mapping reult. Our experiment have revealed that for many popular tream application, uch a networking and multimedia application, the number of VC nee

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1 Reolving Deadlock for Pipelined Stream Application on Network-on-Chip Xiaohang Wang 1,2, Peng Liu 1 1 Department of Information Science and Electronic Engineering, Zheiang Univerity Hangzhou, Zheiang, P. R. China, baikeina@yahoo.com.cn, 1 liupeng@iee.zu.edu.cn Mei Yang 2, Yingtao Jiang 2 2 Department of Electrical and Computer Engineering, Univerity of Nevada, La Vega, NV {meiyang, yingtao}@egr.unlv.edu Abtract When a tream application that demand real-time proceing over continuou data tream i running on a network-on-chip (NoC)-baed multiproceor ytem-on-chip (MPSoC), two type of deadlock may occur: (i) the routingdependent deadlock, and (ii) the meage-dependent deadlock. In thi paper, we focu on the requet-requet type meage-dependent deadlock, the mot devatating deadlock in tream application, and how that thi type of deadlock can be avoided by a proper incluion of virtual channel (VC). We firt prove a ufficient condition that determine the minimum number of VC needed to completely avoid requet-requet type meage-dependent deadlock. We then how that the problem of finding the minimum number of uch VC for a given application i NP-complete, and ubequently, a mixed integral linear programming (MILP)- baed algorithm, referred a Min_VC algorithm, i introduced to olve thi problem. Thi Min_VC algorithm can literally be integrated with any exiting application mapping algorithm to provide deadlock-free mapping reult. The experiment reult hown that for typical tream application, uch a multimedia application, the number of VC needed to avoid deadlock i fairly modet, typically ut 1 or 2 depending on application. That i, with a modet price paid in term of area and power, tream application can run in an NoC-baed ytem completely free of deadlock concern, which i neceary to deliver the quality of ervice (QoS) guarantee required by thee application. Keyword: network-on-chip (NoC), meage-dependent deadlock, virtual channel I. INTRODUCTION Network-on-chip (NoC) ha been widely accepted a a viable communication infratructure for current and future Multiproceor Sytem on Chip (MPSoC) deign [1] tailored for tream application. The increaing importance of tream proceing lie in the fact that many emerging application involve real-time proceing over continuou data tream, uch a VoIP telephony, playback audio/video, IPTV, and enor data analyi [2]. There are unfortunately two type of deadlock that may occur to a pipelined tream application running on an NoCbaed architecture: 1) the routing-dependent deadlock [1] and 2) the meage-dependent deadlock [3, 4]. A meagedependent deadlock i created when ome of thee meage can never be conumed by the conumer tak a the conumption of thee meage i mutually dependent on each other arrival. For example, meage X may block /10/$ IEEE meage Y from arriving at the end proceor/ni while Y i imultaneouly required by the conumer tak to conume X. Thi requet-requet type meage-dependent deadlock can caue devatating effect on a tream application a it may put the whole ytem into a complete tall [3, 4]. To avoid or reolve meage-dependent deadlock in a network, generally two clae of method, reactive method and proactive method, are ued [3, 4, 7]. However, thee exiting method are not uitable for the tream application running on an NoC-baed architecture, for reaon given below. For reactive method, typified by a deadlock recovery mechanim referred a mdiha [7], they cannot deliver the QoS guarantee required by tream application, ince reolving deadlock will caue unpredictably long delay [4]. There exit three poible proactive method that may help avoid deadlock. However, none of thee method will be uitable for tream application which have tringent latency and throughput requirement. (i). Ue of network buffer with an extremely large ize to avoid deadlock. Thi approach i not uitable for NoC deign, a it involve unbearably high area and power cot. In addition, thi method, a pointed out in [4], cannot help avoid the requet-requet type meagedependent deadlock. (ii). Creation of multiple virtual network with one for each meage type. Thi approach, unfortunately, cannot help avoid the requet-requet type meage-dependent deadlock [4]. (iii). Ue of end-to-end flow control. The end-to-end flow control protocol, uch a CTC protocol [3], may ignificantly increae the network latency and communication power due to the uage of additional reply meage for flow control [4]. Virtual channel (VC) have been long employed in many NoC deign to help improve network routing performance. In thi paper, we how that proper incluion of VC can alo provide a practically feaible olution to completely avoid the requet-requet type meagedependent deadlock in an NoC deign. In particular, for the firt time, we have formally proved a ufficient condition that determine the minimum number of VC actually needed to avoid the meage-dependent deadlock. Following thi theory, we propoe an MILP-baed algorithm that can help quickly find thi number, and thi algorithm hall be integrated with exiting application mapping algorithm, like the one reported in [5], to get deadlock-free 93

2 mapping reult. Our experiment have revealed that for many popular tream application, uch a networking and multimedia application, the number of VC needed to avoid deadlock i fairly modet, typically ut 1 or 2 depending on application. That i, with a modet price paid in term of area and power, tream application can run in an NoCbaed ytem completely free of deadlock concern. II. TARGET APPLICATION AND ARCHITECTURE MODEL A. Application model The tream application can be modeled a a ynchronou data flow graph. Definition 1[2] A ynchronou data flow graph (SDFG) i a directed graph SDFG(A, EC), where each vertex a i A repreent a tak (to be conitent, an actor that wa originally defined in [2] i alo referred a a tak in thi text), and a directed edge ec i =(a k, a ) EC repreent the data communication from a k to a. For tak a k, the following notation are defined, EX(a k ) give the wort execution time of tak a k. IN(a k ) i the et of all a k predeceor tak in SDFG. OUT(a k ) i the et of all a k ucceor tak in SDFG. A ource tak i one which ha no predeceor tak. A ink tak i one which ha no ucceor tak. All the tak will be executed repeatedly for a number of iteration to proce the incoming data tream. A tak that need to communicate with other i allowed to do o either at the beginning (i.e. read input data) or at the end (end output data) of an iteration. Let (a k a ) m denote the data (packed in meage) from a k to a after a k finihe it m-th iteration. In thi paper, we aume that all the tak have already been bound to IP core. Definition 2 A tream communication graph (SCG) i a directed acyclic graph SCG(P, E), where a vertex p k P repreent an IP core, and an edge e i =(p k, p ) E repreent the communication between vertice p k and p. ω(e i ) define the amount of data ent from p k to p in bit per econd (bp). Without lo of generality, we aume that each IP core i allocated with one tak. If multiple tak are allocated to a ingle IP core, we can treat thee tak a one macro tak. There are two type of buffer aociated with a tak: the input data buffer and the output data buffer. For any tak, one input data buffer i dedicated to receive the meage from ut one of it predeceor [2]. That i, the number of input data buffer needed i the ame a that of the tak predeceor. For any tak, meage for one of it ucceor will be tored in a dedicated output data buffer before they can be ent out [2]. That i, the number of output data buffer i the ame a that of the tak ucceor. B. Architectural model Fig. 1 how the architecture model ued in thi paper. The NoC ytem under conideration i compoed of NxN tile interconnected by a 2-D meh network. Each tile, indexed by it coordinate (x, y), where 0 x N-1 and 0 y N- 1, ha one router and one proceing node. A router, a hown in Fig. 2, implement wormhole witching. Each meage will be broken into a number of fixed ize packet with each carrying the needed routing information. Each packet will be further decompoed into flit. Aume each phyical channel i plit into V VC, realized by V buffer at each input port with each buffer holding everal flit. A hown in Fig. 2, each proceing node i compoed of four component: a proceor, a bu, a local memory unit and a network interface (NI). The local memory unit hold the input/output data buffer that can be ued by the tak allocated to thi IP core. The NI hold a number of receiving buffer each dedicated to holding everal flit of the meage from one of the tak predeceor. Hence, the number of receiving buffer configured at the NI i the ame a the number of the tak predeceor. Definition 3 An Architecture Characterization Graph (ACG) Ğ=(T, L) i a directed graph, where each vertex t i T repreent a tile (Fig. 1), and each edge l i =(t k, t ) L repreent the link between adacent t k and t. For link l i, bw(l i ) define the bandwidth provided between tile t k and t. c(l i,v) define the link cot of l i, i.e., power conumption for tranmitting one bit data from t k and t with a total of V VC. Figure 1 NoC architecture model. A rectangle box repreent a router and a circle repreent a proceing node. III. MESSAGE-DEPENDENT DEADLOCK IN STREAM APPLICATION AND MOTIVATING EXAMPLE In thi ection, we provide an example to illutrate how a requet-requet type meage-dependent deadlock can occur, followed by important obervation how uch deadlock can be avoided. Aume the SCG ha three IP core on which three tak a, b, and c are allocated, a hown in Fig. 2, ha already been mapped to the ACG with a 1x3 meh uing the mapping algorithm in [3]. The three tak (with a and b a the producer and c a the conumer) form a pipeline. Aume the puhing protocol [4] i applied; that i, a producer tak i allowed to continuouly puh all it generated data into the network until the network i aturated. In thi example, no virtual channel i ued. A buffer N buffer 1 94

3 indicated in Section 2.1, for all three tak to operate properly, c cannot tart a new iteration (ay the i-th iteration) until it receive the data generated in the i-th iteration of a and b in their correponding input data buffer. Once c tart a new iteration, the two input data buffer mut have been cleared. (c) Figure 2 An example of SCG with three proceor mapped with three tak. Deadlock configuration due to requet-requet type meagedependency. (c) Increaing the number of virtual channel can help avoid requet-requet type meage-dependent deadlock. A eriou problem, however, may happen when, for example, b produce data at a higher rate than a and c. Fig. 2 illutrate uch a ituation. Suppoe c ha finihed it (n-1)-th iteration and it i now waiting for (b c) n and (a c) n. In the following, we will how how a cyclic dependency among the meage can be developed. 1) Flit of (b c) n+1 reerve link (1, 2), the wet input buffer of R 2 and the receiving buffer of NI 2 (marked with * in Fig. 2). 2) Flit of (b c) n+1 cannot proceed to the input data buffer dedicated for b in c local memory ince the buffer i occupied by (b c) n which ha not been conumed (cleared) yet. 3) To conume (b c) n, (a c) n need to arrive at the input data buffer dedicated for a in c local memory to allow c to tart the n-th iteration. (Thi dependency i marked a ** in Fig. 2). 4) In Fig. 2, the arrow marked with *** denote that the input data buffer in c local memory dedicated for a wait for the arrival of flit of (a c) n. 5) However, flit of (a c) n cannot proceed ince the wet input buffer of R 2 i already reerved by flit of (b c) n+1. 6) Up to thi point, a deadlock i already formed. Above example ha revealed that a devatating deadlock can be formed. In another word, to avoid any deadlock like the one hown in Fig. 2, ome network control mechanim hould be in place to either proactively prevent any meage generated in different iteration from blocking other to reach their detination, or act reactively to reolve the deadlock once they are detected. A a matter of fact, all the exiting deadlock avoidance method [3, 4, 7], can actually be viewed a a variation of uch control mechanim. A a viable alternative to the exiting deadlock avoidance method, the requet-requet type meagedependent deadlock can be completely avoided by adding a number of virtual channel. For the example hown in Fig. 2, one can ee that the cycle that caue a deadlock in Fig. 2, i completely avoidable by employing two virtual channel at each router (Fig. 2(c)). Since in many NoC deign, virtual channel are ued for helping improve network routing performance [2], the hardware cot of thi approach for avoiding meage-dependent deadlock i well utifiable. IV. DEADLOCK AVOIDANCE USING VIRTUAL CHANNELS A. Sufficient condition for deadlock-avoidance with virtual channel Aume a tream application given a an SCG (Section 2) ha already been mapped to an NoC architecture modeled by an ACG (Section 2). We alo aume that (i) the routing algorithm ued i deadlock-free, and (ii) meage are delivered in-order. Lemma 1 For any tak in a tream application allocated to an IP core in a given SCG, after it finihe the execution of it n-th iteration, it input data buffer are either empty or they are holding meage from it predeceor (n+1)-th iteration. Lemma 2 For a tream application given a a SCG, there exit one virtual path between any two communicating tak o that all meage will arrive at their detination tak, provided that 1) each link i hared by communication le than or equal to the number of virtual channel and 2) the number of receiving buffer at the NI of each tile i equal to the number of predeceor of the mapped IP core in the SCG. Theorem 1 Conider an NoC architecture in which (i) V VC are ued at each router and (ii) the number of receiving buffer at the NI of each tile i et to be equal to the number of it predeceor. If each link i hared by no more than V communication, no requet-requet type meagedependent deadlock can ever be created. The proof of Lemma 1-3 and Theorem 1 are omitted due to pace limit. B. Minimum virtual channel algorithm MinVC problem: Given an ACG(T, L) that a SCG(P, E) i mapped onto, for each communication e i in SCG, find a 95

4 routing path in ACG among all the poible minimal routing path uch that the number of virtual channel needed at each router i minimized, i.e., Min {V}, atifying, l m, V gl ( m, hm( p ), ( )) (1) ei= ( pk, p) E l m, B ω( ei) g( lm, hm( p ), ( )) (2) ei= ( pk, p) E where M(p) i the tile that p i mapped to, and 1 if l h i M( pk ), M( p ) gl ( i, h M( p ), ( )) =. 0 if l h i M ( pk ), M ( p ) The condition given by (1) enure that each link l in ACG i hared by at mot V communication flow, while the condition given by (2) enure that the total bandwidth requirement of all communication flow haring each link l doe not exceed the capacity of link l. Next we will firt how that the MinVC problem i NPcomplete. Then we will preent an ILP-baed olution. Theorem 2 The deciion verion of the MinVC problem i NP-complete. The proof ketch i lited below. The deciion verion of the MinVC problem i to decide whether there exit the minimal routing path in the ACG for all communication in the SCG, while all the reource contraint are atified and no more than V VC are needed at each router. We will prove thi theorem retricting the deciion verion of the MinVC problem to it intance with ω(e i )=1 for all ei, and V=B. Thu, condition (1) and (2) of the MinVC problem are algebraically identical. Thi retriction, from general MinVC to it retricted verion, take O( L + E ) time, where L i the number of link in the ACG. The retricted MinVC problem i equivalent to finding the minimum cot unplittable flow [8] for a et of E communication flow {1,, E }, each flow ending from a ource node i to it detination node d i with demand ω(e i ) for i {1,, E }. The knapack [9] problem can thu be viewed a a pecial cae of the retricted MinVC problem, a hown in Fig. 3. In Fig. 3, for each item in knapack problem [9], there i a correponding flow i (i.e., an edge e i in the SCG) whoe demand ω(e i ) i equal to the ize of each item. The cot of each direct edge from node to d i i et to w i / i where w i and i repreent the weight and ize of the i-th item, repectively. Cot of all the other edge are et to 0. The capacity of the edge from node to v i equal to the capacity of the knapack while auming all other edge have infinite capacity. Therefore, the minimum cot flow from all i to d i, i {1,, E }, upon atifying all the demand, lead to an optimal olution to the knapack problem and vice vera. The knapack problem i NP-complete [9], and o i the MinVC problem which can be tranformed to the knapack problem. w1 1 w2 2 w E 1 E 1 Figure 3 Formulation of the Knapack problem [9] a the retricted MinVC problem. The MinVC problem can be approximated by formulating it a a mixed integer linear programming problem given below. Here, MP i i the et of all minimal path between the two tile mapped by the two IP core of edge e i, and PATH i, i the -th minimal path in MP i. f i,k = 1 if e i take the k th minimum path. Eqn. (2) et a 0 otherwie contraint that only one of the minimal path will be allocated for each communication. Eqn. (3) et that each link will not accommodate more than V communication. Eqn. (4) repreent the bandwidth contraint of each link. Our experiment ha hown that when lp_olve [10] i ued to olve Min_VC, the running time i le than 0.1ec for a 6 6 meh-baed NoC (obtained from a PC with one Intel Core2 P GHz proceor and 2GB RAM). Min_VC(M, MP) Input: (1) M: a mapped reult (2) MP: a et of all minimum path for all communication flow Output: (1) V: the number of VC needed for all router (2) { f ik, }: the et of minimal path for all e i Procedure body: { call lp_olve to olve the following equation: Obective: min V (1) Contraint: fik, = 1, ei (MP i i the et of all minimal path et for e i ); (2) k MPi fik, V, link l ; (3) ei l PATHi,, k MPi ω( ei) fi, k B, link l ; (4) ei l PATHi, } V. EXPERIMENTS In our experiment, the mapping proce i baed on an exiting mapping algorithm [5]. A. Simulation reult Fig. 4 how a ynthetic application. The execution time of each tage i modeled by a random proce with the mean and variance are choen randomly. For the mapping reult in Fig. 4, it ha been found that 2 VC are needed to completely avoid any deadlock. The CMMS ytem in Fig. 5 i compoed of both a video/audio encoder and a video/audio decoder. The video and audio encoder are ynchronized, and o are the video and audio decoder. The tak in the video codec are w E E 96

5 yntheized a follow. The mean, variance and the Hurt parameter of the execution time of each tage are from [11] We aume that the target platform run QCIF format video which ha 99 macro block in one frame. The video proceing part i pipelined at the macro block level and i ynchronized with the audio proceing at the end of each frame. For thi application, 1 VC i found ufficient to avoid deadlock. Figure 4 The SCG of ynthetic application. The mapping reult. Figure 5 The SCG of CMMS. The mapping of reult. Table I how the power and area reult for each application with the number of VC needed to avoid deadlock. The reult hown are normalized with repect to a baeline deign where no VC i ued. Of the three application, the maximum number of VC needed to avoid deadlock i 2. In the wort cenario, the power and area penaltie are 16% and 17%, repectively, which i tolerable for gaining the benefit of avoiding meage-dependent deadlock that otherwie will have devatating effect on tream application. With thee number of VC, the application have no routing dependent and meage dependent deadlock oberved. TABLE I. THE AREA AND POWER OVERHEAD TO AVOID DEADLOCKS FOR THE THREE APPLICATIONS. Application VC required Power Area Synthetic x 1.17x CMMS 1 1x 1x VI. CONCLUSION In thi paper, we preented a practical method to avoid the requet-requet type meage-dependent deadlock problem that can eriouly impact the performance of a pipelined tream application running on an NoC architecture. We howed that the requet-requet type meage-dependent deadlock can be avoided by adding the right number of virtual channel (VC) and formally proved a ufficient condition which determine the minimum number of VC actually needed to obtain uch a deadlockfree NoC deign. We further howed the problem of finding the minimum number VC i NP-complete and thu propoed an ILP-baed olution which can be and hould be integrated into any mapping algorithm whenever a deadlock-free deign i deired. Experiment baed on three tream application confirmed that deadlock have been avoided with a modet increae of power and area. REFERENCES [1] M. Palei, R. Holmark, S. Kumar, and V. Catania, "Application pecific routing algorithm for Network on Chip," IEEE Tran Parallel and Ditributed Sytem, vol. 20, no. 3, pp , [2] N. K. Kavaldiev, "A run-time reconfigurable Network-on-Chip for treaming DSP application," Phd thei, Univerity of Twente, [3] N. Concer, L. Bononi, M. Soulié, R. Locatelli, and L. P. Carloni, "CTC: An end-to-end flow control protocol for multi-core ytemon-chip," in Proc 3rd ACM/IEEE Int'l Symp on Network-on-Chip, 2009, pp [4] A. Hanon, K. Gooen, and A. Radulecu, "Avoiding meagedependent deadlock in network-baed Sytem-on-Chip," VLSI Deign, vol. 2007, no., pp. 1-10, [5] G. Acia, V. Catania, and M. Palei, "Mapping core on network-onchip," Int'l J Computational Intelligence Reearch, vol. 1, no. 2, pp , [6] X. Wang, M. Yang, Y. Jiang, and P. Liu, "A power-aware mapping approach to map ip core onto noc under bandwidth and latency contraint," to appear in ACM Tran. Architecture and Code Optimization. [7] Y. H. Song and T. M. Pinkton, "A progreive approach to handling meage-dependent deadlock in parallel computer ytem," IEEE Tran Parallel and Ditributed Sytem, vol. 14, no. 3, pp , [8] M. Skutella, "Approximating the ingle ource unplittable min-cot flow problem," Mathematical Programming, vol. 91, no. 3, pp , [9] M. R. Garey and D. S. Johnon, Computer and Intractability: A Guide to the Theory of NP-completene: Freeman San Francico, [10] lp olve 5.5. [Online]. Available: lpolve.ourceforge.net/5.5/. [11] C. Lampert, M. Militzer, and P. Ro. XviD MPEG4 core library. 97