Efficient End-to-End Communication Services for Mixed Criticality Avionics Systems

Transcription

1 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) Effcent End-to-End Communcaton Sevces fo Mxed Ctcalty Avoncs Systems Yng Fang Yu Hua Xue Lu McGll Unvesty Huazhong Unv. of Sc. and Tech. McGll Unvesty Monteal, Canada Wuhan, Chna Monteal, Canada Abstact Avoncs Full Duplex Swtched Ethenet (AFDX) s a new data netwok standad fo moden avoncs systems. Avoncs systems ae typcal mxed ctcalty systems, whee safetyctcal and non-safety-ctcal applcatons co-exst. Tadtonal AFDX leveages best-effot edundant tansmssons fo flows to mpove the communcaton elablty, esultng n the ncease of end-to-end delays wth weak elablty. In ode to bdge the gap between hgh elablty equements and shot end-toend delays, we popose a novel scheme, named (Holstc End-to-End Redundant Schedulng on AFDX). The dea behnd s to leveage a dffeentated tansmsson mode to dstngush safety-ctcal and non-safety-ctcal flows, as well as an effcent cedt-based schedulng scheme to educe the sevng sze fo each flow. The salent featue of s to obtan O(1) complexty and offe the effcent end-to-end tansmsson sevces and the guaanteed elablty. We mplement on a eal test-bed. Expemental esults demonstate the effcency and effcacy of. I. INTRODUCTION Moden avoncs achtectues am to suppot multple functons on a shaed, sngle and fault-toleant platfom. These functons have dffeent levels of ctcalty and can be classfed nto safety-ctcal and non-safety-ctcal. Fo safety-ctcal systems, elable eal-tme communcaton lnks ae essental, say Avoncs Full Duplex Swtched Ethenet (AFDX). AFDX s a new data netwok standad buldng upon the potocol specfcatons of IEEE 82.3 [1] and ARINC 664 [2]. It has been used n many state-of-the-at acafts, such as Abus A38/A35, Boeng 787, etc., and becomes an mpotant communcaton standad n avoncs applcatons. A standad AFDX system conssts of avoncs subsystems, souce/destnaton end systems and nteconnect netwoks. Avoncs subsystems, such as the flght contol compute and the global postonng, ndcate tadtonal avoncs subsystems on an acaft. The nteconnect netwoks geneally consst of a netwok of swtches fowadng fames to the appopate destnatons. The end systems povde an nteface between avoncs subsystems and the nteconnect netwoks to guaantee eal-tme and elable data tansmsson by usng Vtual Lnks (VLs). Accodng to the AFDX specfcaton [2], we can dentfy a VL by settng ts 16-bt ID, Bandwdth Allocaton Gap (the mnmum nteval between two consecutve fames n the VL) and the lagest length of VL fames. In ode to guaantee tansmsson elablty, the AFDX netwok povdes edundancy management on VLs. In moden avoncs applcaton, the amounts and types of data to be tansmtted sgnfcantly ncease, whle the /14/$31. c 214 IEEE elablty equements of these flows need to be guaanteed. How to povde elable and effcent communcaton fo mxed ctcalty systems has been a non-tval and mpotant poblem. Specfcally, we need to deal wth two man challenges n avoncs applcatons. Challenge 1: Best-effot Redundant Tansmssons. The desgn goal of an AFDX netwok s to offe hgh elablty fo data tansmsson. Hence, based on the standad AFDX specfcaton, the flows need to be edundantly tansmtted to potect the netwok fom mechancal falues n a netwok [3], [4]. Tansmttng each fame n paallel ove two ndependent netwoks nceases the tansmsson oveheads. The edundant management unt at the destnaton end system dentfes and deletes duplcate fames, whch also nceases the computaton complexty. Full edundant tansmsson fo all mxed ctcalty netwok flows consumes too much bandwdth. The taffc congeston n pactce exacebates the bandwdth effcency. Ths causes longe latency fo data tansmsson and nceases the possblty of oveflows n the queue buffe. The elablty goal n pactce s dffcult to acheve. Challenge 2: Ineffcent Schedulng Schemes. AnAFDX netwok contans mult-type heteogeneous flows wth dffeent tansmsson equements, such as avoncs, multmeda and best-effot data. Avoncs flows nvolve flght-ctcal data, thus equng the hghest elable and eal-tme sevces. Best-effot data taffcs ae elated wth non-ctcal avoncs applcatons, such as fle tansmsson and data backup, thus equng the lowest elable and eal-tme sevces. In a pactcal avoncs applcaton, most fames n the avoncs flows ae shot fames [5] [6]. As a esult, compaed wth othe heteogeneous QoS netwoks, shot fames n the AFDX netwok ae pefeed to send. Tadtonal schedulng schemes, such as Fst-In-Fst-Out () [7] and Statc-Poty (SP) [8] [9], ae neffcent to deal wth heteogeneous flows snce they heavly depend on statc one-sze-ft-all schemes. Soted poty schedules, such as Self-Clocked Fa Queung (SCFQ) [], tansmt packets n some poty ode. Soted poty algothms geneally have good latency and faness popetes, but ncu hgh complexty due to the poty sotng pocess [11]. Realwold envonments need to desgn smple algothms that have a constant numbe of opeatons pe packet tansmsson. Round obn algothms, such as Weghted Round Robn (WRR) [12], Defct Round Robn() [13] [14] [15], Elastc Round Robn (ERR) [16] [17], Nested () [11], etc., cyclcally seve fo dffeent flows. Each flow s seved fo up to a gven quantum n pe ound. The ound obn algothms, hence, have O(1) wost-case pe packet complexty /14/$ IEEE 188

2 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) Howeve, has hgh latency and poo faness when the flows wth dffeent ate equements ae scheduled. modfes by leveagng multple fames nsde each fame, thus esultng n a lowe latency bound. Howeve, n pe nne ound of, all flows eceve the same amounts of sevces n spte of the dffeent QoS equements. Moeove, an avoncs packet sze s geneally much smalle than the mnmum sevng sze (.e., a gven quantum) n an nne ound. If the mnmum sevng sze fo avoncs packets can be educed, the aggegated delay fo all flows can be smalle, especally fo lage amounts of smultaneously avng avoncs flows. In ode to addess the above challenges, Holstc End-to- End Redundant Schedulng on AFDX () scheme offes a dffeentated tansmsson mode and smalle sevng szes to allevate the taffc congeston and educe the queung delays. Ths pape makes the followng contbutons: Guaanteed Relablty. Ou scheme only tansmts safety-ctcal flows n a edundant manne, whle othe flows ae tansmtted non-edundantly. Hence, the numbe of the tansmtted fames s sgnfcantly educed and we obtan the lghtweght netwok load. Moeove, the non-safety-ctcal flows cause less congeston, compaed wth the case n the edundant tansmssons. Theefoe, the dea of dffeentated tansmsson mode helps povde the guaanteed elablty fo the mxed ctcalty netwok flows n the avoncs applcatons. Low End-to-End Tansmsson Latency. In ode to meet dffeent tansmsson equements fom heteogeneous flows, we desgn by povdng a flow sevce popotonal to ts guaanteed ate. In ode to educe the queung delay of each flow, n, we decease the sevng sze of each flow n each sevce oppotunty by lmtng the sum (n bytes) of vtual packets. The vtual packet efes to the packet whose length s multpled by a facto that nceases wth the numbe of tansmtted packets. Hence, the sevce nteval fo each flow deceases. Pototype Implementaton. To examne the pefomance of ou poposed scheme, we conduct smulatons on a eal testbed and evaluate end-to-end delays fo heteogeneous flows by usng,, and. All the settngs and confguatons on the test-bed can smulate a typcal AFDX netwok. The esults demonstate the effcacy and effcency of. The est of the pape s oganzed as follows. Secton II pesents the backgounds n the dffeentated tansmsson. Secton III pesents a new swtchng algothm, as well as ts latency bound and faness. Secton IV pesents theoetcal analyss of the AFDX netwok pefomance based on the. Secton V shows the evaluaton esults and analyss va a smulaton pototype. Secton VI pesents the elated wok. Secton VII concludes the pape. II. END-TO-END DELAYS UNDER DIFFERENTIATED TRANSMISSION MODE A. Redundant End-to-End Delays Analyss In ode to offe elable sevces, AFDX povdes a edundancy scheme to potect the netwok aganst falues fom a netwok. The edundancy management s confguable. In a edundant tansmsson manne, the same fame s tansmtted wth dentcal sequence numbe though two ndependent netwoks, e.g., netwoks A and B. Theefoe, n geneal, the destnaton end system wll eceve two copes of the dentcal packet. The destnaton end system only accepts the fst vald fame and dscads the edundant one. The paamete SkewMax epesents the maxmum tme between two eceved copes. Ths value usually depends on the netwok topology and should be povded by the netwok manage. Let D befoe be the delay befoe the packet avng at the destnaton end system. Befoe-destnaton delay D befoe can be splt nto thee pats, ncludng the delay at the souce end system, the delay on tansmsson lnks, and the delay on swtches,.e., D befoe = D souce + D tansmt + D swtch. Specfcally, D souce s the pocessng delay of geneatng constaned flow at the souce end system. It comes fom selectng the tansmtted fame fom a vtual lnk queue, assgnng the sequence numbe, duplcatng the fame and tansmttng the fame and ts copy on the physcal lnks. D tansmt s the tansmsson delay ove the lnks. We usually teat t as a constant when the netwok confguaton s detemned. Moeove, D swtch s the swtchng delay fom souce to destnaton end systems. It can be dvded nto technologcal delay and queung delay. The technologcal delay s bounded by a small constant fo specfed hadwae capacty [18], and the queung delay depends on schedulng algothms. In ths pape, we focus on the queung delay. Let D dest be the pocessng delay at the destnaton end system. Coollay 2.1: The uppe bound of the end-to-end delay of a flow tansmttng though an AFDX netwok edundantly, E (D), sgvenby { D 1 E (D) = befoe + SkewMax + D dest, f Δ 2 >SkewMax Dbefoe 2 + D dest, f Δ 2 <SkewMax whee Dbefoe 1 and D2 befoe espectvely epesent the befoedestnaton delays of ognal and edundant flows, Δ 2 ndcates the avng tme dffeence of the two copes at the destnaton end system, and SkewMax s maxmum tme between ecevng the two copes. Poof: The uppe bound of end-to-end delays ely on the values of SkewMax and Δ 2.IfΔ 2 s lage than SkewMax, the fst fame spends a D dest fo pocessng data and then wats fo a SkewMax to complete the end-to-end tansmsson. Othewse, the end-to-end tansmsson completes when the second fame s dscaded and the uppe bound s the sum of befoe-destnaton delay of the edundant flow and the pocessng delay at the destnaton. B. Non-edundant End-to-End Delays Analyss In a non-edundant tansmsson manne, a flow s tansmtted though ethe the netwok A o B. Hence, the destnaton end system avods de-duplcatng copes. Coollay 2.2: The uppe bound of the end-to-end delay of a flow tansmttng though an AFDX netwok nonedundantly, E n (D), sgvenby E n (D) =D befoe + D dest. 189

3 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) Poof: Fo a flow that s not tansmtted edundantly, the uppe bound of the end-to-end delay can be splt nto fou pats: the delay at the souce end system, the delay on the tansmsson lnk, the delay on the swtches, and delay at the destnaton end system,.e., the delay befoe the packet avng at the destnaton end system, as well as the pocessng delay at the destnaton end system. III. A. Schedulng Desgn SCHEDULER DESIGN FOR s a popula Round Robn schedule wth O(1) complexty. In, each flow s assgned a quantum popotonal to ts shae of bandwdth. Fo each flow, a defct counte ndcates the emanng quantum n the cuent ound. In each ound, a flow can eceve the amount of sevces up to the sum of ts quantum sze and the defct value. The latency and faness of ae not optmal. To mpove the latency of, schedule has been poposed [11]. In, each oute ound of s splt nto smalle nne ounds and a veson of s executed ove these nne ounds. Dung each nne ound, the maxmum of sevces s the sum of the smallest quantum (the quantum value of the flow wth the lowest eseved ate) and the defct value. Snce the smallest quantum s lage than o equal to the maxmum packet sze, t s geneally much lage than the small avoncs packet sze. Futhemoe, the heteogeneous flows wth the same mnmum sze decease the qualty of sevce. In ode to leveage the nput taffc patten and decease the sevng sze of flows, splts each nne ound of nto one o moe smalle mco ounds. In each mco ound, the mnmum sevng sze s elated wth the packet sze. Each flow has a cedt counte (Allowance). At the begnnng of each mco ound, Allowance s ntalzed to the smallest quantum. The packet can be tansmtted only f the packet sze s smalle than o equal to Allowance. Afte successfully tansmttng a packet, Allowance deceases by the vtual sze of the tansmtted packet. The vtual sze equals to the eal packet sze multpled by a facto that nceases wth the numbe of tansmtted packets. As a esult, dffeent flows have vaous sevng szes n one sevce oppotunty. In the oute ounds, chaactezes flow by the quantum Q, the eseved ate ρ, the eseved quantum UQ, and the weght ω. The smallest ate of all actve flows s epesented as ρ mn. Q mn s the quantum value of the flow wth the lowest eseved ate. ω s the weght assgned to flow, and s gven by, ω = ρ. (1) ρ mn Note that ω 1. The quantum Q n s gven by, Q = ω Q mn. (2) Thee defct countes, ODC, IDC and MDC depct the dffeences n the amounts of data actually to be sent, and the amounts that should have been sent n each oute ound, nne ound and mco ound espectvely. Dung each oute ound, the schedule attempts to seve flow wth the quantum of Q. Dung each nne ound, t tes to seve flow wth the quantum of Q mn. Dung each mco ound, the sevng sze s elated wth packet szes, and up to the quantum of Q mn. In ode to mplement, we mantan thee lsts of actve flows, ActveLst(), ActveLst(1) and ActveLst(2). The flows n the ActveLst() have completed sevces fo the cuent oute ound. ActveLst(1) mantans a lst of flows that have completed sevces fo the cuent nne ound. ActveLst(2) mantans anothe lst of flows that ae seved n the cuent mco ound. The schedule can be dvded nto thee pats: Intalze, Enqueue and Dequeue. In the Intalze pocess, all of the defct countes ae set to. A flow whose queue s empty and theefoe s not n any of the thee lsts s called an nactve flow. When an nactve flow becomes actve, t should be added nto the ActveLst(2) and UQ should be set to (Q Q mn ), whle MDC should be set to Q mn.ths pocess calls Enqueue outne. The Dequeue outne schedules packets out of queues. The pseudo-code mplementaton of Dequeue s shown as Fgue 1. The cuent nne ound n pogess ends when the ActveLst(2) becomes empty. In ths case, f the ActveLst(1) s not empty, all flows n the ActveLst(1) have to patcpate n the next nne ound. ActveLst(1) and ActveLst(2) ae exchanged. Othewse, the cuent oute ound n pogess ends and all flows n ActveLst() have to patcpate n the next oute ound. ActveLst() and ActveLst(2) ae exchanged. When the ActveLst(2) s not empty, seves the fst flow n the lst, say flow. When tansmttng a packet fom flow, the schedule fst checks whethe the Allowance s lage than o equal to the vtual packet sze. If so, the packet s tansmtted. MDC deceases by the actual sze (n bytes) of the tansmtted packet, whle Allowance deceases by the vtual packet sze. Othewse, the packet can not be tansmtted and the cuent mco ound sevce fo flow ends. In ths case, f MDC s lage than o equal to the packet sze, flow should be added to the tal of the ActveLst(2) to patcpate n the next mco ound. If the packet sze s lage than MDC, but smalle than the sum of MDC and UQ,flow ends the cuent nne ound sevces. The value of MDC s assgned to IDC to ecod the defct quantum n the nne ound. Flow s added to the tal of the ActveLst(1). The quantum of sevce n the next nne ound can have a mn{uq,q mn } compensaton. If the packet sze s lage than the sum of MDC and UQ, the schedule ends the cuent oute ound sevces fo flow and adds flow to the tal of ActveLst(). The sum of MDC and UQ s assgned to ODC to ecod the defct quantum n the cuent oute ound. The next oute ound obtans a Q sevce compensaton, UQ hence becomes Q. At the begnnng of the fst mco ound n the next oute ound, adds mn{uq,q mn } to MDC and educes UQ by the same value. To select the next packet to be tansmtted, t s unnecessay fo to sot o seach pocess. In, the numbe of opeatons needed to select the next packet s a constant. Hence, the wok complexty of the schedule s O(1). 19

4 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) Dequeue Algothm whle TRUE do f SzeOfActveLst(2)== then f SzeOfActveLst(1)> then MoveActveLstF omto(1, 2); else f SzeOfActveLst()> then MoveActvelstF omto(, 2); end f end f end f f SzeOfActveLst(2)> then = HeadOfActveLst(2); RemoveheadOfActveLst(2); Allowance = Q mn ; count =; epeat Tansmtpacket(Queue()); count ++; Allowance = count LengthOftansmttedP acket; MDC = MDC LenthOftansmttedP acket untl IsEmpty(Queue()) == TRUE) o Allowance < (count +1) LenthOfP acketathead() f IsEmpty(Queue() ==TRUE then MDC =; IDC =; ODC =; DecementSzeOfActveLst(2); else f UQ + MDC < LengthOfP acketathead() then AddQueueT oactvelst(); IncementSzeOfActveLst(); DecementSzeOfActveLst(2); ODC = MDC + UQ ; IDC = ODC ; UQ = Q mn{uq,q mn }; MDC = IDC + mn{uq,q mn }; else f MDC > LengthOfP acketathead() then AddqueueT oactvelst(1); IncementSzeOfActveLst(1); DecementSzeOfActveLst(2); IDC = MDC ; UQ = UQ mn{uq,q mn }; MDC = MDC + mn{uq,q mn }; else AddQueueT oactvelst(2); end f end f end f end f end whle Fg. 1. Dequeue algothm. B. Latency Bound of In ode to analyze the pefomance of, we deve ts uppe bound on the schedulng latency. Let ODC (k) be the defct quantum of flow followng ts k-th oute ound. IDC (k, s) s the defct quantum of flow followng the s- th nne ound nsde the k-th oute ound. MDC (k, s, u) s the defct quantum of flow followng the u-th mco ound on the s-th nne ound nsde the k-th oute ound. (k, s, ) epesents the begnnng of the fst mco ound n the (k, s)- th nne ound. Snce MDC obtans a compensaton at the begnnng of a new nne ound, the equaton s MDC (k, s, ) = IDC (k, s 1) + mn{uq,q mn}. (3) (k, ) epesents the fst nne ound nsde the k-th oute ound. Note that IDC (k, ) = ODC (k 1). The bytes sent by flow dung the (k, s, u)-th mco ound, Sent (k, s, u), sgvenby, Sent (k, s, u) =MDC (k, s, u 1) MDC (k, s, u). (4) Note that u 1. The bytes sent by flow dung the (k, s)-th nne ound, Sent (k, s), sgvenby, Sent (k, s) =Q mn + IDC (k, s 1) IDC (k, s). (5) Note that s 1. The bytes sent by flow dung the k-th oute ound, Sent (k), sgvenby, Sent (k) =ω Q mn + ODC (k 1) ODC (k). (6) Note that k 1, ODC () =. Coollay 3.1: Fo all, the followng epesentaton holds fo each executon of : ODC (k) < m, IDC (k, s) <m, MDC (k, s, u) <m+ Q mn,whee m epesents the bggest sze n bts of those packets that ae actually seved. Poof: Intally, ODC () =, IDC (, ) = MDC (,, ) =. ODC (k) only changes ts value when flow completes the k-th oute ound of sevce. The oute ound ends when the sum of UQ (k) and MDC (k) s less than the length of the packet to be tansmtted. Snce the packet length s no lage than m, natually ODC (k) s less than m. Lkewse, we obtan that IDC (k, s) s less than m. MDC (k, s, u) changes ts value when the (k, s, u)-th mco ound ends. In one sevce oppotunty, at least one packet can be sent n each sevce oppotunty snce Q mn s lage than the maxmum packet sze,.e., Sent (k, s, u) >. Accodng to Equatons (3) and (4), the maxmum value of MDC (k, s, u) should be MDC (k, s, 1), whch s less than Q mn + m. Let τ be the tme nstant that flow becomes actve and concdes wth the begnnng of some oute ound k. Let τ (k, ω,last) be the tme nstant that flow eceves the last mco ound on the (k, ω )-th nne ound of sevce. ω means the mnmum ntege that s lage than o equal to ω.letsent (t 1,t 2 ) be the amount of sevce eceved by flow dung the tme nteval (t 1,t 2 ). At the tme nstance τ (k, ω,last),letg denote the set of flows n the AtveLst(). Let G 1 and G 2 epesent the set of flows n the ActveLst(1) and the ActveLst(2) espectvely. Flow s not ncluded n any of the thee lsts. In ode to acheve the wost-case schedulng latency, we assume that all n flows ae actve n the tme nteval of (τ,τ (k, ω,l) )andflow s the last to eceve sevces n a mco ound. Theoem 3.2: The schedule belongs to the class of Latency-Rate seves, wth an uppe bound on the latency, Θ b fo flow, gvenby, Θ b = 1 ( {ω jq mn} + { ω Q mn} + { ω Q mn}) j G j G 1 j G 2 +( 1 1 )(Q mn m +1)+ 1 (n 1)(m 1) ρ +( 1 1 ρ )( ω 1)Q mn)+( 1 1 ρ )(Q mn m +1). 191

5 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) Poof: Let t(k 1) be the tme to ndcate the completon oft the (k + k 2)-th oute ound. To analyze the latency bound, the fst step s to obtan an uppe bound on the sze of the tme nteval (τ,τ (k, ω,last) ). The tme nteval can be splt nto the followng two sub-ntevals: 1) (τ,t k 1 ): The sub-nteval ncludes (k 1) oute ounds statng at ound k.letw be the sum of all the flow weghts and be the lnk ate. Summazng Equaton (6) ove all n flows and ove (k 1) oute ounds begnnng wth the oute ound k, we obtan t k 1 τ = W (k 1)Qmn + 1 n {ODC j(k 1) ODC j(k + k 2)}. j=1 2) (t k 1,τ (k, ω,last) ): In ths sub-nteval, we consde flow, aswellasflowsnthesetsg, G 1 and G 2. Flows belongng to the set G have completed the (k +k 1)-th oute ound. The total bytes sent by these flows dung the sub-nteval ae Sent j(t k 1,τ (k, ω,last) )= {ω jq mn} j G j G + {ODC j(k + k 2) ODC j(k + k 1)}. j G Flows n the set G 1 have completed the ω -th nne ound of sevce nsde the (k +k 1)-th oute ound. The total bytes sent by these flows dung the sub-nteval ae Sent j(t k 1,τ (k, ω,last) )= { ω Q mn} j G 1 j G 1 + {ODC j(k + k 2) IDC j(k + k 1, ω )}. j G 1 Flows n the set G 2 have completed the (k + k 1, ω,last)-th sevce oppotunty. Snce the last nne ound may get a compensaton less than Q mn, usng Equatons (4) and (5), we obtan Sent j(t k 1,τ (k, ω,last) ) j G 2 { ω Q mn} + {ODC j(k + k 2)} j G 2 j G 2 {MDC j(k + k 1, ω,last)}. j G 2 The total bytes sent by flow dung the sub-nteval ae gven by Sent (t k 1,τ (k, ω,last) ) =( ω 1)Q mn + ODC (k + k 2) IDC (k + k 1, ω 1) + L(), whee L() epesents the bytes sent by flow dung the mco ound one though last on the (k + k 1, ω )-th nne ound, whch s gven by, L() =MDC (k, ω, ) MDC (k, ω,last). Snce the (k, ω,last)-th mco ound s the last sevce oppotunty on the (k, ω )-th nne ound, MDC (k, ω,last) must be less than m. Hence, we have L() MDC (k, ω, ) m +1 Q mn m +1. Note that ODC (k 1) = snce flow becomes actve at the k -th oute ound, accodng to Coollay 3.1, summazng all actve flows ove the two peods, we obtan τ (k, ω,l) τ W (k 1)Qmn + 1 {ω jq mn} j G + 1 { ω Q mn} + 1 { ω Q mn} (7) j G 1 j G L()+ 1 ( ω 1)Qmn + 1 (n 1)(m 1) 1 IDC(k + k 1, ω 1). Dung the tme nteval unde consdeaton, flow eceves sevces ove (k 1) oute ounds, ( ω 1) nne ounds and last mco ounds, Sent (τ,τ (k, ω,l )=(k 1)ω Q mn + ODC (k 1) IDC (k + k 1, ω 1) + ( ω 1)Q mn + L(). Note that the eseved ates ae popotonal to the weghts, usng Equatons (7) and (8), we obtan ( Sent (τ,τ (k, ω,l) ) max {,ρ τ (k, ω,l) τ 1 ( {ω jq mn} + { ω Q mn} j G j G 1 + { ω Q mn}) ( 1 1 )(Q mn m +1) (9) ρ j G 2 1 (n 1)(m 1) ( 1 1 ρ )Q mn ( 1 1 ρ )( ω 1)Q mn )}. The latency bound eaches the uppe bound when IDC (k + k 1, ω 1) = m 1 and L() =Q mn m +1. It s poved n [19] that the latency bound of a schedule can be detemned by consdeng only those peods dung whch a flow s contnuously actve. Fom the Lemma 7 n [19], we know that s a Latency-Rate seve wth a latency less than o equal to Θ b gven by, Θ b = 1 ( {ω jq mn} + { ω Q mn} + { ω Q mn}) j G j G 1 j G 2 +( 1 1 )(Q mn m +1)+ 1 (n 1)(m 1) ρ +( 1 1 ρ )( ω 1)Q mn)+( 1 1 ρ )(Q mn m +1). Theoem 3.3: Fo any executon of the schedule, the nequalty FM < M +2m holds, whee M s the sze of the lagest packet that may potentally ave. Poof: FM s defned to be the maxmum value of FM(t 1,t 2 ) ove all the possble executons of the fa queueng scheme and all possble ntevals (t 1,t 2 ) n an executon [13]. FM(t 1,t 2 ) s the maxmum of ( Sent(t1,t2) ω (8) 192

6 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) Sent j (t 1,t 2) ω j ), ove all pas of flows, j that ae backlogged n the nteval (t 1,t 2 )[13]. Snce woks n ounds, tme hee can be measued n tems of ounds. Fo any tme nteval (t 1,t 2 ), dung whch flow eceves the (x 1,y 1,z 1 )-th mco ound of sevce statng fom the (x,y,z )-th mco ound, we deve Sent (t 1,t 2)=(x 1 x )Q +(y 1 y )Q mn + MDC (x,y,z 1) MDC (x 1,y 1,z 1) (x 1 x )Q +(y 1 y +1)Q mn + m. () Fo a flow j n the set G, the mnmum bytes sent fom flow j ae Sent j(t 1,t 2)=(x 1 x 1)Q j +(ω j y )Q mn + MDC j(x,y,z ) ODC j(x 1 1) (x 1 x 1)Q j +(ω j y )Q mn m. As Q ω deve = Qj ω j (11) = Q mn, usng Equatons () and (11), we Sent (t 1,t 2 ) ω Sent j(t 1,t 2 ) ω j Q mn +2m. (12) The Equaton follows due to ω 1 and ω j 1. Fo the flow j n the sets G 1 Sent j (t 1,t 2) ω j Q mn +2m. and G 2, Sent(t1,t2) ω When Q mn s set to M, we deve FM M +2m. The faness of the schedule s dentcal to that of the scheme[11]. IV. AFDX COMMUNICATIONS BASED ON In, we dstngush safety-ctcal flows fom nonsafety-ctcal flows n avonc applcatons usng dffeent tansmsson modes. To guaantee the communcaton elablty of the safety-ctcal flows, we tansmt them edundantly. To educe the netwok load, we tansmt non-safety-ctcal flows though ethe netwoks A o B. In ode to show the advantages of, we compae wth the schedule that schedules full edundant flows n the same applcatons. Assumpton 4.1: Thee ae N flows n the AFDX netwok, among whch n s flows ae safety-ctcal. Each netwok has n swtches wth the same capacty and confguaton. A. Safety-ctcal Flows Fo a safety-ctcal flow, ts end-to-end delay bound s elated wth the aval tme dffeence on the two netwoks and the system paamete SkewMax. ThevalueofSkewMax s the numbe of swtches cossed by the tansmtted fames and usually povded by the system admnstato. The aval tme dffeence s equal to the befoe-destnaton delay dffeence. In ths pape, we make use of leaky bucket functon as aval cuve,.e., α(t) =σ + ρ t,wheeσ s the bust and ρ s the ate. Fom the Theoem 4 n [19], the maxmum swtchng delay D n of flow n a netwok of latency-ate seves, consstng of n seves n sees, s bounded as n D n σ + Θ j ρ, (13) j=1 whee Θ j s the latency bound of the j-th swtch n the netwok fo flow. In, fo safety-ctcal flows, the ognal fames ae tansmtted though the netwok A, whle the edundant fames ae sent though the netwok B. Thee ae n 1 and n 2 flows on the netwoks A and B espectvely. ω nsafe s the total weght of the non-safety-ctcal flows. On the netwok A, l 1 flows have weghts smalle than ω, and the sum of the weghts s ω l1. On the netwok B, l 2 flows have weghts smalle than ω, and the sum of the weghts s ω l2. Usng the Theoem 3.2 and Equaton (13), the swtchng delay dffeence of flow on the two netwoks s bounded by Dswtch 2 Dswtch 1 = n{ 1 Qmn(ωl2 ω l1 ) + 1 (14) Qmn ω (n2 n1 + l1 l2)+1 (n2 n1)(m 1)}, whee Dswtch 1 and Dswtch 2 ae the swtchng delays on the ognal netwok and the edundant netwok espectvely. Let Δ 1 be the tansmsson nteval between the ognal fame and ts edundant copy at the souce end system bounded by.5ms. The aval tme dffeence Δ 2 n s gven by, Δ 2 = Dswtch 2 Dswtch 1 +Δ 1. Ths aval tme dffeence ndcates the pncples fo flow confguatons: The numbe of non-safety-ctcal flows and the sum of the weghts on one netwok should be appoxmate to those on the othe netwok. Othewse, safety-ctcal flows wat long fo the aval of the copes. The possblty of oveflows and the computaton complexty hence ncease at the end system. Let D swtch 1 and D swtch 2 be the swtchng delays on the netwoks A and B espectvely n the schedule. It s poved n Ref. [11] that the schedule has an uppe bound on the latency Θ fo flow gven by, Θ = 1 {ω jm} + 1 { ω M} j G ove j (n Gove ) j +( ω 1 1)M( 1 )+ 1 (n 1)(m 1) ρ +(m 1)( 1 ρ 1 ). (15) The swtchng delay dffeence s zeo when the two netwoks tansmt the same flows. Theefoe, the aval tme dffeence n s only elated wth Δ 1. If Dswtch 2 Dswtch 1 +Δ 1 <SkewMax, the end-toend delays of tansmttng any packet of flow unde both schemes come fom the edundant netwok. Note that safetyctcal flows ae tansmtted n a edundant manne n, the delays at the souce/destnaton end systems and on the lnks ae the same as those n the schedule. The end-toend delay dffeence ΔE between and hence s equal to the swtchng delay dffeence, and s gven by, ΔE = D swtch 2 D swtch 2 = n{ 1 M ωl1 ω l2 + ω nsafe + 1 (m 1)(N n2)}, 2 whee ω l1 ω l2 depcts the dffeence of the weghts of non-safety-ctcal flows on the two netwoks. The weghts dffeence s smalle than the sum of weghts of all non-safetyctcal flows on the two netwoks,.e., ω l1 ωl2 +ω nsafe >. In addton, fom the defntons of m, N and n 2, (m 1)(N n 2 ) >, we detemne ΔE >. 193

7 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) If D swtch 2 D swtch 1 +Δ 1 > SkewMax and Δ 1 > SkewMax, the end-to-end delays n and come fom the ognal netwok. Accodng to Coollay 2.1, the end-to-end delay dffeence s gven by, ΔE = D swtch 1 D swtch 1 = n{ 1 M ωl2 ω l1 + ω nsafe + 1 (m 1)(N n1)} >. 2 If D swtch 2 D swtch 1 +Δ 1 >SkewMax,butΔ 1 < SkewMax, the end-to-end delays n and come fom the ognal netwok and the edundant netwok espectvely. Snce the delay dffeence at the souce end system s Δ 1, the end-to-end delay dffeence s gven by, ΔE = D swtch 1 D swtch 1 +Δ 1 SkewMax. When n{ 1 M ωl1 ωl2 +ω nsafe (m 1)(N n 2)} > Skewmax Δ 1, the end-to-end delays of safety-ctcal flows unde the scheme tun out to be much shote than those unde the scheme. B. Non-safety-ctcal Flows In, fo a non-safety-ctcal flow j, t s tansmtted only on the netwok A. Thee ae l j1 flows whose weghts ae smalle than ω j on the netwok A, and the sum of the weghts s ω lj1 j. On the netwok B, l j2 flows have weghts smalle than ω j, and the sum of the weghts s ω lj2 j. The swtchng delay D j swtch 1 of the flow j, sgvenby, D j swtch 1 = σj + n{ 1 ρ j Mωlj1 j + 1 ωj M(n1 lj1 1) +( 1 1 )(M m +1)+ 1 (n1 1)(m 1) ρ j +( 1 1 ρ j )( ω j 1)M}. In, the end-to-end delay of the flow s elated wth Δ 1 and SkewMax. The swtchng delay of the flow j on the ognal netwok, D j swtch 1,sgvenby, D j swtch 1 = n{ 1 M(ωlj1 j + ω lj2 j )+ 1 ωj M(N lj1 lj2 1) +( 1 1 )(M m +1)+ 1 (N 1)(m 1) ρ j +( 1 1 )( ω j 1)M} + σj. ρ j ρ j Note that the fames of the flow ae not duplcated at the end systems n, the delays at the souce/destnaton end systems ae shote than those n. Accodng to Coollaes 2.1 and 2.2, we obtan ΔE >D j swtch 1 D j swtch 1 + mn(δ 1,SkewMax) = n{ 1 Mωlj2 j + 1 M ωj (N lj2 n1) + 1 (m 1)(N n1)} + mn(δ1,skewmax) >. Ths equaton poves that the end-to-end delays of non-safetyctcal flows n ae also shote than those n. In summay, the scheme s moe effcent than the tadtonal scheme that schedules full edundant flows. TABLE I. T HE NUMBERS OF HETEROGENEOUS FLOWS (VLS) UNDER DIFFERENT BAG VALUES. BAG (ms) No. of Avoncs No. of Multmeda No. of Data V. PERFORMANCE EVALUATION In ths secton, we pesent the expemental esults fom the mplementatons of multple schedules, ncludng (baselne),, and, to schedule heteogeneous flows. Cuent AFDX potocol only suppots the schedulng scheme. The expements ae confgued accodng to the specfcatons of AFDX netwoks [2]. The expements evaluate the end-to-end delays of dffeent schedulng schemes. Fgue 2 shows the netwok confguaton fo the expements, whch nclude souce end systems, 1 destnaton end system and 4 swtches. In ode to make meanngful compasons, we also mplemented,, and. We use 16-bt values as vtual lnk IDs n the ente AFDX netwok fo the Ethenet fames. A. Expement Setup In the expements, we use thee types of heteogeneous flows,.e., avoncs, multmeda (vdeo & audo) and besteffot data, to evaluate the end-to-end delays unde ou scheme. Tables I and II demonstate the Bandwdth Allocaton Gap (BAG) and fame szes of the thee flows. These settngs come fom a synthetc scenao to smulate a eal AFDX netwok. All lnks ae set to Mbps. All BAGs ae smalle than 128ms and most fames ae shote than bytes accodng to the AFDX specfcaton [2] and the expeences fom eal-wold envonments [2]. In geneal, avoncs VLs demonstate the heavest wokloads among the thee flows. Data Data Avoncs Avoncs E3 E2 E1 Vdeo E5 Vdeo E6 Data Data E E7 E8 S1 S3 Data E4 Vdeo E9 Fg. 2. An AFDX pototype confguaton. We evaluate end-to-end delays of heteogeneous flows that ae peodcally geneated. In the context of desgn, the peodcty s ntepeted as a peod fo tansmttng a peodc message. The expements defne the peodcty to be 4ms. In ths way, peodc flows wth BAGs smalle than 4ms can be eplayed evey 4ms. We eplay othe flows n the tme S2 S4 E11 194

8 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) TABLE II. THE NUMBERS OF HETEROGENEOUS FLOWS (VLS) UNDER FRAME LENGTH VALUES. Fame Length (bytes) No. of Avoncs No. of Multmeda No. of Data > nteval of the own BAG values. The expements leveage dffeent amounts of the tansmtted VLs to show vaable loads. The BAG values ae fom 2 to 128 wth exponental gowth of 2. B. End-to-end Delays Fgue 3 shows the expemental esults when executng,, and fo schedulng avoncs, multmeda (vdeo & audo) and best-effot data. Except, othe schedules tansmt edundant heteogeneous flows. only edundantly tansmts avoncs flows due to the hgh elablty equements. The end-to-end delays ae evaluated wth the nceased numbes of VLs. These schedulng schemes cause dffeent end-to-end delays due to the dffeent schedulng stateges fo heteogeneous flows. obtans the best pefomance snce t can sgnfcantly allevate the netwok congeston and decease e-tansmsson pobablty. Fo dffeent schedulng schemes, we obseve that the delay of s the longest whle that of s the shotest. poduces on aveage 4.72 tmes longe delay than. equally teats heteogeneous flows that have dffeent deadlnes of had eal-tme tansmsson, whch leads to the longest delays among the schedules. schedulng algothm obtans smalle latency snce t uses dffeent quanta to dffeentate heteogeneous flows. Compaed wth, leveages a nested set of multple fames nsde each fame, thus esultng n a sgnfcantly lowe latency bound, whle mantanng the O(1) complexty and faness as. Unlke them, obtans the smallest latency. The eason s that t has smalle sevce unt, whch can be adjusted accodng to the nput taffc lengths. Fo schedulng heteogeneous flows, the evaluaton of endto-end delays nvolves n avoncs, multmeda (vdeo & audo) and best-effot data VLs. The pefomance depends upon fame szes and the schedulng scheme. Fst, as shown n Fgue 3(a), we obseve that the aveage and maxmum latences n avoncs flows ae espectvely 6.1ms and 11.7ms n, 21.2ms and 26.3ms n, 28.3ms and 41.8ms n and 38.5ms and 55.2ms n. The schedule can guaantee the had eal-tme and elablty equements fo avoncs flows. Moeove, as shown n Fgue 3(b), the aveage and maxmum latences of multmeda flows ae espectvely 7.5ms and 12.8ms n, 27.8ms and 38.7ms n, 36.2ms and 55.6ms n and 47.6ms and 74.1ms n. delves substantal pefomance mpovements due to ts patally edundant tansmsson polcy and shote sevce oppotunty gap. The amounts of the tansmtted multmeda flows n decease, and n the meantme these heteogeneous flows do not need to wat fo the edundant copes n the destnaton end systems, thus sgnfcantly educng the endto-end delays. In addton, as shown n Fgue 3(c), the aveage and maxmum latences of data flows ae 11.5ms and 2.3ms n, 33.7ms and 5.9ms n, 49.8ms and 68.2ms n and 6.3ms and 91.7ms n. Compaed wth,, and, the end-to-end latency of the data flows n s also much shote. The eason s that allevates the numbe of data to be e-tansmtted, and futhe mtgates netwok congeston. Fgue 4 shows the end-to-end delays of tansmttng edundant flows fo all schedules. Compaed wth patally edundant tansmsson, we obseve that the delays ncease. Specfcally, fo avoncs flows, the aveage and maxmum delays ae 42.2ms and 6.5ms n, 3.6ms and 51.8ms n, 25.3ms and 32.6ms n, and 6.8ms and 15.6ms n. The eason s that edundant tansmsson fo avoncs flows causes heave netwok load, thus aggavatng netwok congeston. Moeove, as shown n Fgue 4(b), the aveage and maxmum latences of multmeda flows ae espectvely 8.1ms and 18.6ms n, 3.2ms and 47.4ms n, 39.5ms and 62.9ms n and 53.2ms and 79.7ms n. delves substantal pefomance mpovements due to ts shote sevce oppotunty gap. In addton, as shown n Fgue 4(c), the aveage and maxmum latences of data flows ae 12.8ms and 28.2ms n, 36.6ms and 58.2ms n, 52.7ms and 81.6ms n and 71.3ms and 1.2ms n. Compaed wth,, and, the end-to-end latency of data flows n s also much shote. The eason s that educes the mnmum sevce sze, thus deceasng the watng delay fo all flows. Fo dffeent schedulng polces unde the same scenao, we obseve that the delay of s the shotest whle that of s the longest. fals to seve fo dffeent flows wth dffeent quanta, thus leadng to the longest delays among the schedule. The schedule allocates lage quanta to hgh-ate flows, whch leads to low-ate flows watng long fo one sevce oppotunty. Compaed wth, leveages a smalle nne ound, n whch a flow can eceve one sevce oppotunty, hence mpovng the low-ate flows pefomance. Howeve, the mnmum sevng sze n one nne ound s stll too lage fo small sze packets. takes advantages of nput taffc and educes the mnmum sevng sze fo all the flows, especally fo flows contanng small packets. Snce a lage facton of packets n avoncs flows can be shot, effectvely educes the queung tme fo all flows. C. Retansmsson Rate The numbe of etansmtted data s an mpotant metc to evaluate the end-to-end tansmsson pefomance. In ode to povde effcent elablty, data ae geneally etansmtted when packet loss o tmeout occus. The fault model efes to the ntenatonal standad IEC6158 [21], whch can dentfy vaous levels of ntegty o system elablty. In each level, 195

9 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) Numbe of VLs Numbe of VLs Numbe of VLs (a) Avoncs flows. (b) Multmeda flows. (c) Data flows. Fg. 3. End-to-end delays of heteogeneous flows unde,,, and schedules Numbe of Vtual Lnks Numbe of Vtual Lnks Numbe of Vtual Lnks (a) Avoncs flows. (b) Multmeda flows. (c) Data flows. Fg. 4. End-to-end delays of fully edundant flows unde multple schedules. ths standad descbes the pobablty of system-level falue n tme unt. Moeove, n the context of AFDX desgn, the pobablty of falue p of each flow can be computed fom the szes of the flows (.e., SIZE ) and bt eo ates. Fgue 5 shows the etansmsson ates fo schedulng avoncs flows and the data loss ate fo schedulng multmeda and best-effot data flows. The etansmsson and data loss ates can be ntepeted as the same semantcs to evaluate the tansmsson pefomance. Avonc flows use etansmsson and othe flows use dectly data loss n the end-to-end tansmsson. We obseve that compaed wth,, and schedules, can sgnfcantly educe etansmsson ate,.e., 3.6% fo avoncs flows, and decease the data loss ate,.e., 5.2% fo multmeda and data flows. The eason s that t deceases the sevce unt usng the nput taffc chaactestcs and allows each flow to eceve sevce as soon as possble, whch shotens the end-to-end delays substantally. hence deceases the numbe of tme-out packets and the possblty of oveflow n the queue buffe. Moeove, also educes the numbe of packets watng n the queues of ntemedate swtches, hence mtgatng packet loss. VI. RELATED WORK Mxed-ctcalty systems n avoncs applcaton bng new challenges to the AFDX netwok communcatons. Schabag et al. [2] analyze the eal-tme of AFDX netwoks upon swtches that un queung. The esult shows that schedule couldn t suppot heteogeneous flows successfully snce multple flows shae queues dentcally. Baue et al. [9] get the end-to-end delay bound of statc poty schedule by applyng tajectoy appoach. Howeve, both and statc poty schedule fal to suppot heteogeneous flows well. In ode to suppot multple flows tansmsson, the authos n [22] ty to combne statc poty and weghted ound-obn to mpove schedulablty. Lkewse, L et al. [23] popose the schedulng polcy of fxed poty combned wth Round Robn (FP-RR) to mpove the tansmsson delay. Hua et al. [6] select modfed defct ound obn schedule to bette seve heteogeneous flows. In ode to futhe mpove the tansmsson effcacy, they smplfy the de-duplcaton opeaton at the end destnaton system[4]. Rao et al. [24] apply TDMA cossba eal-tme swtch achtectue nto the AFDX netwok desgnment and deve the end-to-end delay bounds usng netwok calculus. Hen Baue et al.[25] focus on AFDX swtch outpots backlog evaluaton usng tajectoy appoach. The wok shows that smalle buffe sze can be used n each AFDX swtch outpot. Tajectoy appoach [26] s also used to measue the endto-end delay besdes thee common methods,.e., netwok calculus, model checkng and queung netwoks smulaton, n the AFDX systems. The wok evewed above focus on how schedules help mpove the end-to-end delays of heteogeneous flow. Unlke the wok, ou wok obseves the taffc tansmsson modes n the AFDX netwok, and demonstates that the dffeentated tansmsson mode contbutes to educe the end-to-end delay whle stll guaanteeng the elablty. Futhemoe, ou poposed algothm effcently schedules heteogeneous flows, whle ncung low complexty. 196

10 214 IEEE 22nd Intenatonal Symposum of Qualty of Sevce (IWQoS) Fg. 5. Retansmsson Rate (%) Data Loss Rate (%) Numbe of VLs (a) Retansmsson ates. Numbe of VLs (b) Data loss ate. Tansmsson pefomance of heteogeneous flows. VII. CONCLUSION In ode to mpove the latency n the avoncs netwok fo the mxed ctcalty systems, we popose an effcent and novel scheme,, to addess the poblems of data tansmsson and neffcency schedulng. uses a dffeentated tansmsson mode and an effcent schedule to schedule heteogeneous flows. We obtan the tght latency bound and faness of by theoetcally analyzng the wokng pncple of swtches. Wth the latency bound of schedule, we study the end-to-end delays fo mxed ctcalty flows usng the Latency-Rate seves. Moeove, we mplement on a eal test-bed. Expemental esults demonstate the effcency and effcacy of ou poposed scheme and show that the pefomance mpovements come fom bette schedulng and a lght-load netwok confguaton. REFERENCES [1] H. Faze, The 82.3z Ggabt Ethenet Standad, IEEE Netwok, vol. 12, no. 3, pp. 6 7, May/June [2] ARINC664, Acaft Data Netwok, Pat 7 Avoncs Full Duplex Swtched Ethenet (AFDX) Netwok, ARINC 5-5/ADN-39, 25. [3] J. Yao, G. Zhu, X. Lu, and A. Jou, Optmal bandwdth allocaton fo non-ctcal taffcs n afdx netwok, Poc. IEEE Confeence on Industal Electoncs and Applcatons, pp , 212. [4] Y. Hua and X. Lu, Schedulng Heteogeneous Flows wth Delay- Awae Deduplcaton fo Avoncs Applcatons, IEEE Tansactons on Paallel and Dstbuted Systems, vol. 23, no. 9, pp , 212. [5] H. Chaaa, J.-L. Schabag, J. Emont, and C. Faboul, Methods fo boundng end-to-end delays on an AFDX netwok, Poc. Euomco Confeence on Real-Tme Systems, 26. [6] Y. Hua and X. Lu, Schedulng desgn and analyss fo end-to-end heteogeneous flows n an avoncs netwok, Poc. INFOCOM, 211. [7] M. Boye and C. Faboul, Tghtenng end to end delay uppe bound fo afdx netwok calculus wth ate latency ffo seves usng netwok calculus, Poc. WFCS, 28. [8] F. Rdouad, J.-L. Schabag, and C. Faboul, Pobablstc uppe bounds fo heteogeneous flows usng a statc poty queueng on an afdx netwok, Poc. IEEE Intenatonal Confeence on Emegng Technologes and Factoy Automaton, pp , 28. [9] H. Baue, J.-L. Schabag, and C. Faboul, Applyng Tajectoy appoach wth statc poty queung fo mpovng the use of avalable AFDX esouces, Real-tme systems, vol. 48, no. 1, pp , 212. [] S. J. Golestan, A self-clocked fa queueng scheme fo boadband applcatons, Poc. INFOCOM, [11] S. S. Kanhee and H. Sethu, Fa, effcent and low-latency packet schedulng usng nested defct ound obn, Poc. HPSR, 21. [12] M. Katevens, S. Sdopoulos, and C. Coucoubets, Weghted oundobn cell multplexng n a geneal-pupose atm swtch chp, Selected Aeas n Communcatons, vol. 9, no. 8, pp , [13] M. Sheedha and G. Vaghese, Effcent fa queung usng defct ound-obn, IEEE Tansactons on Netwokng, vol. 4, no. 3, pp , [14] H. M. Chaska and U. Madhow, Fa schedulng wth tunable latency: a ound-obn appoach, IEEE/ACM Tansactons on Netwokng, vol. 11, no. 4, pp , 23. [15] L. Lenzn, E. Mngozz, and G. Stea, Tadeoffs between low complexty, low latency, and faness wth defct ound-obn schedules, IEEE/ACM Tansactons on Netwokng, vol. 12, no. 4, pp , 24. [16] S. S. Kanhee, H. Sethu, and A. B. Paekh, Fa and effcent packet schedulng usng elastc ound obn, IEEE Tansactons on Paallel and Dstbuted Systems, vol. 13, no. 3, pp , 22. [17] S. S. Kanhee and H. Sethu, Low-latency guaanteed-ate schedulng usng elastc ound obn, Compute Communcatons, vol. 25, no. 14, pp , 22. [18] Y.-C. Jenq, Pefomance analyss of a packet swtch based on snglebuffeed banyan netwok, IEEE Jounal on Selected Aeas n Communcatons, vol. 1, no. 6, pp , [19] D. Stlads and A. Vama, Latency-ate seves: a geneal model fo analyss of taffc schedulng algothms, IEEE/ACM Tansactons on Netwokng, vol. 6, no. 5, pp , [2] J.-L. Schabag, F. Rdouad, and C. Faboul, A pobablstc analyss of end-to-end delays on an AFDX avonc netwok, IEEE Tansactons on Industal Infomatcs, vol. 5, no. 1, pp , 29. [21] Functon safety of electcal/electonc/ pogammable electonc safetyelated system, IEC 6158, [22] M. Boye, N. Navet, M. Fumey, J. Mgge, L. Havet, and T. Avoncs, Combnng statc poty and weghted ound-obn lke packet schedulng n AFDX fo ncemental cetfcaton and mxed-ctcalty suppot, Poc. EUCASS, 213. [23] J. L, H. Guan, J. Yao, G. Zhu, and X. Lu, Pefomance Enhancement and Optmzed Analyss of the Wost Case End-to-End Delay fo AFDX Netwoks, Poc. GeenCom, 212. [24] L. Rao, Q. Wang, X. Lu, and Y. Wang, Analyss of TDMA cossba eal-tme swtch desgn fo AFDX netwoks, Poc. INFOCOM, 212. [25] H. Baue, J. Schabag, and C. Faboul, Wost-case backlog evaluaton of avoncs swtched ethenet netwoks wth the tajectoy appoach, Poc. Euomco Confeence on Real-Tme Systems (ECRTS), pp , 212. [26] H. Baue, J. Schabag, and C. Faboul, Impovng the wost-case delay analyss of an afdx netwok usng an optmzed tajectoy appoach, IEEE Tansactons on Industal Infomatcs, vol. 6, no. 4, pp ,