Deadlock-Free Path-Based Fault-Tolerant Multicast Communications on 2-D Mesh Networks-on-Chip

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1 The CSI Journal on Computer Scence and Engneerng Vol. 6, No. 2 & 4 (b), 2008 Pages Short Paper Deadlock-Free Path-Based Fault-Tolerant Multcast Communcatons on 2-D Mesh Networks-on-Chp Majed ValadBeg Farshad Safae Department of Electrcal & Computer Engneerng, Shahd Behesht Unversty, Tehran, Iran Abstract The move towards nanoscale Integrated Crcuts (ICs) ncreases performance and capacty, but poses process varaton and relablty challenges whch may cause several faults on routers n Networks-on-Chp (NoCs). Whle utlzng healthy routers n an NoCs s desrable, faulty regons wth dfferent shapes are formed gatherng faulty routers. Fault regons can be used to lead the fault-tolerant routng algorthms to perform data transmsson between healthy routers. Besdes, the ncreasng number of collectve communcaton-based servces wth a mass nterest and the parallel ncreasng demand for servce qualty are pavng the way toward end-to-end qualty of servce guarantees. The collectve communcaton servces embrace multcast (the same message s sent from a source node to an arbtrary number of destnaton nodes). Ths paper presents the fault-tolerant mesh-based wormhole-swtched NoCs whch supports deadlock-free path-based multcast routng. Ths technque flls the gap of not havng optmum multcast fault-tolerant wormhole-swtched approaches and also mantans mnmal routng path whch tolerates both convex and concave fault regons whle keepng the area and power overhead at a proper level. Multcast messages are njected to the network by sendng a message header beforehand. The message header contans destnaton addresses to set-up multcast path connectng a source wth multple destnaton nodes. Moreover, the fault nformaton s kept locally and each faultfree processor needs to know the status of the lnk ncdent on t only. Performance of the proposed methodology s smulated under dfferent network condtons and show that t degrades gracefully n the presence of varous fault patterns. Keywords: Networks-on-Chp, Fault-Tolerance, Multcast Communcatons, Multcast Path-Based Routng, Wormhole Message Passng, Faulty Patterns, Performance Evaluaton. 1. Introducton Networks-on-Chp (NoCs) s a challengng research topc, provdng a scalable soluton for multprocessors on chp [1]. The lack of scalablty n bus-based systems and large area overhead of pont-to-pont dedcated lnks on one hand, and the scalablty and performance of swtch-based networks and packet-based communcaton n the nternet and tradtonal parallel computng on the other hand, have motvated researchers to propose packet-swtched NoCs archtectures to overcome complex on-chp communcaton problems [2]. Although the concept of NoCs s nspred from the networks n parallel processors, they have some specfc propertes whch dffer from the tradtonal networks. Compared to tradtonal networks, power consumpton and fault-tolerance are becomng ncreasngly mportant constrants n NoCs desgn [2]. Wth the shrnkng feature sze, the relablty becomes more dffcult to acheve due to smaller voltage supples and hgher amount of computng elements per area unt. It results n smaller nose mmunty and ncreased rsk of cross-talk and other errors [2-4]. Moreover, crtcal leakage currents, hgh feld effects, and process varaton wll lead to more transent and permanent falures of sgnals, logc values and devces and nterconnects [5]. As communcaton nfrastructure s an mportant ssue of today s Systems-on-Chp (SoCs) and Chp-Multprocessors (CMPs), fault-tolerance has to be taken nto account along wth desgn of ths part of chps. Havng the same concept as tradtonal nterconnecton networks, the resources used n tradtonal networks n order to acheve fault-tolerance are not easly avalable n VLSI chps. Routng algorthm, as one

2 M. ValadBeg and F. Safae: Deadlock-Free Path-Based Fault-Tolerant Multcast (Short Paper) 37 of the most mportant aspects of NoCs, has been exploted by many researchers to guarantee relable operaton of the network [6-8], by bypassng the faulty nodes and lnks. Servces n terms of effcent routng and schedulng are crtcal wth respect to the performance of NoCs-based multcore processor systems. Hstorcally, the frstgeneraton multcomputer supported uncast communcaton only (sngle PE sends a message to sngle PE unt). Nowadays, multcomputers have been developed towards collectve communcaton servces. The collectve communcaton servces embrace multcast (the same message s sent from a source node to an arbtrary number of destnaton nodes). In path-based multcast scheme, a source node prepares a message for delvery to a set of destnatons by frst sortng the addresses of the destnatons n the order n whch they are to be delvered and then placng ths sorted lst n the header flts of message. When the header enters a router wth address a, the router checks to see f a s the next address n the header. If so, the address a s removed from the message header and the data flts are forwarded both to the local processor at ths node as well as to the next node on the path. Otherwse, the message s forwarded only to the next node on the path. In ths way, the message s eventually delvered to every destnaton n the header [9]. In ths paper, we study the problem of fault-tolerant multcast communcaton for wormhole-swtched NoCs. Ths s an mportant problem snce multcast communcaton s a natural communcaton prmtve to handle synchronzatons, nvaldatons and updates of cache lnes n NoCs applcatons and also because the NoCs performance s closely related to the robustness of the fault-tolerant routng algorthms of such networks. Regardng the complexty, havng no guarantee Qualtyof-Servce and lack of fault-tolerant multcast communcatons n NoCs, we propose, mplement and evaluate fault-tolerant wormhole-swtched NoCs whch supports deadlock-free path-based multcast routng that leads to easy handlng of faults and also preventng statc fault patterns n NoCs wth 2-D mesh topology. The rest of the paper s organzed as follows. Secton 2 descrbes the necessary background nformaton that s used n the paper. In Secton 3, we revew prevous relevant works. Secton 4 presents the bref of the man contrbuton of the paper. Our fault-tolerant routng methodology whch s coupled wth multcast communcaton s ntroduced n Secton 5. In Secton 6, the expermental results wth dfferent fault regons and other related parameters are presented. Fnally, n Secton 7 we conclude by summarzng our man contrbuton and future works. 2. Prelmnares Ths secton revews some defntons and background of the mesh and descrbes the concept of fault models and fault patterns used n ths paper The Mesh Networks The topology of a network defnes how the nodes are nterconnected and s generally modeled as a graph n whch the vertces represent the nodes and the edges denote the communcaton lnes. The NoC concept has been proposed to overcome the problems of tradtonal wre/bus-based nterconnecton [3]. The NoC uses nterconnecton networks to connect ntellectual propertes (IPs) and to cope wth the ncreased sze and complexty of IPs. Besdes, dfferent topologes of nterconnecton networks can provde dfferent features n NoCs. Among dfferent topologes the 2-D mesh s one of the most popular topology, n whch the routers of NoCs are connected as a 2-D array and each IP s connected to an ndvdual router. The mesh networks, the tree networks, the star networks and the smple loop networks frequently appear n varous applcatons of networks. Many nterconnecton networks are constructed by Cartesan product [10]. Defnton 1 [10]: Let G 1 = ( V 1, E 1 ) and G 2 = ( V 2, E 2 ) be two graphs. The Cartesan product of G 1 and G 2, denoted by G1 G2, s the graph wth vertex set V 1 V 2 such that ( u1, v 1) s joned to ( u2, v2) k tmes f and only f ether u1 = u2 and v 1 s joned to vk 2 tmes n G 2 or v 1 = v 2 and u 1 s joned to uk 2 tmes n G 1. Defnton 2 [10]: The topologcal structure of a 2-D mesh network, Mm ( 1, m 2) s defned as the Cartesan product of two paths Pm P, where 1 m P 2 m s the path graph wth m vertces. Due to ts modularty and symmetry n terms of lnk length, the mesh topology s one of the most desrable topologes regardng to characterstcs; the number of lnks per node does not change f addtonal nodes are added to the mesh. Therefore, the mesh topology offers very good scalablty. Addtonally, the mesh s low cost s because ths network topology conssts of fewer lnks per node than most other archtectures The Fault Model Fault-tolerance s defned as the ablty of a system to contnue operaton despte the presence of faults [8]. In ths sense, fault-tolerance s closely related to concepts such as relablty, avalablty and dependablty as t may serve to provde these features. Faults n a network take many forms, such as hardware faults, software bugs, malcous snffng or removal of packets. The frst step n dealng wth errors s to understand the nature of component falures and then to develop smple models that allow us to reason about the falure and the methods for handlng t. Classfcaton of faults by nature s ether random or systematc faults. Random faults are usually hardware faults affectng the system components, whch occur wth a certan probablty, whle systematc faults such as software falures are faults whch are not random, whether a component has t or not [8]. We assume that such permanent falures are detected and contaned on a node or lnk boundary. Thus, faults are assumed to be fal-stop [11], meanng that we do not consder Byzantne (.e., malcous) faults [8]. In the contexts of fault-tolerant routng, these are common assumptons [8, 11-13]. Faults can also be classfed by ther duraton as transent and permanent faults [8]. Transent faults persst n the system for only a short duraton whle permanent faults

3 The CSI Journal on Computer Scence and Engneerng, Vol. 6, No. 2 & 4 (b), reman n the system untl t s repared and may be ether dynamc or statc. In a dynamc fault model, once a new fault s found, actons are taken n order to approprately handle the faulty component whch allows the system to reconfgure at the hardware level and preserves the orgnal network topology. A statc system provdes a fault-tolerant routng algorthm that wll bypass any faled node The Fault Pattern To smplfy the routng algorthm, adjacent faulty nodes are coalesced nto fault regons, whch may lead to dfferent patterns of faled components. To analyze the performance of fault-tolerant routng algorthms, t s mportant to dentfy and quantfy the fault regons, whch may occur n the network. The shapes of such fault regons are often restrcted by the fault model n use. Furthermore, the fault model may mpose addtonal restrctons on the locatons of the faults. For nstance faults may not be allowed on the edges of the mesh and there may be a mnmum dstance between separate fault regons. A routng algorthm applyng such a fault model s generally to tolerate all fault combnatons conformng to the fault model, thus, the provded faulttolerance s defned by the fault model. In the case that a fault combnaton s not conformng to the fault model n use, healthy nodes are marked as faulty (.e., dsabled) n order to create proper fault regons. Although healthy nodes are dsabled, a fault combnaton s consdered to be tolerated as long as all the nodes that are nether faulty nor dsabled are connected through vald paths. Fault regons extended by faulty components may form convex (also referred to as the block fault model) or concave shaped fault patterns [8, 11-14]. Defnton 3 [8, 11-14]: A convex regon s defned as a regon n whch a lne segment connectng any two ponts n les entrely wthn. If we change the "lne segment" n the standard convex regon defnton to "horzontal or vertcal lne segment", the resulted regon s called rectlnear convex segments [12, 13]. Any regon that s not convex s a concave regon. Examples of convex regons are -shape, -shape and concave regons are L-shape, U-shape, T-shape, H-shape and +-shape. The convex fault model s the smplest fault model n mesh topologes. Under the convex fault model, all fault regons are requred to have a rectangular shape n a 2-D mesh and a cubod shape n a 3-D mesh. Convex faults can be created by markng a node faulty f t has a faulty neghbor/channel n at least two dmensons [11]. A strcter verson of the convex fault model s when to requrng all fault regons to form a square [8]. Because a node wth at most one faulty or dsabled neghbor s not able to determne whether t s part of such a regon solely based on the status of ts faulty neghbors, such fault regons are more complex to construct and mantan than pure block faults f used wth a dynamc fault model [11]. Furthermore, such a fault model s lkely to requre more nodes to be dsabled. The expermental results gve some ndcatons on the percentage of healthy nodes that are dsabled n a mesh when usng square fault regons [11]. In partcular, when 10% of the routers are faulty, on average, less than 12% of the non-faulty nodes are marked as faulty, and the entre network becomes dsabled when about 20% of the nodes are faulty. Although t may appear that such a method s able to tolerate almost 20% of the routers beng faulty, t s not lkely that the NoC s able to perform satsfactory wth such a hgh proporton of the routers dsabled. In order to reduce the number of dsabled healthy nodes, concave fault regons may be used. By not requrng the nodes wthn such shapes to be dsabled, fault-tolerant routng methods supportng concave faults are able to tolerate a wde range of fault patterns wthout dsablng healthy routers. Specfcally, such routng algorthms provde addtonal support for concave fault patterns compared to the convex fault model by also toleratng concave fault regons. Stll, such methods may not be able to tolerate arbtrary fault patterns and may put some restrctons on the shape of the concavtes. 3. Related Work In ths secton, we ntally provde a bref survey of faulttolerant routng algorthms, multcast routngs and multcast fault-tolerant routngs that have been proposed based on mesh topologes. The survey s by no means exhaustve, but serves to provde a general overvew of dfferent approaches. We only dscuss routng algorthms that are targeted at networks wth lossless flow control that s routng algorthms that take deadlocks nto account. Lots of fault-tolerant routng algorthms based on tradtonal nterconnecton networks can be performed aganst statc faults n NoCs. In desgnng of a fault-tolerant routng algorthm, a sutable fault model s one of the most substantal ssues. The fault model can reflect the fault stuatons n a real system. Rectangular blocks (.e., convex faults) are the most common approach to model node falures and to facltate routngs n 2-D meshes. A labelng scheme [14] has been proposed to construct a fault regon wth rectangular shapes. However, rectangular fault patterns nclude many healthy routers. In order to reduce healthy routers n rectangular fault regons, many related works are proposed n the lterature. Boppana and Chalasan [15] proposed a method to tolerate block faults n 2-D meshes (wth dmenson-order routng). Ths method s able to tolerate overlappng f-rngs/chans when usng four vrtual channels and nonoverlappng f-rngs when usng two vrtual channels. Fault regons are also used by Boura and Das [16] who provde support for fully adaptve fault-tolerant routng n n-d meshes usng three vrtual channels. Ths method s based on an adaptve routng algorthm prevously proposed by the same authors [17]. Because rectangular fault regons are used, they also mark healthy routers as faulty n order to establsh fault regons. However, ther method also has a reactvaton mechansm, enablng some nodes that have been marked as faulty to be reactvated f they are drectly connected to a node outsde the fault regon. Chalasan and Boppana [18] extended ther method to support sold fault regons usng four vrtual channels. On the other hand, ths new method does not support overlappng f-rngs or faults on the edges of the mesh. Such a support s provded by Km and Han [19], however, stll usng the same number of vrtual channels (.e., four). Chen and Chu [20], later, managed to reduce the number of vrtual channels to

4 M. ValadBeg and F. Safae: Deadlock-Free Path-Based Fault-Tolerant Multcast (Short Paper) 39 three, stll toleratng overlappng sold faults and faults on the edges. Wu [21] proposed convex regons wth T-shape, L-shape and +-shape fault regons. Besdes, there are some multcast routng algorthms based on tradtonal nterconnecton networks that can be performed n NoCs. A path-based multcast routng algorthm has been proposed n [22, 23]. In ths algorthm, multcast messages are transmtted on one of the two sub networks H u, H l and, each s defnng a Hamltonan path n the network. The dual-path algorthm n [23] uses at most two copes of the multcast message. The multpath algorthm attempts to reduce long latences by settng up to four copes ( 2n for n-dmensonal) of the orgnal multcast message. As per the multpath routng algorthm, all the destnatons of the multcast message are grouped to four dsjont subsets. Each subset of destnatons s servced by one copy of the multcast messages [24]. The column-path algorthm parttons the set of destnatons of a multcast message nto at most 2k subsets (k s the number of columns n the mesh), such that there are at most two messages drected to each column. If a column of the mesh has one or more destnatons n the same row or n rows above that of the source, then one copy of the message s sent to servce all those destnatons. Smlarly, f a column has one or more destnatons n the rows below that of the source, then one copy of the message s sent to servce all those destnatons. One copy of the message s sent to a column f all destnatons n that column are ether below or above the source node; otherwse, two messages are sent to that column [25]. Moreover, Panda et al. [26] have proposed a general technque to provde multcast routng capablty usng the exstng uncast routng method. However, there are few results that exst on multcast fault-tolerant routng. Boppana and Chalasan proposed a fault-tolerant routng of multcast messages n mesh-based wormhole-swtched nterconnecton networks and ths method can tolerate multple convex faults [27]. Also, Chen and Wu [9] presented a dead-lock free path-based faulttolerant multcast algorthm n 2-D meshes that consder faulty block model. 4. Contrbuton NoCs are beng proposed as a global communcaton platform for future SoCs applcatons. Among the merts are: scalablty, reusablty and etc. Buses (a sngle bus, segmented buses or a herarchy of buses) do not scale wth the system sze n bandwdth and clockng frequency. However, t s very effcent n broadcastng. Although a network allows many more concurrent transactons, mplementng multcast may be neffcent f not addressed properly. The normal multcastng scheme transfers multcast messages by routers n the same way as uncast messages. Ths scheme does not guarantee Qualty-of-Servce (QoS) and multcast fault-tolerant routng. Besdes, accordng to the prevous secton few relevant work exst on multcast faulttolerant routng. Based on ths observaton, a fault-tolerant routng algorthm supportng multcast scheme s proposed wth arbtrary fault patterns. The proposed algorthm s more effcent than prevous work and also supports mnmal routng path. It also tolerates both convex and concave fault regons whle keepng the area and power overhead at a proper level. 5. A Multcast Fault-Tolerant Routng In ths secton we present and evaluate a fault-tolerant wormhole-swtched on NoCs whch supports deadlock-free path-based multcast routng and t s able to tolerate a reasonable number of convex and concave fault patterns wthout dsablng healthy routers. In order to acheve ths scope n a smple manner, thereby reducng the costs due to addtonal vrtual channels and ncreased router complexty, a statc fault model [8] was chosen. Our dscusson n ths secton s prmarly on the concept of message passng after that the dea of hole s descrbed. Then, the explanaton of our methodology algorthm and fnally a bref descrpton on deadlock-freedom of the proposed algorthm are presented The Concept of Wormhole Message Passng The concept of wormhole message passng mechansm wth multple destnatons was used n [28] to perform fast multcast operatons wth Hamlton-path-based routng. Under ths mechansm, the header of a worm conssts of multple destnatons. The sender node creates these destnatons as an ordered lst accordng to ther ntended order of traversal. As soon as the worm s njected nto the network, t s routed based on the address n the leadng header flt correspondng to the frst destnaton. Once the worm reaches the router of the frst destnaton node, the flt contanng ths address s removed by the router. Now the worm s routed to the node whose address s contaned n the next header flt (second destnaton n the ordered lst). Whle the flts are beng forwarded by the router of the frst destnaton node to ts adjacent router, they are also coped flt-by-flt to the system buffer of ths node. Ths process s carred out n each ntermedate destnaton node of the ordered lst. When the message reaches the last destnaton, t s not routed any further and gets completely consumed by the last destnaton node [26] The Idea of Hole Let us defne some notaton to llustrate how the proposed method works. : The set of healthy nodes whch contans any fault regons. : The set of healthy nodes nsde, n whch nodes nsde consst of faulty nodes and. : A sem-faulty node. A node s sem-faulty f has two or more faulty or sem-faulty neghbors. s the set of sem-faulty nodes n the network. A fault labelng mechansm s consdered to specfy nodes status for routng decsons. Hence, each router s labeled as F (frst), H (hole), or E (entrance) node. Fault labelng scheme leads to a general fault model whch can crcumvent faulty nodes.

5 The CSI Journal on Computer Scence and Engneerng, Vol. 6, No. 2 & 4 (b), f : The set of frst destnaton nodes n ordered lst nsde ; f - d1 d2 = { n : $ d, d ' d ¹ d,( n),( n) Î } (1) where d 1, d - are two orthogonal drectons of the node 2 n. The above expresson mples that there are two drectons d 1, d 2 whch are not n the same dmenson and the neghbor of the node n on these two drectons s an element of. e : the set of entrance-nodes; e d = { n : $ d ' ( n) Î, n Ï } (2) e Each node n has only one sem-faulty neghbor. h : the set of hole-nodes; h f = { n : n Î, n Ï } (3) Class: A set of one entrance-node, one frst destnaton node n ordered lst and zero or more hole-node (s). Classes may contan some nodes n common. Thus, we gve each class a unque ID n form of ( xyz,, ), whch ( xy, ) specfes coordnates of the entrance-node and z denotes dmenson of the class. A message wll enter n a class f ts frst destnaton n ordered lst belong to the class and a message wll depart a class f ts frst destnaton n ordered lst are outsde the class. Deadlocks are avoded nsde the classes by usng ths scheme. Also, frst destnaton nodes n ordered lst have hgher prorty than hole or entrance-nodes. Thus, a node labeled as frst destnaton node n ordered lst at a tme, t cannot be labeled as hole or entrance-node any after The MEFH Methodology the message header. All recevng nodes wll nclude ther own addresses to the header and forward the message along the opposte drecton. Ths procedure s done n recursve manner untl the message reaches the frst destnaton node (F) n the ordered lst and ths node sends an ACK message back to the entrance-node (E). In the second approach, the role of the frst destnaton node n the ordered lst and entrance- nodes s swtched. Both of the approaches can be employed, but the complexty of the frst approach s less, snce n the frst approach, the node E knows the drecton of ts class and sends massage on the same drecton, but n the second approach, F wll fnd the approprate drecton possbly after a number of retrals. In the followng treatments, we outlne the fundamental steps that take place f the frst approach s used. Step 1: The entrance-node (E) generates a class creatng message whch contans class number. As mentoned before, the class number contans a trple vector whch keeps the locaton detals of E and the drecton of sendng the message. For example, If E s located at (0, 2) and sends message along the Y-dmenson, the class number wll be (0, 2, Y). Then, the message s transmtted to neghborng node x (x Î ). Step 1 s repeated tll all the entrance- nodes e whch belong to succeed to transmt ther related messages. Step 2: In ths step each node that has receved the generated messages from Step 1, looks whether t s the frst node or not. If t s, t must record the message and transmt an ACK message to E on the drecton n whch t receved the message. Otherwse, the message wll be forwarded on the normal way. Fgure 1. llustrates how the fault labelng scheme works. In ths secton, we propose a multcast fault-tolerant routng methodology, namely MEFH, whch routes messages successfully to all destnatons n the presence of more relaxed fault regons than those n [15, 27] wthout any addtonal vrtual channels, as long as the network s not parttoned by fault regons. Further, t can be appled to any fault-tolerant routng algorthm that employs the concept of f-rng. Ths algorthm n the worst case s so smlar to the fault- tolerant Hamltonan path routng whch s expressed n [28]. Note that we have mostly focused on the frst destnaton node n ordered lst whch can easly be appled to all other nodes accordng to the concept of wormhole message passng Set-up the Classes Node fault labelng technque s requred as pre-processng task before the restart of the system, after the falure of one or more nodes or lnks. In ths process, the nternal nodes of the fault regon are detected, and ther addresses and locatons are sent to the entrance-nodes to convert fault regons nto rectangular shaped regons to facltate message routng. The classes can be easly formed n two approaches: top-to-bottom and bottom-to-top. In the frst approach, the entrance-node (E) sends the message for establshng the class along the drecton that ts neghbor s an element of (.e., the set of sem-faulty nodes) and poses ts address nto Fgure 1. Applcaton of the node fault labelng scheme n an D mesh (note that the frst node n fgure means frst destnaton node n order lst) Step 3: All nodes that receve the ACK message ought to mantan some essental hstory nformaton regardng the path that the message has taken. Ths nformaton comprsed the addresses and the class number wthn the message. Carryng addtonal nformaton usually mposes some overhead, unless header has enough bts to accommodate the addtonal nformaton. When ACK reaches E, t s not stored and dscarded. Only the nformaton of all exstng nodes of each-class s recorded n nodes of type E.

6 M. ValadBeg and F. Safae: Deadlock-Free Path-Based Fault-Tolerant Multcast (Short Paper) Constructng an Approprate Multcast-Path In ths secton a method s defned whch s about how the destnaton address s consdered n the message header to fnd a proper path to send the multcast messages. Here s the descrpton of the method whle we assume all destnatons n just one lst. The lst of destnatons n a multdestnaton worm s ordered by the sender node. The orderng depends on two parameters: 1) Multcast-Labelng number of the node 2) Subnetwork prorty Consder a multdestnaton worm wth n destnatons from a source s wth a destnaton lst { d1, d2,..., dn- 1, dn}, the ordered destnaton lst s { d 1, d 2,..., d n-1, d n} and s gven by the followng defnton. Once the message s routed around faults, the algorthm s used to route the message untl t reaches all of ts destnatons. Defnton 4: The Multcast-Labelng assgnment functon l for R C mesh can be expressed n terms of x and y coordnates of nodes as y C + x f y s even lxy (, ) = ìï í (4) ï y C + C - x - 1 f y s odd ïî Defnton 5: The sub network prorty wx () for R C mesh s gven by maxmum of number of destnatons n each subnetwork whch x s expressed as the number of subnetwork. 2 Intally we dvded the network to n subnetworks (n s the dmenson of network) and we obtan the number of nodes for each subnetwork. Then, we fnd n whch subnetwork our source s located. Later on, we update the set of destnatons n a way that all the exstng nodes (n the chosen subnetwork where the source s located) can be placed n an ascendng manner by consderng ther multcast-labelng number. After locatng all exstng nodes n the set, we wll consder the latest chosen destnaton as the new source. Then the set, n whch the closet node to the new source exsts, s chosen and put through the prevous process. After reachng the latest node of the destnaton set, the updated set from destnaton s chosen and s sent wth the message. The message starts routng and meets every node accordng to the orderng destnaton sets. Remark: If the dstance between the current source node source = d s and dk, d l are equal n whch dk, d l are n two dfferent subnetworks the sub network wll be chosen whose w s more than the other. An example of the method s llustrated n Fgure Routng Rules Here we assume that the network supports a routng scheme Â. Even when there are faults n the network, each message s routed usng the algorthm as much as possble. When a message arrves at a node, the next hop for that message s specfed by the ordered destnaton set whch s explaned before. If that hop s on a faulty lnk, then the message s blocked by the fault. The routng logc s enhanced to handle such stuatons so that the message s routed around faults. Fgure 2. Examples of the proposed algorthm. There s one faulty node. The path of multcast message from (2,0) to (1,0), (1,3), (3,4), (4,4), (5,3), (5,2) Here we assume that n each routng rules the source node s denoted as n s and the frst destnaton node n ordered lst asn d. Note that all the comng rules wll be extended to all destnatons n the ordered lst by applyng the steps of whch we explaned before. Consderng the followng rules, a proper routng algorthm can crcumvent any fault patterns wthout dsablng healthy nodes: a) If all fault patterns are convex, all messages wll be routed by the basc fault-tolerant routng algorthm. b) If there exsts some fault regons but n s and n d are not nsde, the message wll be routed by the basc faulttolerant routng algorthm. c) If n d s nsde and n s s not, a msroutng mechansm wll be appled. Nodes outsde have no knowledge about nodes nsde and cannot fnd the proper E node. As a result, a msroutng mechansm can be used to reach destnaton class entrance-node. Msroutng wthout any threshold, may lead to lvelock. The maxmum msroutng hops accordng to the basc fault-tolerant routng algorthm should be defned. When a message passes maxmum legal msroutng hops, t would be absorbed by the current node and wats for a perod of tme to be re-njected nto the network. Absorbed messages have greater prorty than normal messages for re-enterng nto the network. In ths way, starvaton wll be avoded. Here, we consder delay n local buffer to re-nject messages equal to the message length.

7 The CSI Journal on Computer Scence and Engneerng, Vol. 6, No. 2 & 4 (b), d) If n s s nsde and n d s not, the message wll be forwarded to E node frst, and then wll be routed to n d usng the basc fault-tolerant routng algorthm. e) If both n s and n d are nsde, one of these stuatons wll be encountered: n s and n d belong to a same class, or n s and n d belong to dfferent classes. For the frst stuaton, the message wll be forwarded to n d by dmenson-order-routng algorthm. For the second stuaton, the message wll be forwarded to ts class E node. Afterward, t wll be msrouted to reach destnaton class E node. Fnally, t s forwarded from E node ton d Deadlock Avodance Multcast fault tolerant routng s the topc of ths paper. Beng able to utlze the network wthout ntroducng any rsk of deadlock and decrease unnecessary costs at the same tme are the crucal challenges when desgnng ths knd of routng scheme. Hence, the deadlock-freedom s an essental attrbute of any Multcast fault-tolerant routng algorthm. The followng part of ths secton s devoted to provng that the proposed method (.e., MEFH methodology) s deadlockfree. The followng theorem proves the acyclcty of the channel dependency graph of the proposed multcast faulttolerant routng methodology. Lemma 1: The multcast fault-tolerant routng algorthm based on the MEFH methodology causes no deadlock n 2-D meshes that contans any fault regon. Proof: We ntally consder the source node and the frst destnaton node n ordered lst here. Accordng to wormhole message passng and path-based multcast scheme, when the message reaches the frst destnaton node address t wll be the new source and wll be removed from destnatons lst. Then, the second destnaton node becomes the frst destnaton node n ordered lst. As a result, only the proof for the source and the frst destnaton node s explaned here. Ths approach can be appled to all destnatons. Consequently lemma wll be proved. Accordng to the postons of n s and n d, the proof falls nto one of the followng three cases: Case I: n s and n d are nsde. In such case, no changes are made on the deadlock-free orgnal fault-tolerant algorthm. Consequently, the orgnal fault-tolerant routng algorthm guarantees deadlock-freedom. Case II: n s or n d s nsde. In ths case, the routng strategy s dvded nto two phases. Frst, s that a part of the course of message transmsson s n the class and another e part s outsde the class. The ne Î node s the connectng pont of these two phases. Accordng to the routng rules n an attempt to fnd a path to forward a message outsde the class, the orgnal algorthm s deadlockfree. The second phase s that routng s done nsde the class. Accordng to the characterstcs of the class, we had assumed that classes are solated and path selecton scheme s taken on one dmenson; there s no msroutng operaton, no cycle of deadlocked messages exsts and deadlock-freedom can be assured. Case III: Both n s and n d nodes are nsde. If both n s and n d are n the same class, the message s delvered explctly to ts destnaton wthout producng any msroutng. Hence, n ths case no deadlock wll occur, otherwse t s handled smlar to Case II. 6. Smulaton Study In ths secton, we analyze how the proposed method nfluences the network performance for dfferent fault models. Hence, we wll frst descrbe the smulaton model and then the performance results are shown and evaluated. A flt-level, lstener-based object orented smulator [29] has been used to llustrate the performance of the presented method. An 8 8 mesh network wth pont to pont and bdrectonal lnks has been employed for all smulaton experments, and only wormhole swtchng mechansm s appled. We have fxed the number of destnatons at 15. The wormhole swtchng s consdered as the flow control mechansm. When wormhole flow control s appled, a message s not allowed to re-enter the adaptve layer after havng been routed n the escape layer. The smulatons have been performed usng a base message sze of 8 flts, and also the wdth of each flt s 128 bt. We calculated the power consumpton of lnks of each router n 100 nm technology lbrary. In ths technology, V DD s set to 1.1V, the clock frequency s set to 200 MHz, and the length of lnks between two adjacent routers s set to 1 mm for the mesh topology. The message generaton rate s also equal for all the nodes. The performance and power consumpton of our method s evaluated by terms of average message latency (cycles) and total power consumpton (mw) vs. traffc load. Boppana- Chalasan s fault-tolerant routng [15, 18] s used to govern routng on a faulty network. As we have prevously dscussed, the routng methodology requres addtonal vrtual channels n order to be deadlock-free. Thus, 4 vrtual channels wth 8 flts deep buffers are requred by each varaton of the methodology to avod deadlock phenomenon. We have also evaluated the fault-tolerance of the H- shape, L-shape, Block-shape, and overlapped fault patterns n a 2-D (.e., 8 8) mesh topology, as shown n Table 1. For ths topology, all the combnatons up to sx faults (.e., 10% of the total number of routers) have been exhaustvely analyzed. Results for up to 10% faults are shown n Fgures 3 and 4 and the confdence ntervals are always lower than 5%. Table 1. Dfferent varatons of the fault combnatons that utlze the methodology Fault pattern Faulty ponts set H-shape (2,1)(2,2)(2,3)(3,2)(4,1)(4,2)(4,3) Overlapped (2,2)(2,3)(3,3)(3,5)(4,3)(4,5)(4,6) L-shape (2,1)(2,2)(2,3)(2,4)(3,4)(4,4)(5,4) Block-shape (2,2)(2,3)(2,4)(3,2)(3,3)(3,4)(4,2)(4,3)(4,4)

8 M. ValadBeg and F. Safae: Deadlock-Free Path-Based Fault-Tolerant Multcast (Short Paper) 43 Before explanng both fgures and results, we would lke to stress the pont that smulaton studes show that our approach has a good performance n order to support multcast. Moreover, both Fgure 3 and Fgure 4 show a better performance wth 15 destnatons compared to uncast fault tolerant routng that depends on one source and one destnaton. Average Message Latency (Cycle) H-pattern Ovelapped L-pattern Block-pattern Traffc Load(Cycles) Fgure 3. Average message latences vs. traffc load obtaned by the proposed methodology n an 8 8 Mesh wth 15 destnatons and 4 vrtual channels for each fault pattern lsted n Table 1 Total Power Consumton (mw H-pattern Ovelapped L-pattern Block-pattern Traffc Load(Cycles) Fgure 4. Average power consumpton vs. traffc load n an 8 8 Mesh wth 15 destnatons and 4 vrtual channels obtaned by the proposed methodology for each fault pattern lsted n Table 1 Fgure 3 shows the acheved message latency over normalzed accepted traffc n an 8 8 mesh wth 15 destnatons for 4 dfferent shapes of fault patterns presented n Table 1. In ths confguraton, we used 4 vrtual channels per physcal channel. The fgure reveals that for low traffc load, all four fault patterns have the same latency, but they begn to behave dfferently around the moderate and saturaton regons. At overlapped pattern, congested overlapped nodes between two f-rngs lead to ncrease the average message latency and t can be seen that the worst case has been encountered for overlapped pattern. Fgure 4 compares the power consumpton of the network for dfferent varatons of the proposed methodology as a functon of traffc load by each node n an 8 8 mesh wth 15 destnatons and 4 vrtual channels per physcal lnk. Such curves provde an ndcaton on the degree of performance degradaton caused by fault patterns n the network. It s evdent that, as the traffc load n the network ncreases, the power dsspaton dagram of each pattern ncreases almost lnearly before reachng a pont on the curve. Beyond ths pont, the dsspated power decreases abruptly. Accordng to the dagram we wtness hgh level of ntal consumpton of power that s due to the constructon of the path. Then the power consumpton s reduced and reaches a plateau because the path constructon s completed and there s no need for the extra amount of power. Among fault shapes, the Blockpattern s a stuaton that we just use basc fault- tolerant routng algorthm for H-pattern. Ths means sem-faulty nodes n H-pattern wll be consdered faulty. As the fgure demonstrates, however, the state of Block-pattern s better than H-pattern under 0~60% of traffc load. Beyond 60% of maxmum traffc load, smulaton results exhbt meanngful performance degradaton for Block-pattern. The degradaton reason s related to extra faulty nodes. From smulaton studes we can conclude that our proposed methodology obtans proper performance degradaton n the network. 7. Conclusons and Future Works Due to the exponental growth of crcut ntegraton, the relablty of NoCs s concerned wth ts functonalty n the presence of gven falure probabltes of ther enttes. NoCs relablty pertans to nterconnecton networks whose nodes and/or channels have assocated probabltes of beng operatonal. The man contrbuton of ths artcle s that the proposed approach supports multcast routng whch s based on path-based multcast scheme that easly can handle statc faults. Moreover, the path used does not need to be reconstructed when a fault occurs. Further, our approach s deadlock-free, t supports the statc fault model whch s applcable to both convex and concave fault regons. Ths method flls the gap of not havng an optmum multcast fault-tolerant scheme and ths s the frst attempt to mplementng multcast fault-tolerant routng to support fault regons. In a near future we are plannng to not only mprove t but also to perform more research on the ssue and fnd an optmum soluton and also extend the desgn of path-based fault-tolerant multcast to cover dynamc faults n NoCs wth 2-D mesh topology. Acknowledgement Frst Author would lke to thank Mr. Shahed ValadBeg for hs useful comments and help. References [1] F. A. Samman, T. Hollsten, and M. Glesner, "Adaptve and Deadlock-Free Tree-Based Multcast Routng for Network-on-Chp," IEEE Transactons on Very Large Scale Integraton Systems, vol. 18, no. 7, pp , [2] L. Benn and G. De Mchel, "Networks on Chp: a New Paradgm for Systems on Chp Desgn," IEEE Transactons on Computers, vol. 35, no. 1, pp , [3] G. De Mchel and L. Benn, Networks on Chps, Morgan Kaufmann-Publshers, [4] C. Constantnescu, "Trends and Challenges n VLSI Crcut Relablty," IEEE Mcro, vol. 23, no. 4, pp , [5] T. Dumtras, S. Kerner, and R. Marculescu, "Towards on- Chp Fault-Tolerant Communcaton," Proc. Asa and South Pacfc Desgn Automaton Conference, pp , [6] Y. B. Km, and Y. Km, "Fault Tolerant Source Routng for Network-on-chp," Proc. of the IEEE Internatonal

9 The CSI Journal on Computer Scence and Engneerng, Vol. 6, No. 2 & 4 (b), Symposum on Defect and Fault-Tolerance n VLSI Systems, pp , [7] M. Al, M. Welzl, M. Zwcknagl, and S. Hellebrand, "Consderatons for Fault-Tolerant Network on Chps," Proc. of the Internatonal Conference on Mcroelectroncs, pp , [8] J. Duato, S. Yalamanchl, and L. M. N, Interconnecton networks: An Engneerng Approach, Morgan Kaufmann Publshers, [9] X. Chen and J. Wu, "Path-Based Fault-Tolerant Multcastng n Mesh-Connected Multcomputers," The Handbook of Ad Hoc Wreless Networks, CRC Press, [10] L. H. Hsu and C. K. Ln, Graph Theory and Interconnecton Networks, CRC Press, [11] N. A. Nordbotten, Fault-Tolerant Routng n Interconnecton Networks, Ph.D. Thess, Faculty of Mathematcs and Natural Scences, The Unversty of Oslo, [12] J. Wu and Z. Jang, "On Constructng the Mnmum Orthogonal Convex Polygon for the Fault-Tolerant Routng n 2-D Faulty Meshes," IEEE Transactons on Relablty, vol. 54, no. 3, pp , [13] M. H. Farahabady, F. Safae, A. Khonsar, and M. Fathy, "Characterzaton of Spatal Fault Patterns n Interconnecton Networks, Journal of Parallel Computng, vol. 32, no , pp , [14] A. A. Chen, and J. K. Km, "Planar Adaptve Routng: Low Cost Adaptve Networks for Multprocessors, Proc. of the Internatonal Symposum on Computer Archtecture, pp , [15] R. V. Boppana, and S. Chalasan, "Fault-Tolerant Wormhole Routng Algorthms for Mesh Networks," IEEE Transactons on Computers, vol. 44, no. 7, pp , [16] Y. M. Boura, and C. R. Das, "Fault-Tolerant Routng n Mesh Networks," Proc. of the Internatonal Conference on Parallel Processng, pp , [17] Y. M. Boura, and C. R. Das, "Effcent Fully Adaptve Wormhole Routng n n-dmensonal Meshes," Proc. of the Internatonal Conference on Dstrbuted Computng Systems, pp , [18] S. Chalasan, and R. V. Boppana, "Communcaton n Multcomputers wth Nonconvex Faults," IEEE Transactons on Computers, vol. 46, no. 5, pp , [19] S. P. Km, and T. Han, "Fault-Tolerant Wormhole Routng n Mesh wth Overlapped Sold Fault Regons," Parallel Computng, vol. 23, no. 13, pp , [20] C. L. Chen, and G. M. Chu, "A Fault-Tolerant Routng Scheme for Meshes wth Nonconvex Faults," IEEE Transactons on Parallel and Dstrbuted Systems, vol. 12, no. 5, pp , [21] J. Wu, "A Fault-Tolerant and Deadlock-Free Routng Protocol n 2D Meshes Based on Odd-Even Turn Model," IEEE Transactons on Computers, vol. 52, no. 9, pp , [22] D. F. Robnson, P. K. Mcknley, and B. H. C. Cheng, "Path Based Multcast Communcaton n Wormhole Routed Undrectonal Tours Networks," Journal of Parallel and Dstrbuted computng, vol. 45, pp , [23] X. Ln and L. M. N, "Deadlock-Free Multcast Wormhole Routng Multcomputer Networks," Proc. of the Internatonal Symposum on Computer Archtecture, pp , [24] P. Mohapatra and V. Varavthya, "A Hardware Multcast Routng Algorthm for Two Dmensonal Meshes," Proc. of the IEEE Symposum on Parallel and Dstrbuted Processng, pp , [25] R. V. Boppana, S. Chalasan, and C. S. Raghavendra, "Resource Deadlock and Performance of Wormhole Multcast Routng Algorthms," IEEE Transactons on Parallel and Dstrbuted Systems, vol. 9, no. 6, pp , [26] D. K. Panda, S. Snghal, and R. Keshavan, "Multdestnaton Message Passng n Wormhole k-ary n- Cube Networks wth Base Routng Conformed Paths," IEEE Transactons on Parallel and Dstrbuted Systems, vol. 10, no. 1, pp , [27] R. V. Boppana and S. Chalasan, "Falut-Tolerant Multcast Comuncaton n Multcomputers," Proc. of the IEEE Internatonal Conference on Parallel and Dstrbuted Processng, pp , [28] X. Ln, H. Xu, and A.-H. Esafahnan, "Performance Evaluaton of Multcast Wormhole Routng n 2D-Mesh Multcomputers," Proc. of the Internatonal Conference of Parallel Processng, pp , [29] A. Nayeb, S. Meraj, A. Shamae, and H. Sarbaz-Azad, "XMulator: an Object oorented XML-Based Smulator," Proc. of the Asa Internatonal Conference on Modelng and Smulaton, pp , Majed ValadBeg receved the B.Sc. degree n Computer Hardware Engneerng from Shahd Rajaee Unversty, Tehran, Iran, n He s currently M.Sc. student n Computer Archtecture Engneerng n Department of Electrcal and Computer Engneerng, Shahd Behesht Unversty, Tehran, Iran. He s a member of Scorpus smulaton team whch has partcpated n many nternatonal RoboCup Compettons. He s also an IEEE student member. Hs man Researches focus on network-on-chps, nterconnecton networks, and performance evaluaton. E-mal: m.valadbeg@mal.sbu.ac.r

10 M. ValadBeg and F. Safae: Deadlock-Free Path-Based Fault-Tolerant Multcast (Short Paper) 45 Farshad Safae receved the B.Sc., M.Sc., and Ph.D. degrees n Computer Engneerng from Iran Unversty of Scence and Technology (IUST) n 1994, 1997 and 2007, respectvely. He s currently an assstant professor n the Department of Electrcal and Computer Engneerng, Shahd Behesht Unversty, Tehran, Iran. Hs research nterests are performance modellng/evaluaton, Interconnecton networks, computer networks, and hgh performance computer archtecture. E-mal: f_safae@sbu.ac.r Paper Handlng Data: Submtted: Receved n revsed form: Accepted: Correspondng author: Dr. Farshad Safae, Department of Electrcal & Computer Engneerng, Shahd Behesht Unversty, Tehran, Iran.