Timing Analysis of AVB Traffic in TSN Networks using Network Calculus

Transcription

1 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark Tmng nalyss of V Traffc n TSN Neworks usng Nework Calculus Lux Zao Paul Pop Zong Zeng Qao L bsrac Tme-Sensve Neworkng (TSN) s a collecon of sandards a exend Eerne o suppor safey-crcal and real-me applcaons. TSN negraes mulple raffc ypes.e. Tme-Trggered () raffc sceduled based on Gae-Conrol Lss (GCLs) udo-vdeo-rdgng (V) raffc a requres bounded laences and es-effor (E) raffc for wc no guaranees are provded. Ts paper proposes a Nework Calculus-based approac o deermne e wors-case end-o-end delays of V raffc n a TSN nework w bo non-preempon and preempon modes. We consder e effecs of raffc due o GCLs guard bands.e. me wndows a block oer raffc from ransmng and preempon overead on e servce for V raffc. We provde a proof of non-overflow condon for V cred wc s used o conrol e V raffc ransmsson. Te analyss meod s evaluaed on realsc es cases and compared o relaed work. Index Terms Tme-Sensve Neworkng; TSN; udo-vdeo- rdgng; V; mng analyss; Nework Calculus E I. INTRODUCTION erne [] s a well-esablsed nework proocol a as excellen bandwd scalably compably and cos properes. However s no suable for real-me and safey crcal applcaons. Terefore several exensons o Eerne proocol ave been proposed suc as RINC 664 Specfcaon Par 7 (FDX) [] Eerne [] and EerCT [4]. However ey are ncompable w eac oer and as a resul ey canno operae on e same pyscal lnks n a nework wou losng real-me guaranees [5]. Consequenly e IEEE 8. Tme-Sensve Neworkng (TSN) ask group [6] as been workng snce on sandardzng real-me and safey-crcal enancemens for Eerne. In s paper we consder a TSN s supporng V (8.) w e currenly fnsed sub-sandards IEEE 8.Qbv [7] Enancemens for Sceduled Traffc by addng a Tme-ware Saper (TS) and w 8.Qbu [8] for preempon. TSN classfes flows no e ree raffc-ypes based on e crcaly Tme-Trggered () raffc udo-vdeo rdgng (V) raffc [9] and es-effor (E) raffc. raffc suppors ard real-me applcaons a requre very low laency and jer. raffc as e ges prory and s ransmed based on scedule ables called Gae-Conrol Lss (GCLs) a rely on a global syncronzed clock (8.Srev []). V raffc s nended for applcaons a requre bounded end-o-end laences bu as a lower prory an raffc. V (8. ) nroduces wo new saped raffc classes (V Class and ) w bounded wors-case end-o-end delays (WCDs). V uses e Cred-ased Saper (CS) [9] o preven e sarvaon of lower prory flows. E raffc as e lowes prory and s used for applcaons a do no requre any mng guaranees. Te coce of raffc ype for messages depends on e parculares of applcaons. Te scedulably of e sceduled raffc can be guaraneed durng desgn pase by syneszng e GCLs []. However an V flow s scedulable only f s wors-case end-o-end delay (WCD) s smaller an s deadlne. loug laency analyss meods ave been successfully appled o V raffc n V neworks [4] [5] [6] [7] ey do no consder e effec a raffc as on e laency of V raffc n TSN. oreover n order o f for more general case [5] relaxes consrans of parameers (dle slope and send slope) of CS n 8.Qav proocol []. However s may cause cred overflow wc sould no be allowed [8]. Nework Calculus-based analyss o compue e WCDs of Rae-Consraned (RC) raffc w e consderaon of e sac sceduled frames n Eerne as been proposed [9] [] [] bu e ecnque s no applcable for TSN. RC raffc dffers from V and TSN scedules raffc dfferenly from Eerne: Eerne scedules eac ndvdual flows wereas n TSN e GCLs do no refer o ndvdual flows bu o e queues n e oupu pors of nework swces. [] gave smulaon resuls from a concepual mplemenaon of Eerne V w addonal raffc. However CS beavor w raffc n [] s dfferen w s paper wc may cause e cred overflow. nd smulaon gves e expermenal upper bound delays based on scenaros and canno be used for cerfcaons because of e mssed rare evens. Recenly e V Laency a equaon [9] as been exended o consder e raffc n TSN [] based on e same CS beavor w raffc. However dependng on e scenaro e analyss s bo unsafe.e. e delays calculaed are smaller an e exac WCDs and overly pessmsc.e. e WCDs deermned are very large (see Sec. VI for a comparson beween our proposed analyss and []). In addon can only be used o deermne e WCDs of Class V raffc. In s paper we are neresed o propose a mng analyss for V raffc n a TSN nework. Te man conrbuons are:

2 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark ES dl dr dl ES ES/SW TS GCL SW dl SW T T class queue G a e ES dr ES4... V C la ss q u e u e CS G a e SW Fg.. TSN nework opology example V C la ss q u e u e... E class queue CS... G a e... G a e TS We frs gve a proof of non-overflow condon for V cred based on general parameers of CS. Ts s a pre-condon of mng analyss for V raffc. We propose a Nework Calculus-based meod o deermne e WCDs of V flows n a TSN nework consderng e effecs of raffc conrolled by GCLs guard bands for e non-preempon mode and preempon overeads for e preempon mode. We derve e remanng servce curve for V Class and Class respecvely consderng e nonpreempon and preempon negraon modes. We evaluae e proposed approac on realsc es cases ncludng e Oron Crew Exploraon Vecle (CEV) and compare w relaed work.. rcecure odel II. SYSTE ODEL TSN nework s composed of a se of end sysems (ES) and swces (SW) also called nodes conneced va pyscal lnks. Te lnks are full duplex allowng us communcaon n bo drecons and e neworks can be mul-op. Te oupu por of a SW s conneced o one ES or an npu por of anoer SW. n example s presened n Fg. were we ave 4 ESes ES o ES 4 and SWs SW o SW. Te opology of TSN nework s modeled as an undreced G EV were V ES SW s e se of end sysems grap ( ES ) and swces ( SW ) and E s e se of pyscal lnks. V ES SW= ES ES ES ES SW SW For Fg. 4 SW and e pyscal lnks E are depced w black double arrows. dl v v L were L s e se of daaflow lnk a b daaflow lnks n e nework s a dreced edge from v a o v b were v a and vb V can be ESes or SWs. Te pyscal lnk rae s denoed as dl. C. In s paper we assumed a all pyscal lnks ave e same rae C. s ere s only one oupu por for eac daaflow lnk dl can also refer o e oupu por n v a assocaed w e lnk o v b. daaflow roung dr R s an ordered sequence of daaflow lnks connecng a sngle source ES o one or more desnaon ESes. For example n Fg. dr connecs e source end sysem ES o e desnaon end sysems ES and ES 4 wle dr Fg.. TS for an oupu por n ES/SW connecs ES o ES.. pplcaon odel Te asks of applcaons runnng n ESes communcae va flows wc ave a sngle source and may ave mulple desnaons. s menoned TSN suppors ree raffc classes: V and E. We assume a e raffc class for eac applcaon as been decded by e desgner. We defne e ses V _ w E V _ s e se of E all e flows n e TSN nework were e subscrp for V denoes e Class or. Te roung TC. dr of eac flow TC TC V _ E ) s known. For eac flow we know e frame sze l and e perod. s ransmsson n TSN s based on e p ( Gae-Conrol Lss (GCLs) relaed o queues bu no o ndvdual flows e perodcy of eac flow may no be mananed along s daaflow roung. V raffc s compable w e flow model n Eerne V [4]. Togeer w src prory scedulng Eerne V adds a Cred-ased Saper (CS) for eac raffc class. Te flows assgned e same prory belong o e same raffc class (Class or Class ) and frames wn eac raffc class are n FIFO order. For an V flow _ we _ V V know s frame sze l perod V _ p n e source ES V _ and e raffc class belongs o ( Class or ). III. TSN PROTOCOL In s secon we presen ow and V flows are ransmed n TSN. IEEE 8.Srev provdes a clock syncronzaon proocol o a global me base for ransmsson. Takng advanage of e global syncronzed clock IEEE 8.Qbv defnes a Tme-ware Saper (TS) o aceve low laency for raffc by esablsng compleely ndependen me wndows. Fg. gves an llusraon of TS for an oupu por of a node. Eac TS as eg queues for sorng frames a wa o be forwarded on e correspondng lnk one or more for queues wo for V (Class and respecvely) and remanng for queues are used for E. Wen frames from crcal flows arrve a npu pors ey are flered no queues based on er sream denfcaon usng e per-sream flerng and polcng funconaly defned n IEEE

3 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark q ES q q V _ q V _ 4 SW q dr a conenon non-preempon guard band f V _ T C f f f V _ T C q V _ b preempon f f V _ T C q ES q V _ dr addonal fragmen overead Fg. 5. Two negraon modes: non-preempon and preempon q q V _ q V _ 4 q Qc []. Every queue as a gae w wo saes open and closed. Frames wang n e queue are elgble o be forwarded only f e assocaed gae s open. TS conrols e gaes for eac queue accordng o a Gae-Conrol Ls (GCL) wc s desgned offlne and conans e mes wen e assocaed gaes are open and closed. Te GCL s defned for eac oupu por of an ES or SW see e example n Fg.. In e fgure GCLs are gven by ables below e respecve queues. Te open and closed saes are respecvely represened by and. For example e gae for queue (lg green) n ES s open from me o and closed from o 5. Usng e GCLs o scedule forwardng of frames n a roue from source ES o desnaon ES enables raffc suable for ard real-me communcaon. Te leng of GCL s lmed and s repeaed afer a yperperod p wc s e Leas Common ulple GCL (LC) of perods of e nersecng flows sarng e oupu por. Fg. 4 sows usng a Gan car ow frames are ransmed usng e GCLs from Fg.. Te x-axs represens me dmenson wle y-axs s relaed o oupu pors of nodes. oreover e recangles represen frames ransmsson. Te lef sde of recangle means e sar me of e frame ransmed and s wd represens e ransmsson duraon wc s relaed o e frame sze and e pyscal lnk rae. Le us assume a ere are wo flows and q V _ q V _ Fg.. n example of GCLs for oupu pors n ES/SW E S S W E S S W S W S W p p s 5 s a fra m e o f yp e rp e ro d s a fra m e o f Fg. 4. Scedules of frames on daaflow lnks 4 respecvely sen from ES and ES w perod s and 5 s. Ten nex suc wo flows wll be mulplex and sare e queue of oupu por n SW. Tere s an equvalence relaonsp beween e se of GCLs n Fg. and e scedules of frames on daaflow lnks for e assocaed oupu pors sown n Fg. 4. For example a me e gae for raffc n ES s open erefore e frame of s naed o be ransmed from ES SW. Researcers ave proposed meods o synesze e GCLs [] [5] and ave oulned e consrans a ave o be sasfed for scedule feasbly. For example wen assocaed gae for raffc s open e remanng gaes for oer raffc are closed and vce versa. In Fg. e red and blue queues are respecvely dedcaed for Class and of V raffc. me and n SW e gae for e queue s open wle e gaes for bo V Class and Class queues are closed. Durng s perod of me frames from V raffc are forbdden o ransm unl e gae s closed and assocaed V gaes are open from me 4. Terefore V and E raffc are prevened from nang ransmsson n e me wndows reserved for frames. However f an V or a E frame s already n ransmsson a e begnnng of me wndow for (see Fg. 5) raffc may be delayed. Hence TSN uses wo negraon modes. One s non-preempon guard band before eac me wndow of frame [7] as sown n Fg. 5a. Te guard band as e leng of a mum-szed frame a may nerfere w e respecve raffc wc n e wors-case s e Eerne axmum Transmsson Un (TU) of 5 byes. Durng e guard band e gaes assocaed w V and E raffc are closed n advance o make sure a e lnk s dle wen a queue s open for ransmsson. Te non-preempon negraon mode wll lead o wased bandwd due o e guard band bu ensures no delays for raffc. Te oer negraon mode s e preempon mode defned by IEEE 8.Qbu [8] as sown n Fg. 5b. W preempon an V frame wll be nerruped by a frame and s ransmsson s resumed from e soppng pon once e ransmsson of e frame complees. Wen a gae for queue s ready for open e assocaed gae for e preempable V frame wc s already n e process of beng ransmed s open for e duraon o fns ransmng a fragmen before openng e queue [8]. Ten wen resumng ransmsson e remanng V frame wll nclude an overead used o separae and

4 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark 4 cred cred a V _ f E d S l a V _ f E d S l a V _ guard band reassemble a e desnaon ES. Compared o e guard band overead can be neglgble and erefore e use of preempon wll decrease e laency of V raffc and ncrease bandwd. However wll nroduce jer for raffc. Te avalably of an V queue s also deermned by a Cred-ased Saper (CS) and e purpose of CS s o preven e sarvaon of lower prory flows. Hence an enqueued V frame s allowed o be ransmed f () e queue gae s open () e CS allows and () ere are no oer ger prory V frames beng ransmed. In e followng le us frs explan ow CS works n TSN. Eac V class as an assocaed cred value. Te ransmsson of an V frame canno be naed wen s cred s negave. nd e cred s nalzed o zero. In V nework [9] f e V queue no empy cred can be decreased w a send slope ) durng e sdsl ( ransmsson of an frame of V Class and ncreased w an dle slope ) wen Class frames are dsl ( f 4 a V _ f V _ s d S l f V _ (a) non-preempon f overead (b) preempon Fg. 6. CS example a a s d S l a V _ a V _ d S l d S l f V _ s d S l wang o be ransmed. oreover f e V queue s empy and s cred s posve e cred s se o zero; oerwse s ncreased w dle slope unl zero. Ts s also e same w e suaon n TSN nework f e gae for assocaed V raffc queue s open. esdes n TSN nework ere needs addonal consderaon abou V cred wen e me gae s closed wc s sll an open queson [7]. To avod e cred overflow we are neresed o e frozen form n s paper.e. e cred s frozen wen e assocaed V gae s closed. We sow an example n Fg. 6 ow CS works nerfered w and E frames respecvely w wo negraon modes. Recangles on e frs melne represen e ransmsson of frames and down arrows on op gve e arrval mes of frames. Polylnes on e second melne sows e varaon of cred for respecve V class were V Class and are respecvely sown w red and blue. Fg. 6a s sown w e non-preempon mode. n V Class frame f arrves a V _ meanwle a E frame s on ransmsson. Due o non-preempon of E frames f as o wa unl f V _ s d S l 7 8 f V _ V _ f V _ 9 8 f fnsng s ransmsson and cred s ncreased w E e dle slope dsl. me e ransmsson of f s E done. However e V gaes are closed due o e reservaon for raffc and nsuffcen dle nerval (caused guard band) for e wole frame f ransmsson. Terefore cred V _ s frozen durng 4 wen V gaes are closed. Even f an V Class frame f arrves a V _ s cred sould also be frozen. From me 4 snce e gae for queue s closed and Class as ger prory an Class f s allowed V _ o be ransmed. Cred and are respecvely decreased and ncreased w e send slope sdsl and dle slope dsl. Durng e ransmsson of f anoer frame f s V _ V _ enqueued n e Class queue a me 5. Ten a 6 wen frame f fnses ere are wo frames f and V _ V _ V _ f wang o be ransmed. u cred a s me s negve erefore f s no allowed o ransm and V _ V _ f obans e ransmng permsson. e end of f ransmsson f sars ransmsson as s cred V _ V _ as ncreased o greaer an. In Fg. 6b e arrval mes are all e same compared n Fg. 6a. However due o e preempon negraon mode e frame f s delayed from o 4 and e remanng frame f s added w V _ an overead. In addon we can fnd a e ransmsson of V frames n Fg. 6b are fnsed earler an n Fg. 6a. IV. NETWORK CLCULUS CKGROUND Nework Calculus [6] s a maure eory proposed for deermnsc performance analyss. I s used o consruc arrval and servce curve models for e nvesgaed flows and nework nodes. Te arrval and servce curves are defned by means of e mn-plus convoluon. n arrval curve s a model consranng e arrval process R of a flow n wc R represens e npu cumulave funcon counng e oal daa bs of e flow a as arrved n e nework node up o me. We say a R s consraned by f R nf Ru u R u were nf means nfmum (greaes lower bound) and s e noaon of mn-plus convoluon. ypcal example of an arrval curve s e leaky bucke model gven by were represens e mum burs olerance of e flow and s e long-erm average rae of e flow.

5 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark 5 servce curve models e processng capably of * R s e deparure e avalable resource. ssume a process wc s e oupu cumulave funcon a couns e oal daa bs of e flow deparure from e nework node up o me. We say a e nework node offers e servce curve for e flow f * R nf Ru u R u ypcal example of e servce curve s e rae-laency servce curve gven by R T RT were R represens e servce rae T represens e servce laency and e noaon x s equal o x f x and oerwse. If a flow e servce curve R of arrval curve bounded by e arrval curve ' across a server w * en e oupu flow R ' can be sup u u u were sup means supremum (leas upper bound). Le us assume a e flow consraned by e arrval curve raverses e nework node offerng e servce curve. Ten e laency experenced by e flow n e nework node s bounded by e mum orzonal devaon beween and sup nf s s s V. WORST-CSE NLYSIS FOR V TRFFIC. Non-overflow condon for V raffc We frs gve e non-overflow condon for V cred n s secon wc s e pre-condon o bound e cred of V Class and us o e subsequen servce analyss for e V raffc. Le us recall from Sec. III ow V s ransmed. In TSN nework e ransmsson of V raffc s no only relaed o e gae saes bu also o CS. loug ransmssons n bo preempon and non-preempon modes delays V raffc e creds for bo classes are frozen durng ese perods. Terefore we can say a V creds wll no be affeced by raffc. In fac e cred value s relaed o e ransmsson and backlog of V frames durng respecve V gae open and sengs of dle slope dsl and send slope sdsl for eac raffc class wc are confguraon parameers gven by desgner. 8.Qbv [7] gves e cred consrans beween dsl and sdsl.e. sdsl dsl C and [5] consders e more general suaon assumng any dsl and sdsl. However w any knd of parameers for V raffc and e overloaded V raffc may cause e cred overflow wc s a problem a may cause e falure of e an-sarvaon funcon of CS and sould no be allowed. Tus we need o consran dsl and sdsl o make sure e cred of Class s bounded n more general suaon. Ts as no been dscussed n e leraure so far. s Class as ger prory s cred sould be decreased w e assocaed frame ransmsson as soon as e cred s larger an a e end of e ransmsson of anoer lower prory class frame and be ncreased wen e cred s smaller an a e end of e ransmsson of a Class frame. Terefore for any dsl and sdsl cred can sll be bounded by [5] sdsl C lv _ cred l V _ le dsl C u due o e lower prory of Class s cred can be ncreased f frames of Class allows o be ransmed no maer weer e cred s smaller an. Terefore cred may overflow f a greedy Class appens.e. always sendng daa for example n Fg. 7. s e cred s frozen durng e ransmsson and guard bands w bo non-preempon and preempon modes Fg. 7 gnores e frozen pars wen dscussng s problem. In s secon we are neresed o gve e consrans condon a cred does no overflow n more general suaon as gven n e followng Teorem. Teorem Te non-overflow condon of cred s sdsl sdsl dsl dsl Proof: y P y P y Q P Q Class Class Te cred s ncreased only wen Class frames wang n e queue. Ten n e frs rsng perod n Fg. 7 e upper bounds of cred can be reaced a e end of e ransmsson of a mum E frame and e mum number of Class frames w e mum sze. Suc as e duraon n Fg. 7 cred and are ncreased due o e mum E frame ransmsson and en cred ncreases o e upper bound P wen cred sars a e mum value and fnses a e mnmum value as gven n formula (4). P Fg. 7. Example of cred of Class nfnely ncreasng

6 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark 6 However due o e arbrarness of dsl and sdsl P n e frs rsng of cred may no be e real upper bound. s sown n Fg. 7 y s larger an y. Ten a me P even f ere are frames n queue ey canno be forwarded because of e negave cred. Terefore cred mus be ncreased nex and Class raffc obans e servce and s cred s decreased. s long as cred s larger an Class raffc w ger prory wll regan e servce for e wors-case duraon o fns e curren Class frame ransmsson regardless of weer cred s greaer an. ssume a Class regans servce a pon Q n Fg. 7 and a s me cred s decreased from pon P by mn cred yq dsl sdsl P were y Q s e ordnae value of pon Q. Ten cred s decreased agan from e pon Q and cred goes no e second rsng perod. Te mum servce me for Class n e second servce perod s mn y cred sdsl Q s me cred reaces e second ges pon P and s ncreased by dsl Te above dscusson also apples o e subsequen rsng perod of cred. Ten o make cred ncrease fnely yp yp ( ) sould be always rue were P s e ordnae value of e ges pon n e rsng perod of cred. Terefore e non-overflow condon of upper bound of cred s.e. mn sdsl dsl yp y P yq cred dsl sdsl sdsl sdsl dsl dsl W e non-overflow condon n more general case e bounds of cred sasfy [5] sdsl le l V _ dsl lv _ cred ln dsl C C sdsl C were l n lv _ le.. Servce Curve for V raffc w non-preempon and preempon modes In s secon we focus on e servce curve analyss for ) avalable n an oupu por by V Class ( consderng e presence of raffc w e non-preempon and e preempon modes respecvely. Le us sar by dscussng e aggregae arrval curve consderng e mpac of raffc n e oupu por as e remanng servce for V raffc depends on. In Eerne nework aggregae arrval curve s obaned by summng e arrval curve of eac sngle nersecng perodc flows sfng w relave offses []. However n TSN GCLs conrol e gae saes for queue and no e frames. If end sysems are non-sceduled [] flows may lose e naure of e perodcy along e ransmsson pa. In s paper we esabls e aggregae arrval curve w e mpac of raffc based on e raffc wndow. In addon e consran of gurad band effec for e non-preempon mode s merged no e aggregae arrval curve and e consran curve of overeads for e preempon mode s also bul. s menoned n Sec. III e GCL for an oupu por s repeaed afer e yperperod p. Terefore any raffc wndow akes p GCL as a cycle. For a gven GCL n an oupu por can be known a e fne number of raffc wndows n e yperperod p wc s assumed w N. example n Fg. 8 o and o respecvely represen e GCL For example N equals o n Fg. 8. In addon we can also know wen e gae opens and ow long lass. I s assumed a e leng of e raffc wndow n e oupu por s wren as GCL L ( N ) as sown n Fg. 8. oreover e relave offse o j ( j N ) beween e sarng me of e and j wndows s known by akng e wndow as e reference. For offses by akng e wndow w leng L as e reference. Noe a o j equals o f j. Ten a possble aggregae arrval curve can be gven by were a fra m e o f Lj yp e rp e ro d p G C L L L L o o a fra m e o f Fg. 8. GCL for raffc n an oupu por o N j Lj C j pgcl C represens e mum number of bs a a fra m e o f

7 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark 7 yp e rp e ro d p G C L yp e rp e ro d p G C L L L L G G G o o o L o L L a fra m e o f a fra m e o f a fra m e o f a fra m e o f a fra m e o f a fra m e o f Fg. 9. Guard bands before raffc wndows could be ransmed durng e raffc wndow of leng L j ; eac sarcase funcon represens e upper bound of ransmsson n e perodc raffc wndows of leng e relave offses gve e relaonsps beween dfferen raffc wndows n e yperperod. Te proof of formula () s smlar o a n []. Ten by selecng dfferen raffc wndows n e yperperod as e reference we wll oban a se of possble aggregae arrval curves ( N ) from (). In e wors-case e aggregae arrval curve s e upper envelope of all ese possble curves as gven by. Lemma Te aggregae arrval curve for nersecng flows n an oupu por s N However for e non-preempon mode e guard band s esablsed before eac me a e raffc ransmsson sars. Ten e V ransmsson s no permed beween e sar of e guard band and e sar of e raffc wndow. In e wors-case e guard band L before e ( N ) raffc wndow s as long as e mnmum of e ransmsson me of mum sze of V frames compeng e oupu por and dle me nerval beween wo consecuve raffc wndows.e. N % N and wndows. For example n Fg. 9 L G equals o e ransmsson me of e mum V frame snce ere s a muc larger dle me beween e nd and e raffc wndows. u L G equals o e dle me beween e and e s wndows wc s smaller an e ransmsson me of e mum V frame. For e consran of guard bands [] consrucs a separae overall guard band (also called mely block n Eerne) curve. u n s paper we wll G G L ; j merge guard bands effecs no e consrucon of aggregae arrval curve due o e fac a guard bands may only appear mmedaely before eac raffc wndow and e cred for e respecve V raffc s frozen durng guard bands and raffc wndows. Here s assumed as a new wndow called G+ wndow w leng L LG. Lemma W e non-preempon mode e aggregae arrval curve for nersecng flows and guard bands n an oupu por s gven by o L L N j G j G G Lj LG j C N j pgcl wc s smlar o e curves n () and (). Here we ave j G j L L C jus by addng e wors-case number of bs caused by e j guard band o e mum bs of frames ransmed n e j raffc wndow bo of wc pospone e servce for V raffc. oreover due o e possble of dfferen leng of guard band e dsance beween new G+ wndows may cange wc s refleced by L L n (). G j G For e preempon mode f an V frame s preemped an overead s added w e remanng V frame. In e wors-case eac raffc wndow preemps a frame of V Class as sown n Fg.. I s assumed a e leng of e overead s L C. Overeads can be aken as e separae par causng e laency of V raffc. Snce e overead wll only appear mmedaely afer eac raffc wndow e consran curve of overeads can be gven by e followng Lemma. Lemma W e preempon mode e overead arrval curve n an oupu por s gven by o L j N j L C N j pgcl were L j s e leng of j raffc wndow. In e followng we focus on e analyss of servce curve for V Class n e oupu por. Regardless of modes any me nerval can be decomposed by Fg.. Overeads afer raffc wndows were represens e rsng me of cred j j represens e descen me of cred and k k s e frozen me of cred as sown w cred for example n Fg.. Te servce could only be suppled for V raffc durng e descen me of cred. Ten e remanng servce for V raffc w respecve negraon modes s gven n e followng eorems.

8 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark 8 Teorem Te servce curve for V Class ( ) w non-preempon mode n an oupu por s gven by npr V_ u C dsl G cred supu dsl sdsl u C dsl were npr represens e non-preempon negraon mode G s s gven by Lemma f for non-preempon mode and cred cred cred s e upper bound of cred gven by (4) and (9). Proof: ssume a R (resp. R G * * * R (resp. R RG R ) and ) are e arrval and deparure processes of V flows of Class (resp. flows guard bands) crossng roug e oupu por. Le s be e begnnng of e laes server busy perod. me s e * R s R s backlogs for all flows are empy.e. * R s R s * R s R s and cred s. f E guard band G f f V _ G For some arbrary me s e nerval s can be decomposed by For e non-preempon mode s caused by e guard bands and raffc wndows.e. G and represens e duraon of frame ransmsson of V Class. Terefore we ave. V _ f V _ f V _ G (a) non-preempon f E f V _ f Ten e varaon of cred durng e me nerval sasfes overead f V _ V _ (b) preempon f V _ Fg.. Decomposed nerval w dfferen negraon modes cred cred s cred dsl sdsl G dsl V _ dsl sdsl Terefore w non-preempon mode we oban e relaonsp of servce mes for V Class raffc and guard bands n any nerval V _ G dsl cred dsl sdsl (7) oreover for e wors-case e oupu frames of raffc durng can be gven by R R s R R s C * * * and smlarly e wased servce durng s due o guard bands R R s R R s C. * * * G G G G G Tus can be lmed by G G G C R R R s R s C G Ten consderng (7) and (8) e oupu frames of V Class over e nerval s bounded by R R s C * * V _ C C dsl cred G dsl sdsl Snce e deparure cumulave funcon wde-sense ncreasng funcon we ave and * * sup R R s Terefore u s C * * R R s * u u C dsl cred R s a G dsl sdsl..

9 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark 9 * R R s npr V _ u C dsl G cred sup u u dsl sdsl C dsl s Ten for s npr npr * s V V R nf R s s R. npr Tus w non-preempon negraon mode s e servce curve for V Class. V _ Teorem Te servce curve for V Class ( w preempon mode n an oupu por s gven by. ) pr C dsl u u V_ sup u dsl sdsl u C C dsl sdsl cred dsl dsl were pr represens e preempon negraon mode and are respecvely gven by Lemma and Lemma. Proof: ssume a R (resp. R * * * R (resp. R R R ) and ) are e arrval and deparure processes of V flows of Class (resp. flows overeads) crossng roug e oupu por. Le s be e begnnng of e laes server busy perod. me s e backlogs for all * * R s R s R s R s flows are empy.e. * R s R s and cred s. For e preempon mode represens e leng of raffc wndows durng e arbrary nerval s and can be broken down no e duraons of frame ransmsson of V Class and overeads duraon due o preempon.e. V _ Ten e varaon of cred n sasfes cred cred s cred dsl sdsl dsl V _ dsl sdsl Tus w preempon mode we oban e relaonsp of servce mes for V Class addonal servce me for V overeads and wndows duraon n any nerval V _ dsl dsl sdsl cred dsl sdsl Snce for e wors-case e oupu frames of raffc durng s R R s R R s C * * * and e addonal servce for V overeads durng gven by Tus R R s R R s C. * * * can be lmed by * and smlarly can be R R s C C sasfes C Ten consderng () () and () e oupu frames of Class over e nerval s bounded by * * C dsl V _ dsl sdsl C R R s C dsl sdsl cred C dsl dsl pr Smlarly we can ge e servce curve for V V _ Class w e preempon negraon mode. ccordng o e nework calculus eory e upper bound laency of an Class flow n e oupu por s V _ gven by e mum orzonal devaon beween e arrval curve of nersecng flows of V Class and e V _ servce curve for V Class n e oupu por V _ D V _ V _ V _ were e servce curve s from Teorem or Teorem dependng on wc negraon modes o coose. Te arrval curve n e oupu por of e node can be gven by

10 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark TLE I PRETERS OF TRFFIC IN TC WCDs ( s ) V _ V _ V _ V _ V _ were V _ s e burs of e flow V _ n and V _ s e long-erm rae of V _ n. In e oupu por of source end sysem V _ lv _ and l p. In addon e oupu arrval V _ V _ V _ curve V _ ' for e oupu por can be aken as e npu arrval curve for e nex oupu por of e V _ node along e daaflow roung of V _ and can be gven by [6] NC/TSN RTN6 Fg.. Comparson of WCDs by NC/TSN and RTN6 D V _ V _ V _ D V _ V _ V _ y dssemnang e compuaon of laency bounds along e roung V _. dr e WCD of e flow s obaned by V _ e sum of delays from s source ES o s desnaon ES D D d V _ V _ ec V _. dr were d ec s e consan ecncal laency n a SW. VI. EXPERIENTL RESULTS For e evaluaon of our approac we ave used four es cases based on e Oron Crew Exploraon Vecle (CEV) [8] adaped o use TSN respecvely named ere TC o TC4. CEV as a opology of ESes 5 SWs and 9 roues conneced by daaflow lnks ransmng a Gbps. Our proposed analyss s mplemened n C++ usng e RTC oolbox [9] runnng on a compuer w Inel Core 7-5 CPU a.9 GHz and 4 G of R. To compare our meod usng nework calculus (called NC/TSN) w e exsng approac n [] (called RTN6) V flows. (a) Frame szes and perods of raffc Flow Sze Perod Sze Perod Flow () (ms) () (ms) (b) Frame szes perods and raffc class of V raffc Flow Sze Perod Sze Perod ype Flow () (ms) () (ms) ype RC 6 5 RC RC 57 5 RC9 6 5 RC 7 5 RC 8 5 RC4 5 5 RC 8 5 RC5 4 5 RC 8 5 RC6 9 5 RC 48 5 RC RC4 8 5 RC8 5 RC RC9 5 RC6 6 5 RC 55 5 RC7 5 RC 6 5 RC8 4 5 RC 4 5 RC9 4 5 RC 4 5 RC 9 5 RC4 4 5 RC 68 5 RC5 4 5 RC 57 5 RC RC 6 5 RC7 4 5 RC4 7 5 we use a es case TC drecly from [] ncludng 5 flows and 4 V flows of Class. RTN6 can be only used o calculae e WCDs for V Class consderng e preempon mode. We sow e WCD resuls n Fg.. s we can see from Fg. RTN6 obans very pessmsc WCDs snce s aken as an approxmaon dependng on e scenaro. Our proposed analyss reduces e pessmsm on average by 98.% and 99.7% mum. In TC we are neresed o verfy ow our meod andles e wo negraon modes.e. non-preempon and preempon. TC s a more general case runnng 5 flows V flows of Class and 4 V flows of Class (ncludng mulcas flows). Te deals of e and V flows are presened n TLE I and e GCLs ave been generaed usng [5]. In addon e dle slopes of Class and are respecvely 6% and 5% of e oal bandwd and we assume a parameers of CS sasfes sdsl dsl C n s expermen. Te compared resuls are sown n Fg.. Te WCDs for e preempon and non-preempon modes are respecvely marked w x and symbols. WCDs are also dsngused w Class and by red and blue symbols respecvely. s expeced e laency bounds w e preempon mode are lower an e bounds w non-preempon mode snce e leng of e mum guard band s longer an e leng of preempon overead. On average non-preempon leads o 8.7% larger WCDs. Ts

11 Tecncal repor June 7 DTU Compue Tecncal Unversy of Denmark WCDs ( s ) preempon non-preempon V flows Fg.. Comparson of WCDs w preempon and non-preempon modes nomalzed WCDs % % 7% V flows Fg. 4. Comparson of WCDs under dfferen bandwd ulzaon number s relaed o e porosy of GCLs wc means e densy (nensve or sparse) of GCL wndows. In order o verfy e nfluence of wndows on V raffc we consder ree es cases TC TC and TC4 w dfferen bandwd ulzaon of raffc respecvely of % % and 7%. Here we assume a ere are same V raffc flows n suc ree es cases and e TSN nework s w e non-preempon negraon mode. Fg. 4 sows e compared resuls. In order o represen clearly we use e WCDs of V raffc obaned under 7% bandwd ulzaon of raffc as e baselne (e + symbols formng a orzonal lne).e. e values on e y-axs sow e percenage devaon of WCDs wc s normalzed o. Te upper bounds laency under oer bandwd ulzaon are normalzed Nor x D D 7% x V _ V _ 7% DV _ were x represens bandwd ulzaon of raffc. s sown n Fg. 4 snce raffc as e ges prory e ger bandwd s used by raffc e larger wll be e WCDs of V raffc as expeced. VII. CONCLUSION ND FUTURE WORK Ts paper sows ow e Nework Calculus approac can be appled for e laency bounds of V raffc n TSN neworks. Compared o e exsng approaces Nework Calculus approac provdes safe upper bounds on WCDs and reduces e pessmsm. Te paper consders bo negraon modes.e. non-preempon and preempon modes n a TSN nework. lso we model e nfluence of raffc wndows conrolled by e GCLs on e V raffc. frs conrbuon of s paper deals w a proof of non-overflow condon for V cred based on general parameers of CS wc s a pre-condon of mng analyss for V raffc. second conrbuon s e modelng of e arrval consrans of raffc based on e GCL wndows addonal guard bands for e non-preempon mode and exra preempon overeads for e preempon modes. rd conrbuon s a we derve e remanng servce curve for V Class and Class respecvely w e nonpreempon and preempon negraon modes. In e end s paper evaluaes e proposed approac on realsc es cases e Oron Crew Exploraon Vecle (CEV). Compared w e exsng approaces e approac n s

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