,ρ ), that s, the arrval curve of the th sub-flow of α t) = + ρ t and the Equaton 5) are satsfed. αt) = α 1 t) + α 2 t) + + α m t) σ = σ 1 + σ σ m 5) ρ = ρ 1 + ρ ρ m Take a path of anyone as an example, based on the status of wreless channel, each node n the path provdes the varable capacty of servce. As shown n Fg. 4, the nodes n the th path have the servce curves β 1, β 2,......, and β n, respectvely. Based on the Theorem 2, the path wth n nodes as a whole has the servce curve β = β 1 β 2 β n. For any node n the network, no matter what schedulng algorthm s adopted, ts servce curve can be descrbed as rate-delay servce curve [14]. Thus, n the th path, the servce curve provded by the j th node can be denoted as Equaton 6), n whch r j s the long-term average rate of data transmsson n the j th node, and T j s the packet delay caused by the node. [ β j t) = r j t T j ] + = {r j t T j ) f t > T j 0 otherwse From the propertes of rate-delay functon, the servce curve provded by the th path can be deduced as the followng equatons: β t) = β 1 β 2 β nt) = r [t T ] + r = mn { r 1,r2, },rn 7) T = T 1 + T T n It s known that a packet delay of a path has relaton wth the processng capacty of the path, and the hgher processng capacty, the less packet delay t has n the path. A packet delay n the end-to-end transmsson ncludes two parts,.e., fxed delay and varant delay. A fxed delay ncludes transmsson delay and propagaton delay, and a 6)

5 Appl. Math. Inf. Sc. 7, No. 2L, ) / varant delay comes from queung. To the th path, assume a fxed delay denoted as f, and the varant delay as v for any tme t, then the delay n the path can be represented by Equaton 8). d t) = f + v t) 8) In a stable queung system, the research work n [15, 16] shows that the upper bound of queung delay must be the maxmum busy perod. Thus, to the flow R constraned by the arrval curve α t) = + ρ t, the upper bound of queung delay can be expressed as: v bound = nf{t 0 : α t) r t 0} = r ρ. Thus, the varant delay n the th path satsfes the nequalty 10), v t). 10) r ρ In addton, transmsson delay and propagaton delay n a sngle hop depend on wreless channel, and are mostly unchanged part. Assume that h s the hop count n the th path, and c s the sum of transmsson delay and propagaton delay n a sngle hop, the fxed delay would be 9) f = h c. 11) Based on 8), 9), 10), and 11), the delay bound D n the th path can be represented by D = h c + r ρ. 12) For any two paths, the delay varaton satsfes the nequalty 13): σ d d j f f j + max, r ρ σ j r j ρ j ) 13) From the defnton 2 and the nequalty 13), the delay varaton upper bound V m n Fg. 3 should be V m = max d d j 1 j m max f f j + max 1, j mand j 1 k m = max 1, j mand j h h j c+ max 1 k m σk r k ρ k σk ) r k ρ k ). 14) As shown n nequalty 14), the former part of V m s fxed, and the latter one s varable. Therefore, we should pay attenton on the latter part for the decrease of delay varaton among these m paths. 4 Traffc Allocaton for Delay Varaton Optmzaton In mult-path routng, for the real-tme applcaton, the delay n each path should be less than the maxmum allowed delay, and the delay varaton among all paths should be as small as possble. To the gven maxmum allowed delay, the delay n any path should satsfy: h c + r ρ 1 m). 15) The nequalty 15) can be converted to the nequalty 16), n whch ρ s the constraned rate for the nput flow, also called the Maxmum Allowed Rate MAR) of the nput flow n the path. ρ r h c 1 m). 16) As shown nequalty 16), the larger of servce rate r, the larger MAR satsfyng the delay requrement s. Combnng 5) and 16), the followng nequalty s derved. ρ = 1 m ρ 1 m r 1 m h c 17) Inequalty Equaton 17) shows that the rate of nput flow s constraned by some condtons. If the rate s larger than the gven threshold, the excessve amount of packets should be backlogged at some nodes, and the end-to-end delay would fal to satsfy the QoS requrement. In consderaton of QoS n mult-path routng, the delay of each path must satsfy the gven requrement. Furthermore, delay varaton among all paths has an mportant mpact on the routng performance, and should be optmzed as far as possble. Thus, the problem studed n ths paper can be converted to the followng lnear programmng problem. ) σk mn max 1 k m r k ρ k s.t. ρ r 1 m) h c ρ 1 + ρ ρ m = ρ σ 1 + σ σ m = σ 4.1 Algorthm Descrpton Consderng the complexty of the mathematc soluton, a smple greedy algorthm s proposed to fnd the effcent soluton. For smplcty, we assume that all nodes n a WMN be homogeneous. In detal, all node-to-node lnks n a path have the same transmsson delay and propagaton delay wth σ 1 = σ 2 = = σ m = σ/m.

6 472 Feng Zeng et al: Delay Varaton Optmzed Traffc Allocaton Based on Network Calculus MaxDelay ms) EVEN-AOMDV RTT-AOMDV TADVO-AOMDV Delay Varaton ms) EVEN-AOMDV RTT-AOMDV TADVO-AOMDV Send Rate Mbps) Send Rate Mbps) Fg. 5 MaxDelay. Fg. 6 Delay Varaton. Then, a greedy algorthm TADVO Traffc Allocaton for Delay Varaton Optmzaton) s presented as follows: Input: ρ, σ,, m, r 1 m) Output: the MARs of all paths ρ 1, ρ 2,......, ρ m ) Step 1: Computng the upper bounds of ρ 1, ρ 2,......, and ρ m based on the nequalty 16), and the results are denoted as B 1, B 2,......, and B m, respectvely. Step 2: Computng the ntal allocaton result ρ 1, ρ 2,......, ρ m ) based on the Equaton 18): ρ = ρ B B j 1 m) 18) 1 j m Step 3: For the current allocaton result ρ 1, ρ 2,......, ρ m ), based on Equaton 9), computng the queung delay upper bounds of all paths. Step 4: For paths wth the mnmum and maxmum queung delay upper bounds, ther constraned rate s denoted as ρ max and ρ mn wth decreasng ρ max and ncreasng ρ mn by a probng value n order to reduce the delay varaton among all paths, that s, to mnmze max 1 k m σk r k ρ k ). Step 5: If max σk 1 k m s never reduced, the algorthm stops. Otherwse, go to Step 4). r k ρ k ) 4.2 Algorthm Implementaton TADVO algorthm should be run on the source node, and the needed data and parameters can be collected from routng nformaton. In algorthm mplementaton, the followng methods are used. 1) The hop count h 1 m) of each path can be obtaned from the nformaton of routng protocol. 2) For the parameter c n nequalty 16), an dle path wth h hops s used to end-to-end delay measurement. Assume the delay be D h, then c s near to D h /h because the queung delay n an dle path can be neglgble. 3) Each node sets up a tmer to estmate the average servce rate recently, and the scheme of routng request and reply wll tell the source of mnmal servce rate of the nodes n a gven path. From Equaton 7), the servce rate r 1 m) of each path s the mnmal servce rate of the nodes n the path. Thus, the approxmate servce rate of each path can be found out. 4) To the parameters, ρ can be consdered as the long-term average rate of the nput flow, and s the nstantaneous burst of traffc. Both parameters can be obtaned through settng up tmers for traffc countng n the source node. Once the source node gets needed data and parameters, TADVO algorthm wll be used to calculate the constraned MAR for each path. Then, the source node transmts the packets forward to each path proportonal to ts MAR. The data collecton, parameter generaton, and TADVO algorthm wll be scheduled perodcally for reflectng the new change of network status. 5 Smulatons In the smulaton, TADVO algorthm and the related scheme are mplemented n the NS-2 [17], and joned wth AOMDV routng protocol. The new mult-path routng protocol s called TADVO-AOMDV, whch wll be n comparson wth EVEN-AOMDV and RTT-AOMDV on the performance n terms of delay, delay varaton among the paths, and network throughput. EVEN-AOMDV s an AOMDV based mult-path routng wth the traffc evenly allocated among the paths, and RTT-AOMDV allocates the traffc n proporton of the Round-Trp Tme RTT) on the paths.

7 Appl. Math. Inf. Sc. 7, No. 2L, ) / End-to-End Throughput Mbps) Fg. 7 Network Throughput. EVEN-AOMDV RTT-AOMDV TADVO-AOMDV Send Rate Mbps) transmsson rate, TADVO-AOMDV outperforms the other two n the term of MaxDelay. When the sendng rate s 1.8Mbps or 2.0 Mbps, the three protocols have almost the same results. In our opnon, when the network s at ts maxmum capacty at that tme, there wll be no room for performance optmzaton. As far as the delay varaton s concerned, TADVO- AOMDV performs better than the other two, as s shown n Fg. 6. The result shows that TADVO algorthm plays an effcent role n traffc allocaton. On the other hand, the traffc allocaton algorthm TADVO adds the complexty to TADVO-AOMDV routng protocol, and TADVO-AOMDV has hgher overhead than the other two. As shown n Fg. 7, for TADVO-AOMDV, the mprovement of the delay and ts varaton s at the cost of lttle decrease of throughput. 5.1 Smulaton Envronment Frst of all, the WMN wth 50 nodes s generated, n whch 10 CBR flows are runnng wth the varant rate. Then, TADVO-AOMDV, EVEN-AOMDV and RTT-AOMDV wll be employed respectvely. Fnally, the smulaton result wll be collected and analyzed for both protocols. In the smulaton, some testng packets are sent for the measurement of end-to-end delay and ts varaton. In the header of testng packet, a feld of sendtme s used to record the start tme for the sender. When the destnatons receve a testng packet, the end-to-end delay of ths packet can be calculated through the arrval tme mnus the sendtme. In ths paper, we care the maxmum delay of these routng paths. For the measurement of delay varaton, some back-to-back packets are delvered through the dfferent routes, and the maxmum delay varaton of these packets wll be obtaned at the destnaton sde. In the NS-2, IEEE s used as the MAC and physcal layer protocol. The network contans 50 nodes located randomly n the feld of 1500m 1500m; the nomnal bt rate s 2Mbps; transmsson range s 250m; the number of CBR flows s 10; the length of nterface queue s set to 50, and the type of queue s CMUPrQueue; the total runnng tme s 100 seconds. 5.2 Smulaton Results Under the dfferent network condtons, the measurement of Maxmum Delay MaxDelay) of the paths and the varaton s carred out for the three protocols, respectvely, and the result s shown n Fgs. 5 and 6. As shown n Fg. 5, when the network s lghtly loaded, due to less complexty, EVEN-AOMDV has the less MaxDelay than RTT-AOMDV and TADVO-AOMDV. However, wth the ncreasng of data 6 Concluson In mult-path routng, traffc allocaton scheme among all paths has an mportant mpact on end-to-end delay and ts varaton. In ths paper, based on network calculus, the upper bounds of end-to-end delay and delay varaton n all paths are deduced. For end-to-end delay satsfyng the requrement and delay varaton optmzaton, the constraned nput rate for each path s analyzed, and a traffc allocaton TADVO s proposed. The smulaton shows that the TADVO-AOMDV outperforms the other two AOMDV based protocols n terms of maxmum delay of the multple paths and delay varaton. In short, TADVO s an effcent scheme for delay varaton optmzaton n mult-path routng. Acknowledgment Ths research was fnancally supported by the Natonal Natural Scence Foundaton of Chna under Grant No , Research Fund for the Doctoral Program of Hgher Educaton of Chna under Grant No , and the Central Unverstes Fundamental Research Funds for Central South Unversty. References [1] X. Wu, J. Lu and G. Chen, Analyss of Bottleneck Delay and Throughput n Wreless Mesh Networks. In: IEEE MASS, , 2006). [2] M.K. Marna and S.R. Das, On-demand multpath dstance vector routng n ad hoc networks. In: Nnth Internatonal Conference on Network Protocols, Nov 2001). [3] J.J. Marc Mosko and Garca-Luna-Aceves, Multpath Routng n Wreless Mesh Networks, In: WIMESN 05, Santa Clara, CA, 2005).

8 474 Feng Zeng et al: Delay Varaton Optmzed Traffc Allocaton Based on Network Calculus... [4] R. Draves, J. Padhye and B. Zll, Routng n mult-rado, mult-hop wreless mesh networks, In: ACM Mobcom, ). [5] N.S. Nandraju, D.S. Nandraju and D.P. Agrawal, Multpath Routng n Wreless Mesh Networks, In: IEEE Internatonal Conference on Moble Ad hoc and Sensor Systems MASS), ). [6] R. Banner and A. Orda, Multpath Routng Algorthms for Congeston Mnmzaton[J]. IEEE/ACM Transactons on Networkng, 152): ). [7] I.F. Akyldz and X. Wang, A survey on wreless mesh networks[j]. Communcatons Magazne, IEEE, 439): ). [8] L. Le, Multpath routng desgn for wreless mesh networks, In: IEEE Global Telecommuncatons Conference GLOBECOM), Houston, TX, Unted states: Insttute of Electrcal and Electroncs Engneers Inc., ). [9] P.K. Bed, P. Gupta and T.K. Gupta, A congeston-aware and load-balanced geographc multpath routng protocol for WMN, In: Internatonal Conference on Sustanable Energy and Intellgent Systems SEISCON), IET, July 2011). [10] Z. Qu, W. Ren and Q. Wang, A new node-dsjont mult-path routng algorthm of wreless Mesh network, In: Internatonal Conference on Computer, Mechatroncs, Control and Electronc Engneerng CMCE), IEEE, ). [11] Y. L, A reputaton system for wreless mesh network usng mult-path routng protocol, In: IEEE 30th Internatonal Performance Computng and Communcatons Conference IPCCC), IEEE, ). [12] Y. Hu, W. He, S. Yang et al., Mult-gateway multpath routng protocol for s WMN, In: IEEE 6th Internatonal Conference on Wreless and Moble Computng, Networkng and Communcatons, IEEE, ). [13] B. Rong, Y. Qan, K. Lu et al., Multpath routng over wreless mesh networks for multple descrpton vdeo transmsson[j]. IEEE Journal on Selected Areas n Communcatons, 283): ). [14] R.L. Cruz, A calculus for network delay, part I and II[J]. IEEE Transactons on Informaton Theory, 371): ). [15] S. Mao, S. Shvendra, Y. Panwar and T. Hou, On Mnmzng End-to-End Delay Wth Optmal Traffc Parttonng[J]. IEEE Transactons on Vehcular Technology, 552): ). [16] C.-S. Chang, Stablty, queue length, and delay of determnstc and stochastc queueng networks[j]. IEEE Transactons on Automatc Control, 395): ). [17] K. Fall and K Varadhan, Ns Manual, In: The VINT Project, ). Feng Zeng receved the PhD degree n computer applcaton technology n 2010, from Central South Unversty, Chna. He s Assocate Professor of Software Engneerng at Central South Unversty, Chna. Hs man research nterests nclude wreless mesh network, QoS routng and network calculus. He s a member of Chna Computer Federaton. Lan Yao receved her B.Eng. degree n communcaton engneerng n 2000, M.Sc. degree n appled mathematcs n 2006, both from Hunan Unversty, Chna. She s currently a Ph.D. canddate n appled mathematcs at Hunan Unversty, Chna. She s Assocate Professor of Computatonal Mathematcs at Hunan Unversty, Chna. Her man research nterests are data mnng, optmzaton theory and wreless network. Zhgang Chen s a professor at School of Software, Central South Unversty, Chna. Hs research nterests are n QoS mechansm for IP networkweb servce, and wreless network. He s the supervsor of Network Computng and Dstrbuted Processng Laboratory at School of Software, Central South Unversty. He obtaned hs Ph.D. and M.Sc. degrees n Computer Scence from Central South Unversty. He s a member of Chna Computer Federaton.

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