Using non-preemptive regions and path modification to improve schedulability of real-time traffic over priority-based NoCs

Transcription

1 Real-Tme Syst (2017) 53: DOI /s Usng non-preemptve regons and path modfcaton to mprove schedulablty of real-tme traffc over prorty-based NoCs Meng Lu 1 Matthas Becker 1 Mors Behnam 1 Thomas Nolte 1 Publshed onlne: 12 June 2017 The Author(s) Ths artcle s an open access publcaton Abstract Network-on-Chp (NoC) s a preferred communcaton medum for massvely parallel platforms. Fxed-prorty based schedulng usng vrtual-channels s one of the promsng solutons to support real-tme traffc n on-chp networks. Most of the exstng works regardng prorty-based NoCs use a flt-level preemptve schedulng. Under such a mechansm, preemptons can only happen between the transmssons of successve flts but not durng the transmsson of a sngle flt. In ths paper, we present a modfed framework where the non-preemptve regon of each NoC packet ncreases from a sngle flt. Usng the proposed approach, the response tmes of certan traffc flows can be reduced, whch can thus mprove the schedulablty of the whole network. As a result, the utlzaton of NoCs can be mproved by admttng more real-tme traffc. Schedulablty tests regardng the proposed framework are presented along wth the proof of the correctness. Addtonally, we also propose a path modfcaton approach on top of the non-preemptve regon based method to further mprove schedulablty. A number of experments have been performed to evaluate the proposed solutons, where we can observe sgnfcant mprovement on schedulablty compared to the orgnal flt-level preemptve NoCs. Ths work s an extended verson of the paper presented at RTCSA 2016 (Lu et al. 2016). B Meng Lu meng.lu@mdh.se Matthas Becker matthas.becker@mdh.se Mors Behnam mors.behnam@mdh.se Thomas Nolte thomas.nolte@mdh.se 1 Mälardalen Unversty, Västerås, Sweden

2 Real-Tme Syst (2017) 53: Keywords Network-on-Chp Real-tme traffc Response tme analyss Routng 1 Introducton Many-core processors are ganng a growng attenton n ndustry because of ther hgh computng capablty along wth lmted hardware cost. Such a platform conssts of a large number of components nterconnected wth each other. The data communcaton between components s typcally acheved by a Network-on-Chp (NoC) (Benn and DeMchel 2002). Wormhole-swtchng s a wdely used technque n the exstng NoC mplementatons (N and McKnley 1993). Under such a mechansm, once a router receves the header flt of a packet, the router can start to transmt wthout watng for the arrval of the whole packet. Consequently, each router requres much smaller buffers compared to a store-and-forward communcaton network (e.g. Ethernet). A number of network topologes have been desgned for NoCs, among whch the 2-dmensonal mesh-based archtecture s the most commonly used. In such NoCs, adjacent nodes are typcally connected by undrectonal channels through routers located on each node (e.g. Fg. 1a). Dfferent NoC desgns have been proposed n the lterature (e.g. Wentzlaff et al. 2007; Baron 2010; De Dnechn et al. 2014). In ths paper, we focus on vrtual-channel (VC) based NoCs (Dally 1992). Usng the VC technque, each physcal channel s shared by multple VCs. A transmsson control can be acheved at the output port of each router, so that preemptons between VCs can be supported. In most of related works usng the same NoC archtecture, preemptons can only happen between the transmsson of dfferent flts, but not durng the transmsson of a sngle flt. In Song et al. (1997), the authors have examned the applcablty of VC based wormholeswtched NoCs for real-tme traffc. For real-tme applcatons, the performance does not only rely on the functonal correctness, but t also depends on the tmelness. In other words, a number of specfc tme requrements must be fulflled (e.g. a packet needs to be transmtted wthn a gven tme duraton called deadlne), otherwse the system may get a degraded performance or t may even suffer catastrophc consequences. Therefore, whle runnng real-tme applcatons on NoC based many-core platforms, the tme propertes need to be consdered carefully. Due to ths reason, durng the desgn phase of a real-tme system, desgners need to verfy f all the tme requrements can be satsfed. In order to provde such a guarantee, real-tme NoCs may only admt a certan amount of traffc whch s much lower than the capacty that the network can actually handle. In other words, the desgned networks may not be suffcently utlzed, whch may cause a waste of resource. Therefore, n ths paper, we propose a new framework of VC based wormhole-swtched NoCs n order to mprove the schedulablty of the whole network, so that more real-tme traffc can be admtted. The proposed soluton ntroduces a non-preemptve regon to each NoC packet, so that the response tme (also known as end-to-end latency or traversal tme) of a packet can be potentally reduced wthout causng any deadlne mss of other packets. To select proper szes of non-preemptve regons, two heurstc approaches are proposed. Moreover, we also present a path modfcaton approach on top of the above soluton to further save flows from mssng ther

3 888 Real-Tme Syst (2017) 53: Fg. 1 a An example of a 2D-mesh based NoC. b Abstracts the router archtecture n order to support lmted-preemptve schedulng Compu ng Unt Router (a) Input Flt Processng VC Alloca on Swtch Arbtra on Flt Processng Route compute Preemp ve regon count-down Sgnalng swtch arbtra on (b) deadlnes when only applyng non-preemptve regons s not suffcent. Accordng to the evaluaton results, the proposed method of usng non-preemptve regons acheves hgher schedulablty ratos compared to the flt-level preemptve NoCs. The path modfcaton approach can further provde more sgnfcant mprovement on schedulablty, however, t requres much more processng tme especally when the network contans a large number of flows. 1.1 Contrbutons Ths paper ncludes the followng contrbutons: We present a new NoC framework where non-preemptve regons are ntroduced to NoC packets n order to mprove the schedulablty of real-tme traffc. Two heurstc approaches are proposed for selectng proper szes of nonpreemptve regons. A suffcent schedulablty test of the proposed framework s provded. A path modfcaton method s presented to further mprove schedulablty. A number of experments are mplemented, ncludng analyss based tests, smulaton based tests and an ndustral case study. The results clearly show the mprovement of the proposed solutons regardng schedulablty compared to the orgnal flt-level preemptve NoCs.

4 Real-Tme Syst (2017) 53: Related work For real-tme applcatons, t s mportant that the tme behavors are predctable. In order to guarantee the predctablty of NoCs, a number of research works have been proposed n the lterature, such as the Æthereal NoC (Goossens et al. 2005), the Tme-Trggered Network-on-Chp (Paukovts and Kopetz 2008), the Back Sucton flow-control scheme (Demer and Ernst 2010), and fxed-prorty based NoCs (Sh and Burns 2008, 2009b). To verfy f the gven tme requrements can be satsfed, sutable schedulablty tests are necessary durng the desgn phase of a real-tme system. Methods to compute the end-to-end latency of a packet n round-robn arbtrated NoCs have been presented n Ferrandz et al. (2009), Dasar et al. (2014). Targetng fxed-prorty based NoCs, the authors n Sh and Burns (2008, 2009a, b) present a Response Tme Analyss (RTA) based on the well-known analyss for task schedulng (Joseph and Pandya 1986). Kashf et al. (2015) have proposed a stage-level latency analyss whch can provde tghter estmates of latences compared to the analyss presented n Sh and Burns (2008). However, the stage-level analyss s based on a condton that, the buffer at each router s large enough such that the transmsson of a packet cannot be delayed because the buffer at a downstream router s full. Unfortunately, due to the desgn prncple of NoCs, the buffer sze of each router s typcally qute small (e.g. only holdng several flts (Wentzlaff et al. 2007; Baron 2010) whch does not support the above condton. When the buffer sze s not suffcent, the analyss n Kashf et al. (2015) can produce optmstc results. Recently, the authors n Xong et al. (2016) have shown that the analyss of Sh and Burns (2008) can be optmstc when a NoC buffer can hold more than a sngle flt, and they proposed a new method to resolve the optmstc problem. The network consdered n ths paper uses a fxed-prorty based schedulng polcy. Our proposed analyss s based on the work n Sh and Burns (2008, 2009a) wth modfcatons to support the new features. Task schedulng on a sngle-core processor has been well-studed n the past decades. Recently, lmted preemptve schedulng receves a growng attenton as a generalzaton of the exstng fully-preemptve and non-preemptve schedulng, whch can acheve better schedulablty compared to the tradtonal fxed-prorty based schedulng. The exstng lmted-preemptve schedulng uses three man approaches: (1) changng the prorty of a task once the task s executed (e.g. Saksena and Wang 2000; Wang and Saksena 1999); (2) executng certan parts of a task n a nonpreemptve manner (e.g. Brl et al. 2009; Bertogna et al. 2011a, b; Davs and Bertogna 2012); (3) a combnaton of the two former approaches (e.g. Brl et al. 2012). All these works target task schedulng on processors. However, to the best of our knowledge, such a technque has not been appled on data communcaton over NoCs. Therefore, n ths paper, we am to nvestgate the combnaton of wormhole-swtched NoCs and the lmted preemptve schedulng for real-tme traffc. We ntroduce a non-preemptve regon to each NoC packet, and we present algorthms to select sutable lengths of such regons.

5 890 Real-Tme Syst (2017) 53: Organzaton The remander of ths paper s organzed as follows. In Sect. 2, we present the network model consdered n ths paper. The transmsson polces for packets wth non-preemptve regons are descrbed n Sect. 3. Secton 4 recaptulates the exstng RTA for fxed-prorty based NoCs. Secton 5 llustrates more detals of the proposed non-preemptve regon based framework where we present dfferent algorthms to select the lengths of non-preemptve regons. In Sect. 6, we ntroduce the path modfcaton method based on the above framework. The evaluaton of the proposed approach s presented n Sect. 7. Fnally, n Sect. 8 we draw conclusons along wth some deas about future work. 2 Network model In ths paper we focus on a wormhole swtched NoC wth a 2D-mesh based topology. An example s shown n Fg. 1a, where each node contans a computng unt along wth a router. Each par of adjacent nodes are connected by a full-duplex lnk wth a fxed bandwdth. The network contans a set F of n perodc or sporadc real-tme packet flows denoted as F ={f 1, f 2,..., f n }. A flow refers to a seres of packets that have the same characterstcs. Each flow contans an nfnte number of packets (also called nstances herenafter). A flow f can be characterzed as f ={L, T, D, P, R }. L represents the complete packet sze of f ncludng all the necessary segments (e.g. payload, header, tal-flt, etc.). T denotes the perod f f s perodc, or the mnmum nter-arrval tme f f s sporadc. Each flow has an arbtrary relatve deadlne, whch s denoted by D.Aflow f s defned as schedulable, f ts response tme R s no larger than the deadlne D (.e. R D ). The flow set F s defned as schedulable, f all the flows n F can meet ther deadlnes (R D, f F). P represents the unque 1 fxed-prorty of f. Each flow f has a fxed transmsson route/path (denoted as R ) whch ncludes all the lnks from the source node (denoted as Sr ) untl the destnaton node (denoted as Ds ). We assume that the buffer sze of each router s one flt n order to smplfy the current tme analyss. An extenson consderng arbtrary buffer szes wll be conducted n the future work. 3 Transmsson polcy In ths secton, we present the transmsson polcy used n the proposed framework where packets can have non-preemptve regons, along wth some dscussons regardng the hardware support. The flt-level preemptve schedulng has been presented n many earler works. Under such a mechansm, once a router receves a sngle flt of a packet, the router 1 In ths paper, we only assume dstnct prortes. However, we need to clarfy that usng a prorty sharng polcy does not requre any change n the proposed framework. Alternatvely, the tmng analyss and the selecton of non-preemptve regons need to be modfed.

6 Real-Tme Syst (2017) 53: can start to transmt the receved flt wthout watng for the arrval of the complete packet. The routng nformaton s commonly stored n the header flt of each packet. When a router receves a header flt, the router needs to determne the followng transmsson route and assgn the packet to a specfc VC. The followng flts can thus be transmtted drectly usng the assgned VC wthout requrng a complete processng. Snce the transmsson unt s flt, preemptons cannot occur durng the transmsson of a sngle flt, but can happen between the transmssons of two successve flts. Thus ths type of schedulng s named flt-level preemptve schedulng. Our proposed framework s based on the flt-level preempton wth a modfcaton of non-preemptve regons. Ths approach s nspred by the work presented n Bertogna et al. (2011a), where the authors show that by addng non-preemptve regons to tasks, the schedulablty of the whole fxed-prorty based task set can be effectvely mproved. In a tradtonal flt-level preemptve NoC, each flt can be consdered as a nonpreemptve regon, snce ts transmsson cannot be preempted. In our framework, we group a number of successve flts nto one larger non-preemptve regon. To smplfy the mplementaton as well as the analyss, the non-preemptve regon s always placed at the end of each packet. The remanng flts, whch are ahead of the non-preemptve regon, wll be transmtted as usual usng the flt-level preemptve schedulng. These flts are thus called the preemptve regon of a packet herenafter. Ths approach s n between of the flt-level preemptve schedulng and the complete non-preemptve schedulng, thus t can be named as lmted preemptve schedulng. An abstract of the router archtecture s presented n Fg. 1b, whch s smlar to the router proposed n the Intel SCC (Baron 2010). The man structure s the same as found n routers used n other prorty based wormhole-swtched NoCs. Addtonally, the flt processng block of each router requres a modfcaton, n order to support the lmted preemptve schedulng. The sze of the non-preemptve regon of each packet s computed offlne (more detals n Sect. 5) and stored n the header flt. When the header flt of a packet arrves at a router, the router wll set a counter of the preemptve regon. The counter s used to montor the dstance to the non-preemptve regon of ths packet. When the nonpreemptve regon has not been reached, the flts are transmtted usng the flt-level preemptve schedulng where the utlzed VC uses ts ntal prorty level. Once the non-preemptve regon s about to be transmtted on an output lnk, the correspondng VC wll swtch to the hghest prorty level such that no other packet can preempt at ths router. Consequently, at each router, only one packet can be n the non-preemptve state. The event to promote the prorty of a packet s mplctly propagated by the packet tself and hence affects each router ndependently. In other words, no synchronzaton s requred between routers. When the last flt of the non-preemptve regon has passed, the correspondng VC wll swtch back to ts orgnal prorty level. Snce only one VC at each router can have non-preemptve transmsson at a tme, we only need to reserve one addtonal prorty level at each router whch s hgher than the ntal prortes of all the VCs. Note that when a packet s n the non-preemptve state at a certan router, the proposed method only guarantees that ths packet cannot be preempted at ths router and all upstream routers (.e. the routers along the path towards the source node). However, ths packet can suffer preemptons at downstream routers (.e. the routers

7 892 Real-Tme Syst (2017) 53: along the path towards the destnaton node), because the preemptve regon transmtted ahead can stll be preempted whch can further delay the transmsson of the non-preemptve regon. In other words, when the transmsson of a packet reaches ts non-preemptve regon at a router, ths packet s not completely non-preemptve. Ths s one of the man dfferences between non-preemptve regons n packets over NoCs and non-preemptve regons n tasks on sngle-core processors. When a task on a sngle-core processor reaches ts non-preemptve regon, t cannot be preempted by any other tasks. Therefore, the effect of utlzng non-preemptve regons on NoC packets may not be as sgnfcant as on tasks on sngle-core processors. 4 Recaptulate the RTA for flt-level preemptve NoCs In Sh and Burns (2008), the authors have presented a RTA for NoCs wth dstnct prortes. Ths analyss s extended later n Sh and Burns (2009a) to support a prorty sharng polcy as well as arbtrary deadlnes based on the results n Lehoczky (1990). However, the analyss n Sh and Burns (2009a) does not nclude the blockng delay caused by lower prorty flows, and the ncluded delays caused by the prorty sharng mechansm s not necessary for ths paper. Therefore, we frst present a modfed analyss based on the work presented n Sh and Burns (2009a). Smlar to the analyss presented n Sh and Burns (2009a), the maxmum length of the -level busy-perod can be computed as W = B + W T C + I (W ) (1) where B, C and I represent the blockng delay (caused by flows wth lower prortes), the basc transmsson tme, and the nterference (caused by flows wth hgher prortes) of f respectvely. The blockng delay B can be calculated as B = L R max ( f p S B ) (L R p ) δ p (2) where S B s a flow set ncludng all the flows whch can cause blockng to f, and δ p represents the length of the blockng that f p can cause to f at each hop. Under the flt-level preemptve mechansm, δ p equates to the transmsson tme of a sngle flt over one lnk (denoted as τ). The basc transmsson tme (.e. wthout any blockng or nterference) of f over R (denoted by C ) s computed as C = ( L ς ) + noh(sr, Ds ) τ (3) where ς denotes the sze of a sngle flt, and noh(sr, Ds ) represents the number of hops along the route of f.

8 Real-Tme Syst (2017) 53: If a flow f j (P j > P ) shares certan lnks wth f, the transmsson of f j can ncrease the response tme of f by causng nterference. Ths type of nterference s called drect nterference. However, even f a flow f x (P x > P j > P ) does not share any lnk wth f, f x can stll affect the response tme of f. Such behavor can happen when f x share lnks wth f j. By causng drect nterference to f j, f x can change the mnmum nter-arrval tmes between nstances of f j, whch can further affect the response tme of f. Ths type of nterference that f x causes to f s named ndrect nterference. In Sh and Burns (2008), the authors show that the effect of ndrect nterference can be bounded by addng an extra jtter (named nterference jtter, denoted by J j I )to f j durng the analyss of f. Such a jtter of f j can be upperbounded by R j C j. The nterference delay of f wthn a tme duraton of W can then be computed as I (W ) = f j S D W + J I j T j C j (4) where S D represents the set of flows whch can cause drect nterference to f. Equaton 1 can be calculated usng fxed-pont teratons (Joseph and Pandya 1986). The calculaton starts wth W (0) = B + C, and termnates when the computed W converges (.e. the mnmum n s found that W (n 1) = W (n)). Once W s calculated, the number of nstances wthn the largest -level busy-perod can be computed accordngly as K = W Assume that the frst nstance of f (.e. denoted by f,1 ) s released at tme 0, then the fnshng tme of any nstance f,k ( k K ) wthn the -level busy-perod can be calculated as F,k = B + kc + I (F,k ) (6) The response tme of each nstance can then be computed as T (5) R,k = F,k (k 1) T (7) Accordngly, the Worst-Case Response Tme (WCRT) s calculated as R = max (R,k) (8) k [1,K ] 5 Schedulng NoC packets wth non-preemptve regons As presented n Sect. 3, n our proposed framework, a non-preemptve regon s ntroduced to each NoC packet whch s placed at the end of each packet. Wth an ncreased non-preemptve regon, a flow can get less nterference, but t can also cause

9 894 Real-Tme Syst (2017) 53: A B C D E Fg. 2 An example of NoC flows wth non-preemptve regons more blockng to hgher prorty flows at the same tme. Therefore, the szes of nonpreemptve regons need to be carefully selected. We frst revse the RTA presented n Sect. 4 to support non-preemptve regons n NoC flows. Then we propose a soluton to compute the blockng tolerance of each flow. Fnally, the sze of the non-preemptve regon of each flow can be selected based on the computed blockng tolerance. 5.1 Extended RTA of packets wth non-preemptve regons On a sngle core processor, once the executon of a non-preemptve regon of a certan task starts, ths executon cannot be preempted by any other task. However, on a wormhole-swtched NoC, when a non-preemptve regon of a certan flow starts ts transmsson, t can stll be preempted. For example, assume that f x has the lowest prorty n the example shown n Fg. 2. Assume that a non-preemptve regon of f x starts ts transmsson on Lnk(A, B) at tme t, and the head of the non-preemptve regon arrves at node B at t 1.Flow f whch has hgher prorty than f x arrves at node B at tme t 2 whch s slghtly earler than t 1 (.e. t < t 2 < t 1 ). In ths case, f x has to wat untl f releases Lnk(B, C), even though f arrves at the route of f x durng the transmsson of the non-preemptve regon of f x. Thus, we pont out a fact that the non-preemptve regon of a flow f s completely non-preemptve, when the head of the non-preemptve regon starts ts transmsson on the output-lnk of N lasti. N lasti s the frst node n R, after whch no more flows wth hgher prortes can encounter f for the frst tme. For example, assume that f has the lowest prorty n the example shown n Fg. 2. N lasti wll be node B, snce f x and f j encounter f at node B for the frst tme. Once the non-preemptve regon of f starts ts transmsson on Lnk(B, C), t cannot be preempted any more. Based on the above dscusson, we dvde the response tme of the kth nstance of f nto two parts: R,k = R pe,k + Rnpe,k (9) (1) the frst part (denoted as R pe,k ) s the tme duraton snce f,k s released on the network untl the non-preemptve regon (.e. the last segment of a packet) s about to be transmtted on N lasti, durng whch the transmsson of f,k s stll flt-level preemptve; (2) the second part (denoted as R npe ) begns when the non-preemptve regon starts ts transmsson on N lasti untl f,k completely arrves at Ds (.e. the transmsson of the whole packet s completed), durng whch the transmsson of f,k s completely non-preemptve. The consttuton of R,k s llustrated n Fg. 3.

10 Real-Tme Syst (2017) 53: ,1 s released, s fnshed,, Preemp ve Completely Non-preemp ve 1 0, Fg. 3 The response tme of f,k For the flt-level preemptve part, the calculaton s smlar to Eqs. 1 8.WeuseS npe,k to represent the startng tme of the non-preemptve regon of a packet f,k ( k K ) (see Fg. 3). Assume that f,1 s released at tme 0, all the preemptons arrved before S npe,k are possble to delay f,k. Thus, the fnshng tme of f,k (accordng to Eq. 6) can be computed as: As shown n Fg. 3, S npe,k F,k = B + kc + S npe,k f j S D S npe,k can then be computed by: = F,k R npe ( npe) I S,k = f j S D S npe,k T j + J I j C j ( npe) npe = B + kc + I S,k R + J j I C j (10) T j where K s computed usng Eq. 5, and the calculaton of R npe wll be presented n Sect TheR pe,k of f,k can then be computed by: The response tme of f,k s therefore: R pe,k = Snpe,k (k 1) T (11) R,k = S npe,k (k 1) T + R npe (12) We can then obtan the WCRT of f usng Eq. 8. Based on the above analyss, we can prove that the response tme of a NoC flow can be mnmzed by selectng ts non-preemptve regon as large as possble. Theorem 1 Decreasng the length of the non-preemptve regon of a flow f n a fxedprorty based wormhole-swtched NoC cannot decrease the response tme of f whle all the other parameters reman the same.

11 896 Real-Tme Syst (2017) 53: Proof Assume that the orgnal transmsson tme of the non-preemptve regon of a packet f,k s R npe, and f,k has the worst-case response tme. We need to prove that when (as a result of decreasng the length of the non-preemptve regon) we decrease R npe to R npe = R npe r (0 < r < R npe ), the new response tme R,k becomes no smaller than the orgnal one R,k (.e. R,k R,k). Ths can be proven usng nducton. Equaton 10 s solved usng fxed-pont teratons, whch starts wth S npe,k (0) = B + kc R npe. Accordngly, we can also get S npe,k (0) = B + kc ( R npe r ) = S npe,k (0) + r Then n the second teraton, we have S npe,k (1) = B + kc R npe ( npe + I S,k (0)) ( S npe,k (1) = B + kc R npe npe + I S,k (0) ) ( npe) Snce I S,k s a non-decreasng functon, we can obtan that ( npe I S,k (0) ) ( npe I S,k (0)) ( B + kc R npe npe + I S,k (0) ) Now assume that S npe,k B + kc R npe S npe,k (q) S npe,k (1) S npe,k (1) + r + r + I ( S npe,k (0)) (q) + r, we need to prove that Snpe,k (q + 1) ( npe) S,k, we can get S npe,k (q + 1) + r. Due to the non-decreasng property of I Therefore, gven R npe can obtan that S npe,k R,k R,k ( npe I S,k (q) ) ( npe I S,k (q)) ( B + kc R npe npe + I S,k (q) ) B + kc R npe S npe,k + r + I ( S npe,k (q)) (q + 1) S npe,k (q + 1) + r < R npe,wehaves npe,k (k 1) T + R npe S npe,k S npe,k + r. Accordng to Eq. 12,we (k 1) T + R npe + r Ths completes the proof.

12 Real-Tme Syst (2017) 53: Accordng to Theorem 1, when we ncrease the sze of the non-preemptve regon of a certan flow f, f can have a shorter response tme. However, the flows wth prortes hgher than P may get larger response tmes, because they may suffer more blockng from f. Therefore, the non-preemptve regon of each flow cannot be nfntely large (up to the sze of the whole packet), and t should be carefully nvestgated by balancng the effects on all related flows. 5.2 Computng the blockng tolerance In ths secton, we present the computaton of the blockng tolerance of each flow. The blockng tolerance of f (.e. denoted by β ) s the maxmum blockng delay that f can tolerate wthout causng a deadlne mss. In other words, the flows n S B should not cause blockng to f for more than β. Frst, we reformat the response tme analyss for NoC flows n order to smplfy the followng presentaton. In the above RTA, the purpose of usng the fxed-pont based calculatons s to teratvely compute a convergency of the -level busy-perod. If the computed -level busy-perod at a certan teraton can reach the release tme of a new packet, the analyss wll contnue to the next teraton where the -level busy-perod wll become larger. On the other hand, f the same computed -level busy-perod s obtaned from two successve teratons (.e. the computed -level busy-perod cannot reach the release tme of any packet wth hgher prortes), the analyss can be termnated. Therefore, the analyss s actually regardng the length of the -level busy-perod and the release tmes of flows wth hgher prortes. We defne,k as the set of releases tmes of flows n S D wthn the tme duraton snce a packet f,k s released wth ts crtcal nstant untl the deadlne of f,k s reached. Assume that the -level busy-perod starts at tme 0, then,k can be defned as,k = [ (k 1)T,(k 1)T + D R npe ] { } max(0,(p 1)T j J j I ), p N, f j S D { (k 1)T + D R npe } Note that the scenaro of f,k just reachng ts deadlne also needs to be taken nto account n,k. Then the RTA for NoC flows can be reformatted as follows. Theorem 2 A NoC flow f s schedulable f k [1, K ], t,k, such that B + kc R npe + I (t) t Proof The -level busy-perod conssts of the blockng delay (B ), the transmsson of f tself (kc ), and the nterference from flows n S D (I ). As dscussed n Sect. 5.1, once the non-preemptve regon of a packet f,k starts ts transmsson after node N lasti, later-arrved packets wth hgher prortes cannot preempt f,k anymore. Therefore, gven a tme duraton [0, t], only the workload of B + kc R npe + I (t) actually affects f new arrvals of nterference need to be consdered.

13 898 Real-Tme Syst (2017) 53: When the workload of B + kc R npe + I (t) exceeds the length of t, the nonpreemptve regon of f,k cannot start ts transmsson at N lasti. In ths case, the new arrvals whch are released at tme nstant t can stll preempt f,k, whch wll contrbute to the growth of the -level busy-perod. Consequently, the computaton wll not termnate at tme t. When B + kc R npe + I (t) t, the workload of B + kc R npe + I (t) can be fnshed before tme nstant t. In ths case, the non-preemptve regon of f,k can start ts transmsson before or at t. Therefore, the packets arrved at or later than t cannot affect the -level busy-perod anymore. Accordng to the defnton of,k,the maxmum t s (k 1)T + D R npe. Thus, B + kc R npe + I (t) t mples that the packet f,k whch s released at tme (k 1)T must fnsh ts transmsson no later than ts deadlne. Accordng to Theorem 2, n order to guarantee that any packet f,k can meet ts deadlne, we should have t,k : B + kc R npe + I (t) t B t kc + R npe I (t) Snce any t, that can be found satsfyng the above condton, can make f,k meet ts deadlne, we can observe an upper-bound of B as β,k = max t,k ( t kc + R npe I (t) ) (13) An upper-bound of B, whch can guarantee that all the nstances of f can meet deadlnes, can then be computed as β = mn β,k (14) k [1,K ] Whle calculatng K usng Eq. 5, we need to know the blockng delay (see Eq. 1). As a result, before computng β usng Eq. 14, we need to know the value of K whch depends on an unknown blockng delay. In order to solve such crcular-dependency problem, we use a smlar approach as presented n Bertogna et al. (2011a). The soluton s based on the fact that β = mn β,k k [1,K ] β β,k, k [1, K ] Snce Eq. 1 s a non-decreasng functon regardng the blockng delay, usng β wll not compute a larger -level busy-perod than usng any other β,k. Therefore, we use β,1 to compute an approxmate ˆK ( ˆK K ). The man procedure of computng β s presented n Algorthm 1. As dscussed earler, we frst compute β,1 (lne 2) whch s used for the calculaton of the approxmate

14 Real-Tme Syst (2017) 53: ˆK. Our approach s proposed on top of the exstng flt-level preemptve mechansm. Therefore, each flow has a certan amount of non-avodable blockng delay due to basc flt-level preemptons. The set of lnks, where f may experence blockng delays, are denoted as ϕ, whch s defned as def ϕ == (R R j ) f j S B Such a basc blockng delay can be bounded by nr(ϕ ) τ, where nr(ϕ ) denotes the number of lnks n ϕ. If the computed β,1 s smaller than nr(ϕ ) τ, whch means that f,1 may mss ts deadlne even only experencng basc blockng, the algorthm can thus be termnated. If a vald β,1 s found, we can compute an approxmate -level busy-perod usng Eq. 1,aswellasthe ˆK usng Eq. 5 (lne 7). The blockng tolerance of each nstance wthn the -level busy-perod can then be calculated usng Eq. 13 (lne 9-14). Smlar to the dscusson of β,1, when any β,k s smaller than nr(ϕ ) τ, the algorthm can be termnated. Fnally, a sutable β can be selected by Eq. 14 (lne 15). Algorthm 1 Compute β 1: //compute β,1 2: β,1 usng Eq. 13 3: f β,1 < nr(ϕ ) τ then 4: return Unschedulable 5: end f 6: //compute ˆK 7: ˆK usng Eq. 5 and 1, where B = β,1 n Eq. 1 8: //compute β 9: for all kn[2, ˆK ] do 10: β,k usng Eq : f β,k < nr(ϕ ) τ then 12: return Unschedulable 13: end f 14: end for 15: β usng Eq : return β 5.3 Selectng the lengths of non-preemptve regons In ths secton, we present how to select the length of the non-preemptve regon of each NoC flow. We use L npe to represent the length of the non-preemptve regon of f. The blockng delay, that f can cause to any flows wth hgher prortes over one physcal lnk, can then be computed as c npe = Lnpe ς τ (15) where ς represents the sze of a sngle flt, and τ denotes the transmsson tme of a sngle flt over one lnk. Once c npe s known, L npe can also be computed based on

15 900 Real-Tme Syst (2017) 53: Eq. 15. Accordngly, R npe R npe can then be calculated as ( = c npe + noh ( N lasti ) ), Ds 1 τ (16) Therefore, the am s to fnd a sutable c npe for each flow f. As proved n Theorem 1, ncreasng the length of the non-preemptve regon of a flow can potentally decrease ts response tme. However, as the non-preemptve regon of a flow ncreases, the related flows wth hgher prortes may have longer response tmes due to the ncrease of blockng delays. In Sect. 5.2, we have presented how to calculate the blockng tolerance of each flow. As long as the blockng delay of each flow does not exceed ts blockng tolerance, ths flow s stll guaranteed to be schedulable. Therefore, the selecton of the non-preemptve regon of a flow f s based on the rule that the blockng delay, that f can cause to any related flow f j wth a hgher prorty (.e. f j S D ), should not exceed the blockng tolerance of f j (.e. β j ). Accordng to Eq. 2, we know that each NoC flow may experence blockng over multple lnks. Therefore, n order to guarantee the schedulablty of a flow f,the summaton of all the blockng that f may suffer along ts route should be upperbounded by ts blockng tolerance (.e. B β ). In other words, the blockng tolerance of f needs to be dstrbuted to all the lnks where blockng may occur. Based on dfferent dstrbutons of the blockng tolerance of a flow f, the selecton of the nonpreemptve regons of the flows n S B wll dffer as well. In ths paper, we present two dfferent approaches to dstrbute the blockng tolerance of each flow Even dstrbuton of blockng tolerance In the frst approach (named Even Dstrbuton of Blockng Tolerance, EDBT), we evenly dstrbute the blockng tolerance of a flow f to all the lnks where f may get blockng (.e. ϕ ). Accordngly, the blockng tolerance assgned to each lnk n ϕ s computed as β u β = (17) max(1, nr(ϕ )) where nr(ϕ ) denotes the number of lnks n ϕ. When nr(ϕ ) = 0, f wll not experence any blockng. Therefore, we only need to consder the stuatons where nr(ϕ ) s at least 1. At each lnk, the transmsson tme of a non-preemptve regon of f should not cause blockng to any flow f j ( f j S D ) more than β u j (.e. c npe β u j ). In the best case, flow f can be completely non-preemptve. Therefore, the transmsson tme of the non-preemptve regon of f over one lnk can be calculated as c npe ( ( ) ) = mn c, mn β u j (18) f j S D where c represents the maxmum transmsson tme of a whole packet of f over one lnk whch can be computed as L ς τ.

16 Real-Tme Syst (2017) 53: Algorthm 2 Schedulablty Test wth c npe selected usng EDBT 1: for all f F n a descendng order of prortes do 2: c npe usng Eq. 18 3: R npe usng Eq. 16 4: β usng Algorthm 1 5: f β < nr(ϕ ) τ /* Algorthm 1 returns Unschedulable */ then 6: return Unschedulable 7: end f 8: end for 9: return Schedulable The selecton procedure s presented n Algorthm 2. Snce Eq. 18 requres the blockng tolerance of flows wth hgher prortes, the algorthm starts from the flow wth the hghest prorty (lne 1). If the algorthm termnates wthout returnng Unschedulable, the flow set s guaranteed to be schedulable wth the selected non-preemptve regons Hgher-prortes-favored dstrbuton of blockng tolerance In the second soluton, we try to take the actual nformaton of lower prorty flows nto account whle dstrbutng the blockng tolerance of each flow. Ths dstrbuton algorthm (Algorthm 3) tres to provde more satsfacton to flows wth hgher prortes, thus t s named Hgher-Prortes-favored Dstrbuton of Blockng Tolerance (HPDBT). Algorthm 3 Schedulablty Test wth c npe selected usng HPDBT 1: for all f F n a descendng order of prortes do 2: c npe usng Eq. 19 3: for all f j S D do 4: for all l (R R j ) do 5: β j,l = max(0, c npe β j,l ) 6: β j,l = max(β j,l, c npe ) 7: β j = β j β j,l 8: end for 9: end for 10: R npe usng Eq : β usng Algorthm 1 12: β,l = 0, l ϕ 13: β = β 14: f β < nr(ϕ ) τ /* Algorthm 1 returns Unschedulable */ then 15: return Unschedulable 16: end f 17: end for 18: return Schedulable As dscussed earler, the selecton of the non-preemptve regon of a flow depends on the blockng tolerance of flows wth hgher prortes as well. Therefore, whle

17 902 Real-Tme Syst (2017) 53: A B C D Assume: =10 > > > - A er selec ng the non-preemp ve regon of f n, (, ) =2, (, ) =2, =6 Fg. 4 An example of applyng HPDBT calculatng the lengths of non-preemptve regons, we start from the flow wth the hghest prorty. In ths approach, we separate the capacty of the blockng tolerance of f nto two parts: the assgned blockng tolerance on each lnk l (denoted as β,l, l ϕ ), and the remanng blockng tolerance (denoted as β ). Intally, β,l = 0 and β = β (lne 6 7). We know that each packet can experence a blockng at most once on each lnk. In other words, the blockng tolerance of f j assgned to a certan lnk l s shared by all the flows n S B j that also pass lnk l. Therefore, a flow f ( f S B j ), whch shares lnk l wth f j, can reuse the exstng blockng tolerance of f j whch has already been assgned to l. If f requres more blockng tolerance from f j n order to get the maxmum non-preemptve regon, the algorthm wll try to assgn an ncremental blockng tolerance to the current one. Otherwse, the algorthm keeps the current blockng tolerance assgned on ths lnk. The transmsson tme of the non-preemptve regon of f over one lnk can thus be calculated as c npe ( ( ( β ))) j = mn c, mn mn f j S D l (R R j) nr ( ) + β j,l R R j Once the non-preemptve regon of f s selected, the correspondng blockng tolerance capactes of f j need to be updated (lne 9 15). An example showng how blockng tolerance s dstrbuted under HPDBT s presented n Example 1. Example 1 As shown n Fg. 4, assume that there are four flows n the network. We show how β m s dstrbuted under HPDBT. After the non-preemptve regon selecton for f n, we get β m,lnk(b,c) = 2, β m,lnk(c,d) = 2 and βm = 6. Now we consder the followng two cases. Case 1 Assume that c j equates to 1. In ths case, the current dstrbuton of β m does not requre any change, because the current β m,lnk(c,d) s large enough for f j to get ts maxmum c npe j. Consequently, f can utlze the blockng tolerance of f m up to 6 (.e. β m,lnk(a,b) can be up to 6). (19)

18 Real-Tme Syst (2017) 53: Case 2 Assume that c j equates to 5. In ths case, the current β m,lnk(c,d) s not suffcent for f j to get ts maxmum c npe j. Thus, β m,lnk(c,d) s ncreased to 5, and βm s reduced to 3. As a result, f can only utlze the blockng tolerance of f m up to 3. The above selecton procedure s repeated untl all the flows have been processed. If Algorthm 3 termnates wthout returnng Unschedulable, the whole flow set s schedulable wth the selected non-preemptve regons. As dscussed earler, f the blockng delay of a flow does not exceed ts vald blockng tolerance, ths flow s stll guaranteed to be schedulable. On the other hand, accordng to Theorem 1, ncreasng the non-preemptve regon of a flow cannot ncrease ts response tme. Therefore, f a flow s schedulable n the orgnal flt-level preemptve NoC, t wll stll meet ts deadlne wth the non-preemptve regons selected usng the above proposed approaches. If a flow msses ts deadlne n the orgnal flt-level preemptve NoC, t s potentally schedulable wth ncreased non-preemptve regons selected usng our approaches. In other words, our proposed solutons can only acheve a better or the same schedulablty rato compared to the orgnal flt-level preemptve NoC, but cannot make t worse. 6 Path modfcaton scheme In Sect. 5, we have presented how to ntroduce non-preemptve regons to packets n prorty-based NoCs amng to mprove the schedulablty of the whole flow set. As explaned earler, the mprovement hghly depends on the laxty 2 of flows wth hgher prortes. The larger laxty a flow has, the more blockng ths flow can tolerate (.e. havng a greater blockng tolerance). On the other hand, a flow wth a smaller laxty can tolerate less blockng. Consequently, for some cases, utlzng non-preemptve regons cannot save flows from mssng ther deadlnes because of lttle laxty of the flows wth hgher prortes. Therefore, targetng the flows stll mssng ther deadlnes after ntroducng non-preemptve regons, we need other approaches to further mprove ther schedulablty. The XY-routng polcy s one of the most popular routng algorthms for NoCs wth a 2D-mesh based topology (Cota et al. 2011). Snce t s deadlock-free and easy to mplement, t has been used by many processor vendors (e.g. Wentzlaff et al. 2007; Baron 2010). However, as dscussed n Nkolc et al. (2016), XY-routng has the dsadvantage that t does not flexbly dstrbute transmsson workload n the network, whch can result n neffcent utlzaton of bandwdth. An example s depcted n Fg. 5 to show such a dsadvantage. As shown n Fg. 5a, under the XY-routng polcy, all the three flows can cause contenton to each other due to sharng the same physcal lnk. However, f we change the routes of these flows accordng to Fg. 5b, the contenton s reduced sgnfcantly. Thus, modfyng the routes of flows n a NoC s a potental soluton to save flows from mssng ther deadlnes when only applyng non-preemptve regons s not suffcent. In ths secton, we present a Path/route Modfcaton (PM) approach to further mprove the schedulablty of NoC flows wth non-preemptve 2 The laxty of a flow f s the tme dstance from ts fnshng tme untl ts deadlne (.e. D R ).

19 904 Real-Tme Syst (2017) 53: Fg. 5 An example showng the dsadvantage of XY-routng (a) Wth XY -rou ng 3 (b) Wthout XY-rou ng 3 Fg. 6 An example showng route canddates regons. Note, that the proposed path modfcaton mechansm s ndependent of the non-preemptve regon selecton algorthms. To smplfy the presentaton, we use HPDBT as an example to present the path modfcaton approach. The path modfcaton method s llustrated n Algorthm 4. We use XY-routng as the ntal routng polcy for the whole flow set (lne 1). We then apply Algorthm 3 (or Algorthm 2) to select proper non-preemptve regon for each flow (lnes 3 7). If the algorthm gves a postve result showng that all the flows meet ther deadlnes, the current desgn can be drectly approved wthout applyng path modfcaton (lne 8 and 34). On the other hand, f the algorthm returns a negatve result showng that a certan flow f s unschedulable (lne 16), we start the path modfcaton process to save f from mssng ts deadlne. Frst, we need to dentfy a number of route canddates for each flow. Apparently, f all the possble routes of f are consdered as ts route canddates, the search space can become huge as the number of routers ncreases. Therefore, n ths work, the route canddate dentfcaton process follows a mnmal path polcy (Nkolc et al. 2016). Gven the coordnates of the source and destnaton nodes of f (denoted as [x Sr, y Sr ] and [x Ds, y Ds ]), the mnmum number of hops nvolved n the route R s x Sr x Ds + y Sr y Ds. Under the mnmal path polcy, the number of hops ncluded n each route canddate equates to the mnmum number of hops computed above. In Nkolc et al. (2016), the authors have dscussed the benefts of the mnmal path polcy, ncludng achevng constant solaton latences, reducng soluton space, smplfyng mplementaton, and avodng deadlocks. To acheve the mnmal path polcy, we need to follow the prncple that a flow can only propagate towards ts destnaton node. For example, f the destnaton node s located on the south-east of the source node, the transmsson of ths flow should never go towards the north or the west. An example s presented n Fg. 6 showng the route canddates of a flow

20 Real-Tme Syst (2017) 53: Algorthm 4 Schedulablty Test wth c npe selected usng HPDBT and path modfcaton 1: Assgn routes of all the flows n F usng XY-routng 2: for all f F n a descendng order of prortes do 3: c npe usng Eq. 19 4: R npe usng Eq. 16 5: β usng Algorthm 1 6: β,l = 0, l ϕ 7: β = β 8: f β nr(ϕ ) τ /* Algorthm 1 returns Schedulable */ then 9: for all f j S D do 10: for all l (R R j ) do 11: β j,l = max(0, c npe β j,l ) 12: β j,l = max(β j,l, c npe ) 13: β j = β j β j,l 14: end for 15: end for 16: else 17: /* Algorthm 1 returns Unschedulable, and path modfcaton s requred*/ 18: foundtolerance False 19: whle (β < nr(ϕ ) τ) (RCL = ) do 20: Get the route canddate wth the best heurstc from RC L 21: Remove the selected canddate from RC L 22: Repeat lne 3 to 7 23: f β nr(ϕ ) τ /* Algorthm 1 returns Schedulable */ then 24: foundtolerance True 25: Repeat lne 9 to 15 26: Break 27: end f 28: end whle 29: f foundtolerance = False then 30: return Unschedulable 31: end f 32: end f 33: end for 34: return Schedulable wth gven source and destnaton nodes. We use RCL to represent the lst of route canddates for f. After dentfyng the route canddate lst for each flow, we need to select one of the canddates for each path modfcaton process. The authors n Nkolc et al. (2016) have shown that performng an exhaustve search to fnd the optmal route canddate s mpractcal even though the soluton space has been reduced by the mnmal path polcy. Therefore, n ths paper, we propose a heurstc based approach to select route canddates. The utlzed heurstc s to choose the route canddate whch has the lowest number of flows from S D passng through. Such a heurstc ams to fnd a route where f can experence less nterference such that f has a hgher probablty to meet ts deadlne and to provde relatvely large blockng tolerance for flows wth lower prortes. Algorthm 5 demonstrates the heurstc based selecton of a route canddate for f.

21 906 Real-Tme Syst (2017) 53: Algorthm 5 Heurstc based selecton of route canddate for f 1: Input: S D, RCL 2: mnintfls szeof (S D ) 3: canddate null 4: for all rc RCL do 5: nr Int Fls 0 6: for all f j S D do 7: f ( l n rc) (l n R j ) then 8: nr Int Fls ++ 9: end f 10: end for 11: f nr Int Fls mnintfls then 12: mnintfls nr Int Fls 13: canddate rc 14: end f 15: end for 16: return canddate Once a route canddate of f s chosen, we repeat the selecton process of the nonpreemptve regon for f (Algorthm 4, lne 22). If f s stll unschedulable wth the current route canddate, the algorthm contnues to check other canddates n RCL. The processng on f termnates when (1) f becomes schedulable, n whch case the algorthm starts to analyze the next flow n F (Algorthm 4, lnes 23 26); or (2) there are not canddates remaned n RCL, n whch case the algorthm aborts returnng a result of Unschedulable (Algorthm 4, lnes 29 and 30). Smlar to Algorthms 2 and 3, Algorthm 4 processes flows n a descendng order of ther prortes. Ths s used to guarantee that once a vald non-preemptve regon of a flow f s selected, the later processng of other flows (ncludng both non-preemptve regon selecton and path modfcaton) cannot affect the schedulablty of f. Thus, there s no need to recheck the schedulablty of the flows whch have been already processed. Moreover, f a flow s schedulable wth ts ntal route, no path modfcaton wll be appled on t. If a flow s unschedulable wth ts ntal route, the path modfcaton wll be performed whch can potentally make ths flow become schedulable. Therefore, we can conclude that usng path modfcaton can acheve ether a hgher or an equal schedulablty rato compared to a soluton wthout path modfcaton. 7 Evaluaton We have generated a number of experments to evaluate the performance of the proposed approaches. The evaluaton s mplemented usng Python 2.7. The experments are performed on a computer usng Wndow 7 and equpped wth Intel U@2.2 GHz CPU and 16 GB RAM. 7.1 Evaluaton of EDBT and HPDBT Frst, we present the evaluaton outcomes of EDBT and HPDBT. The evaluaton conssts of analyss based tests, smulaton based tests, along wth an ndustral case study based on an automotve applcaton.

22 Real-Tme Syst (2017) 53: Schedulablty Rat o 80% 60% 40% 20% 0% Packet sze [5, 50] FLP EDBT HPDBT 40% 45% 50% 55% 60% 65% 70% Maxmum Lnk U lza on Fg. 7 Results regardng the maxmum lnk utlzaton wth packet sze selected from [5, 50] Analyss based evaluaton In ths set of evaluatons, we compare our proposed approaches (.e. EDBT and HPDBT) wth the orgnal flt-level preemptve NoC (denoted by FLP) based on offlne analyses. The network consdered n the evaluaton uses a D meshed topology, and t contans 100 flows. The source and the destnaton of each flow s randomly selected. All the flows are routed usng the XY-routng algorthm whch s wdely supported n most of the exstng NoC mplementatons. The sze of each flow s randomly 3 generated from the range of [5, 1000] flts. The utlzaton of each flow s randomly selected from [0.03, 10%]. The prortes of flows are assgned usng the Rate Monotonc (RM) algorthm (Lu and Layland 1973). We generate two groups of experments n order to nvestgate the effects of dfferent system parameters. In the frst set of experments, we show how network utlzaton and flow sze affect the performance of the proposed approaches. The results are presented n Fgs. 7, 8, 9. As shown n Fg. 7, as the maxmum lnk utlzaton (.e. lnk utlzaton denotes the total utlzaton of all the flows passng a certan lnk) goes up, the schedulablty ratos of all the three approaches decrease. EDBT s slghtly better than FLP, whle HPDBT obvously domnates the other approaches. When the utlzaton s between 0.4 and 0.55, EDBT can mprove the schedulablty by around 3% compared to FLP, and HPDBT can mprove the schedulablty by more than 10%. Fgures 8 and 9 show the results of experments where we ncrease the szes of flows. Smlar to the observaton from Fg. 7, the schedulablty ratos decrease as the maxmum lnk utlzaton goes up. HPDBT s always better than EDBT and FLP, whle EDBT s slghtly better than FLP. In the second set of experments, we nvestgate the effect of the path length of each flow. In ths set of experments, we ncrease the selecton range of the utlzaton of each flow to [1, 10%], n order to show the results more clearly. As presented n Fg. 10, wth the same settng of packet szes and perods, the schedulablty ratos decrease as the path lengths of flows ncrease. Ths s because when the path length of 3 In our experments, all the randomly selected parameters are followng a unform dstrbuton wthn the gven ranges.

23 908 Real-Tme Syst (2017) 53: Schedulablty Rat o 100% 80% 60% 40% 20% Packet sze [100, 300] FLP EDBT HPDBT 0% 40% 45% 50% 55% 60% 65% Maxmum Lnk U lza on Fg. 8 Results regardng the maxmum lnk utlzaton wth packet sze selected from [100, 300] Schedulablty Rat o 100% 80% 60% 40% 20% Packet sze [500, 1000] FLP EDBT HPDBT 0% 40% 45% 50% 55% 60% Maxmum Lnk U lza on Fg. 9 Results regardng the maxmum lnk utlzaton wth packet sze selected from [500, 1000] Schedulablty Rat o 100% 80% 60% 40% 20% Packet sze [5, 1000] FLP EDBT HPDBT 0% Maxmum Number of Hops per Flow Fg. 10 Results regardng the maxmum number of hops per flow wth packet sze selected from [5, 1000] aflow f ncreases, f can experence more blockng (.e. the sze of ϕ maygoup). On the other hand, as computed n Eq. 3, the basc transmsson tme of each packet also ncreases. Both effects can cause a growth of the -level busy-perod, whch may nvolve more nterference to f as well. Therefore, the schedulablty rato decreases when the path lengths go up. Moreover, when the paths are short, we can observe that EDBT and HPDBT have very close performance. However, as the path lengths go up, the drawback of EDBT becomes more obvous, and HPDBT performs clearly better.

24 Real-Tme Syst (2017) 53: Accordng to the above evaluaton results, we can clearly observe that the proposed approaches can mprove the schedulablty rato compared to the orgnal flt-level preemptve NoC. The mprovement acheved by HPDBT s more obvous compared to the mprovement acheved by EDBT. Even though we dd observe several cases where the flow sets are schedulable wth EDBT but unschedulable wth HPDBT, such cases occur very rarely Smulaton based evaluaton In addton to the analyss based evaluaton, we have also randomly generated a number of test cases to show how much mprovement from HPDBT can be observed n gven smulaton scenaros. We have developed a cycle-accurate smulator as a proofof-concept. In the smulator, the processng overhead whle a packet traverses each router s consdered. The amount of the processng overhead s based on the nformaton provded n Baron (2010). In these tests, we focus on the comparson between the orgnal flt-level preemptve schedulng (.e. FLP) and the lmted-preemptve schedulng usng HPDBT. The results are represented by the maxmum nflaton factor of each flow set. The maxmum nflaton factor of a flow set shows how much packet szes can be nflated whle all the deadlnes are stll met. For example, f the nflaton factor of a flow set s 1.5, each flow can have a packet sze whch s at most 50% larger than the orgnal sze whle keepng the flow set stll schedulable. On the other hand, f the nflaton factor s 0.8, each flow has to decrease ts packet sze by at least 20% n order to meet all the deadlnes. Therefore, gven the same flow set, the schedulng framework whch can acheve a hgher nflaton factor performs better, snce ths framework s able to afford more real-tme traffc. The network stll uses a 8 8 2D meshed topology. 50 flows are generated for each test. The utlzaton of each flow s randomly selected from the range of [5%, 10%], and the packet sze s randomly generated from the range of [100, 300] flts. Each set of experment s run for at least 2 tmes of the hyper-perod of all the flows (.e. 2 LCM(F)). The results of 10 example tests are presented n Table 1. We can observe that HPDBT always acheves a hgher nflaton factor compared to FLP, no matter n the analyss based results or the smulaton based results. The dfference between FLP and HPDBT from the analyss results s between 0.01 and 0.11, and the dfference from the smulaton results vares from 0.01 to Snce these tests are randomly selected, they may not show the extreme performance of the proposed framework. However, the mprovement of HPDBT compared to FLP can be clearly observed Case study A case study s also generated to examne the mprovement of HPDBT compared to FLP. The case study s based on an autonomous vehcle applcaton, whch has been utlzed n Sh et al. (2012), Indrusak (2014). The applcaton comprses a number of tasks performng dfferent functonaltes such as obstacle detecton va stereo photogrammetry, navgaton control, and stablty control. The whole network ncludes

25 910 Real-Tme Syst (2017) 53: Table 1 Examples showng the dfference between FLP and HPDBT, presented by nflaton factors of the flow sets Test ndex FLP HPDBT Analyss Smulaton Analyss Smulaton The bold number represents the maxmum value of each column 38 real-tme flows for nter-task communcatons. The system s deployed on a 4 4 2D meshed NoC platform wth the X Y routng algorthm. The NoC frequency s set to 100 MHz, and the bandwdth of each lnk s 3.2 Gbt/s. More detals of the flow set parameters and the task mappng can be found n Sh (2009). In order to observe the dfference between our proposed framework and the platform wth the orgnal FLP, we apply a stress test on the above applcaton. An addtonal testng flow s added nto the network. The perod of the testng flow s equal to the shortest perod n the orgnal flow set (.e s), whch mples that the testng flow has the hghest prorty. The senstvty test ams to fnd the maxmum packet sze of the testng flow such that the whole flow set keeps schedulable. In order to shorten the testng process, we set an nflaton factor 45 to the orgnal flow set (.e. the total utlzaton of the orgnal flow set ncreases 45 tmes). Accordng to the results, usng the platform wth lmted-preemptve schedulng, the testng flow can transmt 2312 more flts every 0.04 s whch equates to 226 kb data per second. 7.2 Evaluaton for path modfcaton We have also generated a number of experments to evaluate the further mprovement acheved by the path modfcaton approach ntroduced n Sect. 6. The consdered NoC uses a 4 4 2D-meshed topology, and t contans 50 real-tme flows. The utlzaton of each flow s randomly selected from two ranges, [5, 10%] and [0.03, 10%]. The packet sze of each flow s randomly generated from [100, 300] flts. We compare the performance of three frameworks, where one framework uses only HPDBT (wthout PM), one framework uses HPDBT together wth PM (denoted as HPDBT-PM) and one framework uses FLP wth PM (denoted as FLP-PM). In the frst set of experments, the utlzaton of each flow s generated from [5, 10%], and the results are shown n Fg 11. As the maxmum lnk utlzaton ncreases from 45

26 Real-Tme Syst (2017) 53: Schedulablty Rat o 100% 80% 60% 40% 20% U lza on Range [5%, 10%] HPDBT HPDBT-PM FLP-PM 0% 45% 50% 55% 60% 65% Maxmum Lnk U lza on Fg. 11 Comparson between HPDBT, HPDBT-PM and FLP-PM regardng schedulablty rato. Utlzaton of each flow s selected from [5, 10%] Schedulablty Rat o 100% 80% 60% 40% 20% U lza on Range [0.03%, 10%] HPDBT HPDBT-PM FLP-PM 0% 45% 50% 55% 60% 65% Maxmum Lnk U lza on Fg. 12 Comparson between HPDBT, HPDBT-PM and FLP-PM regardng schedulablty rato. Utlzaton of each flow s selected from [0.03, 10%] to 65%, the schedulablty rato acheved by HPDBT drops from 61 to 13%, whle the schedulablty rato acheved by HPDBT-PM decreases from 87 to 69%. On the other hand, the schedulablty rato of FLP-PM drops from 75 to 38%. We can clearly observe that usng path modfcaton can ndeed mprove the schedulablty. The mprovement becomes more sgnfcant as the maxmum lnk utlzaton goes up. Moreover, by comparng the results of HPDBT and FLP-PM, we can also observe that the path modfcaton based approach can mprove schedulablty more effectvely compared to the lmted preempton based soluton. In the second set of experments, we enlarge the range of flow utlzaton to [0.03, 10%]. The results are depcted n Fg. 12, where we can obtan a smlar observaton that usng path modfcaton can sgnfcantly mprove the schedulablty. The above results have already shown the advantage of applyng path modfcaton. On the other hand, we realze that the path modfcaton mechansm requres more processng tme due to explorng the soluton space. Therefore, we have also generated a number of experments comparng the processng tme of HPDBT and HPDBT-PM. The consdered network s 4 4 2D-meshed NoC. The utlzaton of each flow s randomly selected from [0.03, 10%], and the packet sze s randomly generated from [100, 300]. We ncrease the number of flows n the NoC from 10 to 100 wth a step

27 912 Real-Tme Syst (2017) 53: Average Processn g T m e (s) HPDBT-PM HPDBT Number of Flows Fg. 13 Comparson between HPDBT and HPDBT-PM regardng average processng tme Table 2 Comparson between HPDBT and HPDBT-PM regardng average processng tme. No. of flows HPDBT (ms) HPDBT-PM (ms) Max Mean Std. Max Mean Std of 10. The results are presented n Fg. 13 and Table 2. Accordng to Fg. 13, asthe number of flows goes up, both algorthms requre more processng tme. However, the average processng tme of HPDBT-PM ncreases much faster than HPDBT. When the number of flows ncreases from 10 to 100, the processng tme of HPDBT rases from less than ms whle the processng tme of HPDBT-PM ncreases from 0.5 to 1.9 s. If we ncrease the sze of NoCs, the requred processng tme of HPDBT-PM may further ncrease dramatcally because of the larger search space. For example, n a4 4 NoC, a flow can have at most 20 route canddates. However, n a 6 6 NoC, the maxmum number of route canddates for a flow s 252, and ths number becomes even 3432 n a 8 8 NoC. Therefore, we can conclude that the path modfcaton approach s an effectve means to mprove schedulablty, however, t can be constraned by the scalablty. 8 Concluson and future works In ths paper, we present a new schedulng framework of wormhole-swtched NoCs wth VCs, where non-preemptve regons are ntroduced to NoC packets. The proposed

28 Real-Tme Syst (2017) 53: soluton ams to mprove the schedulablty of the whole network. A schedulablty test of the proposed framework s provded along wth the proof of ts correctness. Addtonally, we also present a path modfcaton approach based on the above framework n order to further mprove schedulablty. Accordng to the evaluaton results, the proposed approaches can always acheve hgher schedulablty ratos compared to the orgnal flt-level preemptve NoC. As a future work, the framework can be extended to support prorty sharng polces, so that the requred number of VCs can be reduced. Moreover, we also plan to apply the proposed approaches on NoCs wth arbtrary buffer szes. Open Access Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton 4.0 Internatonal Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded you gve approprate credt to the orgnal author(s) and the source, provde a lnk to the Creatve Commons lcense, and ndcate f changes were made. References Baron M (2010) The sngle-chp cloud computer ntel networks 48 pentums on a chp, Intel Benn L, De Mchel G (2002) Networks on chps: a new soc paradgm, Computer Bertogna M, Buttazzo G, Yao G (2011a) Improvng feasblty of fxed prorty tasks usng non-preemptve regons. In 32nd real-tme systems symposum (RTSS), IEEE Bertogna M, Xhan O, Marnon M, Esposto F, Buttazzo G (2011b) Optmal selecton of preempton ponts to mnmze preempton overhead. In: 23rd Euromcro conference on real-tme systems (ECRTS), IEEE Brl RJ, Lukken JJ, Verhaegh WE (2009) Worst-case response tme analyss of real-tme tasks under fxed-prorty schedulng wth deferred preempton. Real-Tme Syst 42(1): Brl RJ, Van den Heuvel MM, Keskn U, Lukken JJ (2012) Generalzed fxed-prorty schedulng wth lmted preemptons. In: 24th Euromcro conference on real-tme systems (ECRTS), IEEE Cota É, de Moras Amory A, Lubaszewsk MS (2011) Relablty, avalablty and servceablty of networkson-chp. Sprnger, Berln Dally WJ (1992) Vrtual-channel flow control. IEEE Trans Parallel Dstrb Syst 3(2): Dasar D, Nkolć B, Néls V, Petters SM (2014) Noc contenton analyss usng a branch-and-prune algorthm. TECS 13:113 Davs R, Bertogna M (2012) Optmal fxed prorty schedulng wth deferred pre-empton. In: 33rd real-tme systems symposum (RTSS), IEEE De Dnechn BD, Durand Y, Van Amstel D, Ght A (2014) Guaranteed servces of the NoC of a manycore processor. In: 7th nternatonal workshop on network on chp archtectures (NoCArc), ACM Demer J, Ernst R (2010) Back sucton: servce guarantees for latency-senstve on-chp networks. In: 4th ACM/IEEE nternatonal symposum on networks-on-chp (NoCs), IEEE Ferrandz T, Frances F, Fraboul C (2009) A method of computaton for worst-case delay analyss on spacewre networks. In: 4th nternatonal symposum on ndustral embedded systems (SIES), IEEE Goossens K, Delssen J, Radulescu A (2005) Æthereal network on chp: concepts, archtectures, and mplementatons. Des Test Comput 22: Indrusak LS (2014) End-to-end schedulablty tests for multprocessor embedded systems based on networks-on-chp wth prorty-preemptve arbtraton. J Syst Arch 60(7): Joseph M, Pandya P (1986) Fndng response tmes n a real-tme system. Comput J 29: Kashf H, Gholaman S, Patel H (2015) SLA: a stage-level latency analyss for real-tme communcatonn a ppelned resource model. IEEE Trans Comput 64(4): Lehoczky JP (1990) Fxed prorty schedulng of perodc task sets wth arbtrary deadlnes. In: 11th real-tme systems symposum (RTSS) Lu CI, Layland JW (1973) Schedulng algorthms for multprogrammng n a hard-real-tme envronment. J ACM 20:46 61

29 914 Real-Tme Syst (2017) 53: Lu M, Becker M, Behnam M, Nolte T (2016) Schedulng real-tme packets wth non-preemptve regons on prorty-based NoCs. In: 22nd nternatonal conference on embedded and real-tme computng systems and applcatons (RTCSA), IEEE N LM, McKnley PK (1993) A survey of wormhole routng technques n drect networks. Computer 26(2):62 76 Nkolc B, Pnho LM, Indrusak LS (2016) On routng flexblty of wormhole-swtched prorty-preemptve NoCs. In: 22nd nternatonal conference on embedded and real-tme computng systems and applcatons (RTCSA), IEEE Paukovts C, Kopetz H (2008) Concepts of swtchng n the tme-trggered network-on-chp. In: 14th nternatonal conference on embedded and real-tme computng systems and applcatons (RTCSA), IEEE Saksena M, Wang Y (2000) Scalable real-tme system desgn usng preempton thresholds. In: 21st real-tme systems symposum (RTSS), IEEE Sh Z (2009) Real-tme communcaton servces for networks on chp. PhD thess, Unversty of York Sh Z, Burns A (2008) Real-tme communcaton analyss for on-chp networks wth wormhole swtchng. In: 2nd nternatonal symposum on networks-on-chp NoCs, ACM/IEEE Sh Z, Burns A (2009a) Improvement of schedulablty analyss wth a prorty share polcy n on-chp networks. In: 17th nternatonal conference on real-tme and network systems (RTNS) Sh Z, Burns A (2009b) Real-tme communcaton analyss wth a prorty share polcy n on-chp networks. In: 21st Euromcro conference on real-tme systems (ECRTS), IEEE Sh Z, Burns A, Indrusak LS (2012) Schedulablty analyss for real tme on-chp communcaton wth wormhole swtchng. In: Innovatons n embedded and real-tme systems engneerng for communcaton Song H, Kwon B, Yoon H (1997) Throttle and preempt: a new flow control for real-tme communcatons n wormhole networks. In: 26th nternatonal conference on parallel processng (ICPP), IEEE Wang Y, Saksena M (1999) Schedulng fxed-prorty tasks wth preempton threshold. In: 6th nternatonal conference on real-tme computng systems and applcatons (RTCSA), IEEE Wentzlaff D, Grffn P, Hoffmann H, Bao L, Edwards B, Ramey C, Mattna M, Mao C, Brown JE III, Agarwal A (2007) On-chp nterconnecton archtecture of the tle processor. IEEE Mcro 27:15 31 Xong Q, Lu Z, Wu F, Xe C (2016) Real-tme analyss for wormhole NoC: revsted and revsed. In: 26th edton on great lakes symposum on VLSI, ACM Meng Lu s a PhD student at Mälardalen Unversty snce September, He receved hs B.Sc. degree n Network Engneerng from Tanjn Polytechnc Unversty, Chna n In the year 2011, he got hs Master degree n Network and Dstrbuted Systems from Chalmers Unversty of Technology, Sweden. After one years workng as software developer, he started hs PhD studes n Mälardalen Unversty. He s a member of the Complex Real- Tme Embedded Systems (CORE) group at Mälardalen Real-Tme Research Center (MRTC). Hs research nterests le n real-tme and embedded systems, ncludng real-tme communcaton, networkon-chp, schedulng and tme analyss, stochastc and statstcal analyss.

30 Real-Tme Syst (2017) 53: Matthas Becker s a PhD student at Mälardalen Unversty snce October He receved hs B.Eng. degree n Mechatroncs/Automaton Systems from the Unversty of Appled Scences Esslngen, Germany n In the year 2013 he got hs M.Sc. degree n Computer Scence specalzng n embedded computng from the Unversty of Appled Scences Munch, Germany. He has been a vstng researcher at CISTER - Research Centre n Real-Tme and Embedded Computng Systems n Porto n 2015 and He s a member of the Complex Real-Tme Embedded Systems (CORE) group at Mälardalen Real-Tme Research Center (MRTC). Hs research s n the feld of many-core real-tme systems wth partcular nterest n predctable executon frameworks for ndustral systems. Mors Behnam was awarded a B.Eng., and M.Sc. n Computer and Control Engneerng at the Unversty of Technology, Iraq, and also M.Sc., Lcentate, and PhD n Computer Scence and Engneerng at MDH, Sweden, n 1995, 1998, 2005, 2008 and 2010 respectvely. He has been a vstng researcher at Wayne State Unversty, USA n 2009 and he has been a Postdoctoral Researcher at Unversty of Porto n Hs research nterests nclude real-tme schedulng, synchronzaton protocols, multcore/multprocessor systems, dstrbuted embedded real-tme systems and usng control theores n real-tme schedulng. Thomas Nolte was awarded a B.Eng., M.Sc., Lcentate, and Ph.D. degree n Computer Engneerng from Mälardalen Unversty (MDH), Västerås, Sweden, n 2001, 2002, 2003, and 2006, respectvely. He has been a Vstng Researcher at Unversty of Calforna, Irvne (UCI), Los Angeles, USA, n 2002, and a Vstng Researcher at Unversty of Catana, Italy, n He has been a Postdoctoral Researcher at Unversty of Catana n 2006, and at MDH n Thomas Nolte became an Assstant Professor at MDH n 2008, and Assocate Professor at MDH n he became Full Professor of Computer Scence. Hs research nterests nclude predctable executon and performance of embedded systems, desgn, modelng and analyss of real-tme systems, multcore systems, dstrbuted embedded real-tme systems, nternet-of-thngs and the cloud.