Fault-Tolerant Routing Schemes in RDT(2,2,1)/α-Based Interconnection Network for Networks-on-Chip Designs

Transcription

1 Fault-Toleant Routing Schemes in RDT(,,)/α-Based Inteconnection Netwok fo Netwoks-on-Chip Designs Mei Yang, Tao Li, Yingtao Jiang, and Yulu Yang Dept. of Electical & Compute Engineeing Univesity of Nevada, Las Vegas Las Vegas, NV 54, USA {meiyang, Dept. of Compute Science and Technology Nankai Univesity Tianjing, 37, China Abstact It has been well ecognized that the fault-toleance capability is vital fo a NoC system, since one faulty link/pocesso may isolate a lage faction of pocessos. Continuing fom a pevious pape [3] whee a RDT(,,)/α-based inteconnection netwok fo NoC designs was poposed, in this pape, we investigate fault-toleant outing schemes on NoC systems featuing a RDT-based inteconnection netwok. In specific, we popose two fault-toleant outing schemes in the pesence of eithe single link/node failue o multiple link/node failues. The poposed outing schemes ae based on deteministic outing. Altenative outes ae discoveed by popely selecting the intemediate nodes between the souce and the destination nodes on the ank toi. As of the single link/node failue case, we show that the numbe of outes on the detoued oute geneated by the poposed outing scheme is at most moe than the numbe of outes on the oiginal oute.. Intoduction Advances in VLSI technology will soon allow a single chip to contain moe than one billion tansistos [], indicating that a lage numbe of pocessing units (such as CPU, DSP, multimedia pocesso) shall be integated into one packaged chip. In these new systems, communication esouces ae competed by the vast volume computational esouces. With a communication-centic design style, Netwoks-on-Chip (NoC) [] was poposed to mitigate the complex communication poblems. A NoC system is composed of a lage numbe of pocessing units communicating to othe units though outes acoss the inteconnection netwok. Packets tavel though the netwok by passing one o moe hops between the souce and the destination tiles. As semiconducto technology scales down to nanomete domain, pocessing units (PUs), outes (nodes), and inteconnect links (links) ae all subject to new types of malfunctions and failues that ae hade to pedict and avoid [5]. Paticulaly, failues of nodes/links may isolate a lage numbe of fault-fee PUs. A majo challenge in NoC designs thus is to povide fault toleance unde link/node failue(s). In [3], we poposed an inteconnection netwok achitectue fo NoC based on a special Recusive Diagonal Tous (RDT) stuctue [], named as RDT(,,)/α. In RDT(,,)/α, each node has links to fom base tous (ank-) and uppe toi with the cadinal numbe. RDT(,,)/α povides a pomising solution fo inteconnection netwoks of NoC designs with its distinct advantages: ) high scalability due to its ecusive stuctue, ) low powe consumption due to its smalle diamete and aveage distance, 3) achitectual customizability with its embedded mesh/tous topologies, 4) fault-toleance capability with a constant node degee of, and 5) feasibility of layout compatible with cuent and futue VLSI technologies [7]. In this pape, we attempt to investigate vaious fault-toleant outing schemes applicable to the RDT(,,)/α-based inteconnection netwok. As pointed out in [4][7], adaptive outing which employs vitual [][3] is infeasible fo NoCs due to the need of lage buffes and lookup tables as well as complex shotest-path algoithms. Instead, we conside the deteministic outing based fault-toleant outing schemes which eoute the packets by popely selecting the intemediate outes between the souce and the destination nodes. The poposed fault-toleance outing schemes have no advese impacts on outing in the absence of faults. The est of the pape is oganized as follows. In Section, we give an oveview of the RDT stuctue. In Section 3, we descibe the NoC achitectue, the delay model, and the outing algoithms when no faults ae pesent in the inteconnection netwok. In Section 4, we pesent the fault-toleant outing algoithm unde single link/node failue. In Section 5, the faulttoleant outing algoithm unde multiple link/node failues is pesented. Section 6 concludes the pape.. RDT(,,)/α Stuctue The RDT stuctue [] is constucted by ecusively ovelaying -D diagonal meshes (toi). The base tous is a twodimensional squae aay of N by N nodes, each of which is numbeed with a two-dimensional numbe as follows: (, ) (, ) (, ) (N-, ) (, ) (, ) (, ) (N-, ) (, ) (, ) (, ) (N-, ) (, N-) (, N-) (, N-) (N-, N-) whee N = n k and both n and k ae natual numbes. The tous netwok is fomed with fou links between node(x, y) and its neighboing fou nodes: (mod(x±, N), y) and (x, mod(y±, N)). This base tous is also called ank- tous. On the ank- tous, a new tous-like netwok (ank- tous) is fomed by adding fou links between node (x, y) and nodes (x±n, y±n). The diection of the new tous-like netwok is at an angle of 45 degees to the oiginal tous. On the ank- tous, anothe

2 tous-like netwok (ank- tous) can be fomed by adding fou links in the same manne. Similaly, a ank-() tous can be fomed upon ank- tous. An independent tous on ank-i is one that does not have links to othe toi on ank-i. RDT(n, R, m) is a class of netwoks in which each node has links to fom base tous (ank-) and m uppe toi (the maximum ank is R) with the cadinal numbe n. Thus, the degee of the RDT(n, R, m) is 4(m) []. One of the uppe ank tous is assigned to each node in the RDT(n, R, m) afte n, R, and m ae set. Thus, the stuctue of the RDT(n, R, m) also vaies with diffeent assignments fo uppe ank toi to each node. This assignment is called tous assignment. A netwok in which evey node has links to fom all possible uppe ank toi (i.e. RDT(n, R, R)) is called a pefect RDT (PRDT(n, R)), whee n is the cadinal numbe, and R is the maximum ank. We efe a pefect tous as one that contains all links and no two links ovelap. A PRDT is unealistic due to its lage degee (4(R)). Vaious stuctues of the pactical RDT can be fomed by changing n and m, which povide vaious chaacteistics and can be applied to diffeent applications. We conside a pactical RDT stuctue, RDT(,, )/α, with its tous assignment shown in Fig.. In this assignment, each node has eight links, fou fo the base (ank-) tous and fou fo ank- o ank- toi. Fig. only shows pat of these links. In RDT(,,)/α, we only use fou independent ank- toi with thei souce nodes located at (,), (,), (,) and (3,), espectively. Thity-two ank- toi ae fomed on fou ank- toi (,), (,), (,) and (3,), espectively. Compaed with othe RDT(n, R, m) stuctues (such as RDT(, 4, )/α, RDT(, 4, )/ß []), RDT(,, )/α is much simple and suitable fo netwoks with a thousand o less nodes Figue. Tous assignment fo the RDT(,,)/α. 3. Routing Algoithms without Link/Node Faults 3. The NoC Achitectue Ou study is based on the NoC achitectue shown in Fig., whee each PU is attached on a switch/oute which is connected to the inteconnection links. Fig. 3 shows a possible oute stuctue which consists of input and output pots and inteface to the attached PU. At each input and/o output pot, a limited numbe of buffes ae povided to stoe packets, and a line contolle is used to select the packet to be eceived fom the input link o sent on the output link. A cental contolle pefoms the functions of outing and abitation. Input : link contolle Route Netwok Pocessing unit Figue. NOC achitectue. Injection Switching fabic Cental contolle Routing Pocesso inteface Abitation Ejection Figue 3. Route stuctue. inteface Output 3. Delay Model Fo an NoC application, an impotant pefomance metic is the delay, which depends on the taffic patten of the application and many othe factos, such as packet/flit size, oute s abitation scheme, etc. [7]. In this study, we employ a simple delay model as follows. Fo a NoC netwok shown in Fig., the delay expeienced by a packet on the oute fom the souce PU to its destination PU includes the tansmission delay on the wies (o wie delay), the pocessing delay of the outes and the queuing delay at the outes. We assume the pocessing delay and queuing delay ae the same fo all outes, denoted as T p, T q, espectively. Thee may exist diffeent types of wies with vaious lengths. We denote the unit length wie delay as T, the length of wie type i as l i, and the numbe of wies of type i as n i. Let N be the numbe of hops a packet tavels between a souce to a destination oute and m be the numbe of diffeent types of wies. Then we can detemine the total delay expeienced by a packet as T = ( T T )( N cn T l () total p q ) m i= i i whee c epesents the constant popotional to the poduct of the esistance pe unit length and the capacitance pe unit length. As discussed in [], the effect of length to wie delay can be alleviated by beaking long lines into shote sections with a epeate diving each section. Hence, it is possible to match the wie delay of a long line to the total wie delay of a set of shote lines assuming the length of the long line is less o equal to the sum of the lengths of shote lines in the set. And we assume the pocessing and the queuing delays expeienced at a oute ae fa longe than the wie delay of the line connecting two adjacent outes. Hence the total delay expeienced by a packet is

3 dominated by the sum of the pocessing and queuing delays on the outes (including the intemediate outes, and the souce and destination outes). Hence, Eqn. () can be simplified to T total ( Tp Tq )( N ) () As one can see fom Fig. 4, on the RDT(,, )/α stuctue, if a oute on ank- tous is selected to connect S and D, the numbe of outes on this oute is. This is much less than an altenative oute on ank- tous that has 5 outes. In anothe example, the numbe of outes on the oute fom S to D on ank- tous is, which is much less than that of outes on the coesponding oute on ank- and ank- toi, 5 and, espectively. These two examples indicate that, accoding to Eqn. (), the total delay of a oute can be educed if moe links on highe ank toi ae included S S D Figue 4. Wies on RDT(,, )/α. Fo cleaness, we only show the nodes epesenting outes. All the outing schemes discussed in this pape ae based on the delay model shown in Eqn. (). Fo outing in the RDT(,, )/α-based inteconnection netwok without link/oute failue, we can diectly apply the floating vecto outing algoithm [][], which is based on the vecto outing algoithm [] poposed fo PRDT stuctues. In the following, we will biefly intoduce the two outing algoithms. 3.3 Vecto Routing Algoithm The basic idea of the vecto outing algoithm is to epesent the oute fom a souce node to the destination node with a combination of unit vectos, each of which coesponds to each ank of toi. Fig. 5 shows the diections of the unit vectos fo each ank tous fo RDT(,, )/α, which otate in clockwise diection at an angle of 45 degees as the ank inceases. Y ank- Y ank- Y ank-, ank- ank- D ank- Figue 5. Diections of unit vectos fo RDT(,, )/α. We ae given a vecto fom a souce node to the destination node epesented as A = a by whee and Y ae the unit vectos of the base (ank-) tous. A can be epesented with a combination of the unit vectos, R Y,, R, Y on ank-r to ank- toi as A = a by = vrh R vrvyr... vh vvy... vh vvy whee (v h, v v ) epesents the vecto on ank- tous, whee R. And v h and v v ae maximized in ode to use the uppe ank tous as much as possible. Given the vecto A = a by, we list the vecto outing algoithm as follows. Algoithm Vecto Routing (a, b): begin fo = to R do g (a b)/ f - (a - b)/ v h a - (n * g n * f) v v b - (n * g n * f) a g b f end The vectos ae computed at the souce node and encapsulated into the packet. Then we oute the packet to the nodes following the ode of ank-r, ank-(r-),, ank- vectos. On the same ank tous, the outing is pefomed accoding to a pedetemined ode, fo example, Y outing []. Theoem The maximum numbe of outes that a packet tavels on ank- tous is n when using the vecto outing algoithm, whee n is the cadinal numbe. The poof of Thm. follows the poof of Thm. 5 in []. 3.4 Floating Vecto Routing Algoithm The floating vecto outing algoithm [] was poposed fo pactical RDTs, such as RDT(,, )/α. In this algoithm, the vecto computation is done at the souce node accoding to the vecto outing algoithm fo the PRDT, and stoed in the packet heade. Each oute maintains a simple table indicating the diection to each the neaest node fo each ank of tous. A oute checks the vecto in the packet heade, and sends the packet to the neaest oute on the highest ank tous accoding to the simple table. This pocess is called floating, though which each oute can use any ank of tous by only a single step packet tansfe to a neighbo oute. Based on Thm. and the desciption of the floating vecto outing algoithm, we have: Coollay The maximum numbe of outes that a packet tavels on ank- tous is n when using the floating vecto outing algoithm, whee n is the cadinal numbe. In [3], we have showed the feasibility of using the RDT(,, )/α stuctue as the inteconnection netwok fo a NoC design. In this pape, we futhe exploe the fault-toleance capability of the RDT(,, )/α stuctue. In specific, we popose two faulttoleant outing schemes that intoduce the least exta pocessing and queuing delays (equivalent to the least incease of the numbe of outes as shown in Eqn. ()) on the RDT(,, )/αbased inteconnection netwoks. 4. Fault-Toleant Routing Algoithm unde Single Link/Node Failue 4. Fault Model The following assumptions ae used in this pape. ) Any link o node in the netwok can fail, and the faulty components ae unusable; that is, data will not be tansmitted ove a faulty link o outed though a faulty node. ) The fault model is static, that is, no new faults occu duing a outing pocess. 3) Both souce and

4 destination nodes (on any ank tous) ae fault-fee. 4) The faults occu independently. 5) If a node fails, the fou links associated with the node on ank- tous also fail. 6) Faulty link(s)/node(s) ae known to all othe nodes in the same ank. 4. Single Link/Node Failue Given a pai of souce and destination nodes S and D on the RDT(,, )/α stuctue, using the floating vecto outing algoithm, we know that the oute fom S to D is composed of oute segments on diffeent ank toi and floated oute segments on ank- tous. The oute thus can be epesented as S~S - D ~S -D /S -D /D, whee ~ epesents a floating on ank-, and S and D epesent the souce node and the destination node on the oute segment on a ank- tous, espectively. Note that a oute may consist of all the oute segments o subsets of these oute segments. Fo single link/node failue on one segment floating on ank- tous, we can always find one altenative oute without inceasing the numbe of outes since each oute has fou possible outes (each with the same numbe of hops/outes) to float to a oute on an uppe ank tous. In the following, we enumeate the cases of single link/node failue happening on the oute segment on one ank tous. S I D S I (a) (b) (c) Figue 6. Thee distinct cases of single link failue on ank- tous of the RDT(,, )/α stuctue. By Coollay, we know that on the RDT(,, )/α stuctue, using the floating vecto outing algoithm, the numbe of outes a packet tavels fom S to D is no moe than 3. Hence, thee ae thee possible single link failues on the oute segment on ank-, as shown in Fig. 6, whee faulty links ae maked by. N S I D (a) (b) Figue 7. Two distinct cases of single node failue on ank- tous of the RDT(,, )/α stuctue. D N Fo the same eason of single link failue, thee ae two possible cases of single node failue, as shown in Fig. 7, whee faulty nodes ae maked by. 4.3 Fault-Toleant Routing Algoithm unde Single Link/Node Failue As one can see fom Figs. 6 and 7, if the failue is on the (o Y) diection, then we should detou the packet by sending it though the Y (o ) diection fist. The vecto needs to be changed to eflect the detou if necessay. In each packet, we add a field flag, which is set as floating when the packet is floated to a node o outing when the packet S I S I D is outed to a node on a ank- link, and a vaiable to indicate the cuent ank value. Fig. shows the packet fomat. heade length flag ank-r vectos packet heade... ank- vectos payload length Figue. Packet fomat. Let denote the diection on ank-, diection on ank-, packet payload CRC denote the - Y denote the Y diection on ank-, and Y denote the -Y diection on ank-. A distibuted fault-toleant floating outing algoithm is listed as follows, whee (i x, i y ) epesents the vecto of a node i on ank- tous. Algoithm Floating Vecto Routing unde Single Failue (FVRSF): begin //Step : the souce node computes the vectos, othe nodes //check the flag and decement the vecto value accodingly if i = S and S D then call Vecto Routing to compute vectos fom ank R to set as max{i (v ih, v iv ) (, )} else if flag = outing then if the packet is eceived fom then v h v h - else v h v h if the packet is eceived fom Y then v v v v - else v v v v else if flag = floating then if the packet is eceived fom then v oh v oh - else v oh v oh if the packet is eceived fom Y then v ov v ov - else v ov v ov //Step : check the availability of the link and send the packet //accodingly if i is on ank- then set flag as outing if (v h, v v ) (, ) then if v h and the link on the v h diection (i.e., fo v h > o fo v h <) is not faulty then send the packet to v h diection else if v h = and the link on the v v diection (i.e., Y fo v v > o Y fo v v <) is not faulty then send the packet to v v diection else if v h and the link on the v h diection is faulty then if v v = then send the packet to Y else send the packet to v v diection else if the link on the v v diection is faulty then send the packet to else if find p = - to that (v ph, v pv ) (, ) then p, goto Step else goto end //Step 3: floating to a node neaest to node i on ank- find the non-faulty node j(j x, j y ) on ank- tous with min{abs(i x j x v h ) abs(i y j y v v )} by checking the table on node i set flag as floating if i x j x then send the packet to (j x i x ) diection else send the packet to (j y i y ) diection end

5 Theoem Conside a oute fom a souce node S to a destination node D on the RDT(,, )/α stuctue. If thee exists a single link/node failue on the oiginal oute geneated by the floating vecto outing algoithm, the numbe of outes on the detoued oute (also the shotest oute) geneated by the faulttoleant floating vecto outing algoithm is at most moe than the numbe of outes on the oiginal oute. Poof: As discussed in the fault model, single link/node failue only affects outing on one ank tous. Based on Coollay, we can deive thee possible cases of single link failue as shown in Fig. 6, and the two possible cases of single node failue as shown in Fig. 7. One can veify that, the fault-toleant floating outing algoithm, with the mbedded vecto outing algoithm, computes the shotest oute (with the least numbe of outes) fom S to D on each ank-, and futhe the shotest oute fom S to D. The numbe of outes on the detoued oute geneated by the faulttoleant floating vecto outing algoithm, compaed with the oiginal oute, is eithe equal to the numbe of outes on the oiginal oute (as the case shown in Fig. 7 (a)) o moe than the numbe of outes on the oiginal oute (as the case shown in Fig. 7(b) and the cases shown in Fig. 6). The incease of the numbe of outes on the detoued oute is minimized fo all thee cases. Hence the theoem follows. The above theoem indicates that the exta queuing and pocessing delays is minimized using the FVRSF algoithm. Anothe advantage of the FVRSF algoithm is that each oute decides the best oute based on the fault infomation of its fou links on one ank tous. No global fault infomation thus needs to be maintained at each oute. In this way, the ovehead intoduced is vey low. Fig. illustates two examples of the FVRSF algoithm. The oiginal oute fom S (, ) to D (7, 6) geneated by the floating vecto outing algoithm is (, )-(3, )-(5, 3)-(7, 5)-(7, 6), which tavels though 5 outes. Assume that the link between (3, )-(5, 3) on ank- fails. The detoued oute geneated by the FVRSF algoithm is (, )-(3, )-(, 3)-(3, 5)-(5, 7)-(7, 5)-(7, 6) with 7 outes, which is moe than the numbe of outes on the oiginal oute S S Figue. Two examples of the FVRSF algoithm. As anothe example, the oiginal oute fom S (, ) to D (, ) geneated by the floating outing algoithm is (, )-(, )-(, )-(, )-(, ), which includes 5 outes. In the case of failue of node (, ), the detoued oute geneated by the FVRSF algoithm is (, )-(, )-(, )-(, )-(, ) with 5 outes. Obviously, this is the best detoued oute with the least numbe of outes that a packet has to tavel. 5. Fault-Toleant Routing Algoithm unde Multiple Failues D D 5. Multiple Link/Node Failues Multiple link/node failues may exist on diffeent ank toi of the RDT(,,)/α stuctue. As discussed in Section 4., a node failue can be modeled as multiple link failues. As such, we only conside link failues hee. Based on the constuction of the RDT(,,)/α stuctue, we can decompose multiple link failues on diffeent ank toi into sets of link failues on the same independent tous on one ank tous. In the following, we discuss the fault-toleance outing scheme unde multiple link failues on the same independent tous on one ank- tous. When multiple link/node failues exist on a ank- tous, the FVRSF algoithm cannot geneate the detoued oute with the least numbe of outes since the decision made by each oute is not based on global view of othe failues. In this case, we adopt the method discussed in [6] to identify the best intemediate oute though which the detoued oute uses the least numbe of outes. Note that thee may exist moe than one such intemediate outes. We use I i to denote such intemediate outes between S and D. 5. Fault-Toleant Routing Algoithm unde Multiple Failues When applying the method of identifying the best intemediate oute in combination with the vecto outing algoithm, the following equiements have to be satisfied fo an intemediate oute I i to ensue that the faulty links ae avoided when outing fom S via I i to D on ank- tous. ) All the faulty links shall not appea on all possible S -I i outes geneated by the vecto outing algoithm. ) All the faulty links shall not appea on all possible I i -D outes geneated by the vecto outing algoithm. 3) Thee is no I i giving a shote oute than I i. The fist equiement guaantees that packets can be outed fom S to I i, and the second equiement guaantees that packets can be outed fom I i to D. Since the vecto outing algoithm is a deteministic outing scheme, these two equiements ae sufficient to ensue that packets can avoid the faulty links. The thid equiement guaantees that the final oute is the shotest possible oute. d Let R S be the set of outes eachable though vecto outing fom S, let R d D be the set of outes that can each D though vecto outing. Let n(i, j) be the numbe of outes on the minimal delay oute fom oute i to oute j. We define R k as follows: a oute I is in R k if and only if n(s, I) n(i, D) = n(s, D) k. Let k be the smallest k fo which R k R d S R d D is nonempty. Then we have: Theoem 3 A oute I satisfies all thee equiements if and only if I R k R d S R d D. The fault-toleant outing algoithm unde multiple failues is descibed as follows, whee (Iv ih, Iv iv ) epesents the vecto fo the intemediate oute on the ank- tous with link failues. Coespondingly, in the packet heade, a new field of the intemediate node vecto on the cuent ank will be inseted. Algoithm Floating Vecto Routing unde Multiple Failues (FVRMF): begin //Step : the souce node computes the vectos, othe nodes //check the flag and decement the vecto value accodingly if i = S and S D then call Vecto Routing to compute vectos fom ank R to else if flag = outing then set as the highest ank with (v h, v v ) (, )

6 if (Iv ih,iv iv ) (, ) then if the packet is eceived fom then Iv ih Iv ih - else Iv ih Iv ih if the packet is eceived fom Y then Iv iv Iv iv - else Iv iv Iv iv if (v h,v v ) (, ) then if the packet is eceived fom then v h v h - else v h v h if the packet is eceived fom Y then v v v v - else v v v v else if flag = floating then if the packet is eceived fom then v oh v oh - else v oh v oh if the packet is eceived fom Y then v ov v ov - else v ov v ov //Step : if the oute is the souce node on ank-, identify //the intemediate oute and update the vecto list if i is on ank- then if flag = floating then set flag as outing S i D (v h, v v ) compute R d S as defined compute R d D as defined k compute R k as defined while R k R d S R d D = do k k compute R k as defined set I as one oute in R k R S d R D d inset I=(Iv ih, Iv iv ) to the intemediate oute list on ank- if (Iv ih, Iv iv ) (, ) then if Iv ih then send the packet to Iv ih diection else send the packet to Iv iv diection if (v h, v v ) (, ) then if v h then send the packet to v h diection else send the packet to v v diection else if find p = - to that (v ph, v pv ) (, ) then p, goto step else goto end //Step 3: floating to a node neaest to node i on ank- find the non-faulty node j(j x, j y ) on ank- tous with min{abs(i x j x v h ) abs(i y j y -v v )} by checking the table on node i set flag as floating if i x j x then send the packet to (j x i x ) diection else send the packet to (j y i y ) diection end S Figue. An example of the FVRMF algoithm. I D Fig. shows an example of the FVRMF algoithm unde multiple failues on the same ank tous. Thee ae thee link failues on ank- tous shown in dotted lines. Accoding to the FVRMF algoithm, I will be selected as the best intemediate oute between S D with the minimized numbe of outes. If thee exists a possible oute between a souce node to a destination node, we can find a best detoued oute with the least numbe of outes using the FVRMF algoithm. Howeve, due to the complexness of multiple failues, thee is no bound on the numbe of outes that will be used on the detoued oute. 6. Conclusion In this pape, we investigate fault-toleant outing schemes on NoC systems featuing a RDT-based inteconnection netwok. We poposed the FVRSF and FVRMF algoithms fo faulttoleant outing unde single link/node failue o multiple link/node failues espectively. Both algoithms ae based on deteministic outing, and hence, no vitual channel is needed. We showed that using FVRSF algoithm, the numbe of outes on the detoued oute is at most moe than the numbe of outes on the oiginal oute. The FVRMF algoithm guaantees that an altenative oute is always found by identifying the best intemediate oute. Futue wok includes the study of the delay pefomance unde eal taffic pattens and the study of faulttoleant outing schemes unde diffeent delay and fault models. Refeences [] L. Benini and G.D. Micheli, Netwoks on chips: a new SoC paadigm, IEEE Compute, pp. 7-7, Jan.. [] R. Casado et al., A potocol fo deadlock-fee dynamic econfiguation in high speed local aea netwoks, IEEE Tans. Paallel & Distibuted Systems, vol., no., pp. 5-3,. [3] W. J. Dally and H. Aoki, Deadlock-fee adaptive outing in multicomputes netwoks using vitual, IEEE Tans. Paallel & Distibuted Systems, vol. 4, no. 4, pp , 3. [4] Dally W. J. and B. Towles, Route Packets, Not Wies: On-Chip Inteconnection Netwoks, in Poc. Design Automation Conf.,, pp [5] T. Dumitas, S. Kene, and S. Maculescu, Towads on-chip faulttoleant communication, in Poc. ASP-DAC, 3, pp [6] M.E. G omez, J. Duato, J. Flich, P. L opez, A. Robles, N.A. Nodbotten, O. Lysne, and T. Skeie, An efficient fault-toleant outing methodology fo meshes and toi, Compute Achitectue Lettes, vol. 3, pp. -3, Jul. 4. [7] J. Hu and R. Maculescu, Enegy- and pefomance-awae mapping fo egula NoC achitectues, IEEE Tans. Compute-Aided Design, vol. 4, no. 4, Ap. 5. [] ITRS, Intenational Technology Roadmap fo Semiconductos, Update. [] T. Li, Y. Yu, P. Li, J. u,. Ma and Y. Yang, Pactical outing and tous assignment fo RDT, in Poc. ISPAN, 4, pp [] J. Liu, M. Shen, L. Zheng, and H. Tenhunen, System level inteconnect design fo netwok-on-chip using inteconnect IPs, in Poc. Int l Wokshop System-Level Inteconnect, 3, pp [] L.M. Ni and P.K. McKinley, A suvey of womhole outing techniques in diect netwoks, Compute, vol. 6, no., pp. 6-76, 3. [] Y. Yang, A. Funahashi, A. Jouaku, H. Nishi, H. Amano, and T. Sueyoshi, Recusive diagonal tous: an inteconnection netwok fo massively paallel computes, IEEE Tans. Paallel & Distibuted Systems, vol., no. 7, pp. 7-75, Jul.. [3] Y. Yu, M. Yang, Y. Yang, and Y. Jiang, A RDT-based inteconnection netwok fo scalable NoC designs, in Poc. IEEE ITCC, 5, pp