performance analysis of minimal path fault tolerant routing in noc

Vol.28 No.4/5/6 JOURNAL OF ELECTRONICS (CHINA) November 2011

PERFORMANCE ANALYSIS OF MINIMAL PATH FAULT TOLERANT ROUTING IN NOC1

M. Ahmed V. Laxmi M. S. Gaur

(Department of Computer Engineering, Malaviya National Institute of Technology, Jaipur 3020017, India)

Abstract Occurrence of faults in Network on Chip (NoC) is inevitable as the feature size is con-tinuously decreasing and processing elements are increasing in numbers. Faults can be revocable if it is transient. Transient fault may occur inside router, or in the core or in communication wires. Examples of transient faults are overflow of buffers in router, clock skew, cross talk, etc.. Revocation of transient faults can be done by retransmission of faulty packets using oblivious or adaptive routing algorithms. Irrevocable faults causes non-functionality of segment and mainly occurs during fabrication process. NoC reliability increases with the efficient routing algorithms, which can handle the maximum faults without deadlock in network. As transient faults are temporary and can be easily revoked using re-transmission of packet, permanent faults require efficient routing to route the packet by bypassing the nonfunctional segments. Thus, our focus is on the analysis of adaptive minimal path fault tolerant routing to handle the permanent faults. Comparative analysis between partial adaptive fault tolerance routing West-First, North-Last, Negative-First, Odd Even, and Minimal path Fault Tolerant routing (MinFT) algorithms with the nodes and links failure is performed using NoC Interconnect RoutinG and Application Modeling simulator (NIRGAM) for the 2D Mesh topology. Result suggests that MinFT ensures data transmission under worst conditions as compared to other adaptive routing algorithms .

Key words Minimal path Fault Tolerant (MinFT); Adaptive Routing; Network on Chip (NoC)

CLC index TP302

DOI 10.1007/s11767-012-0701-6

I. Introduction Accomplishment or breakdown of Network on

Chip (NoC) with regular or irregular topology is highly dependent on the efficiency of applied routing algorithms. The technology is scaling ex-ponentially using deep submicron technology (SDM) to achieve fast communication with low power, high reliability, and efficiency. It is more likely of oc-currence of transient faults or manufacturing de-fects in the silicon chip area. Research is intended toward this to explore efficient routing mechanism for better utilization of resources under the faulty conditions. Fault tolerant routing techniques pro-vide path from source to destination in the presence of faults with the certain degree of tolerance.

1 Manuscript received date: January 4, 2011; revised date:

November 24, 2011 Communication author: Mushtaq Ahmed, born in 1970, male, Assistant Professor. Department of Computer En-gineering Malaviya National Institute of Technology, Jaipur, India 302017. Email: [email protected].

Various fault tolerant routing algorithms based on turn model routing proposed by C. J. Glass[1,2] exist but they are non minimal. Wu[3] proposed Odd Even turn model based fault tolerant routing and shows better performance in terms of latency and throughput.

Flooding mechanism is used in Ref. [4] to route packets to handle faults in network leading to higher energy consumption. Limitations of various flooding mechanism are addressed in Ref. [5] with the limitations of a low packet injection rate. Ef-fectiveness of turn model fault tolerant adaptive negative first routing is shown in comparison of N random walk in Ref. [6].

An Artificial Potential Field (APF) model is proposed in Ref. [7] for designing non minimal fault tolerant routing algorithms in 2D mesh NoC. The APF model is constructed by repulsive potential fields and attractive potential fields. They are generated by faulty and destination nodes respec-tively.

Our focus is to explore the partial adaptive

588 JOURNAL OF ELECTRONICS (CHINA), Vol.28 No.4/5/6, November 2011

routing to sustain under a certain degree of toler-ance. This paper is organized as follows. Section II discusses partially adaptive routing algorithms. Section III briefly introduces fault, fault tolerant techniques and implementation of partial adaptive fault tolerant routing using different applications and configurations. Section IV deals with experi-mental comparison of MinFT[8] and other fault tolerant routing algorithms. Finally result analysis and concluding remarks are presented in Section V.

II. Adaptive Routing Adaptive routings are more efficient and pro-

vides deadlock free routing over the congested network[9]. An efficient adaptive routing on NoC determines overall success or failure of design. Adaptive routing provides flexible path by refor-mations without deadlock between source and destination.

1. Definition

For a network Graph ( , )G N C= where N is number of nodes and C is number of channels, an adaptive routing algorithm ( ; )nR R n N= ∈ for each node ,n N∈ is a subset of routing algorithms

{ ; }dn sR G d N n= ∈ − applied to subset of graph

satisfying the following: (1) For a walk in a path at least two distinct

nodes are required. (2) In a given graph ( , )G N C= consisting

input channel c and output channels c ′ such that ( ),d

scc E G′ ∈ a message from source S would start from output channel ( )c ic d′ = to destination D using the path P as a sequence 1 1 2 2, ( , ), ,n s a n

2 3 3 1 1( , ), , , , ( , ),k k k ks a n n s a n− − where in are nodes and 1( , )i is a + are channels for 1 1.i K≤ ≤ −

(3) If there exists a path between source and destination via input and output channel such that

( )( )e cmc c E G

′′ ″ ∈ then a message m will reach desti-nation D using routing algorithm xR ,such that there must not be a deadlock condition in the channel dependency graph or extended channel dependency graph. The channel dependency graph is the directed graph ( ) ( , ),m mD R C E= where edges

{ }

( ).dm s

d N s

E E G∈ −

= ∪

2. Routing algorithms

West first routing West first implies make first

turn from source node towards west side either clock wise or anti clock wise then if anti clock turn south, east at last north or if clock wise turn north, east then at last south as shown in Fig. 1(a). Re-stricted or least used turns are mentioned with dotted lines. North last routing The algorithm implies that route the packet adaptively (anti-clock wise) west, south, east then at last North or clock wise east, south, west then at last north direction. Restricted turns in North Last routing are given as shown in Fig. 1(b). Negative first routing The algorithm implies that all turns from positive directions to negative di-rections are prohibited. Only west to east cycle and north to south cycle is allowed. Forwarding message first routed towards west or south till the offset is zero and then turns towards east or north direction as shown in Fig. 1(c).

Fig. 1 Turn models for adaptive routing

Odd even routing Chiu[2] proposed odd-even turn model routing with the following restrictions. (a) Packets generated from any node at any even column are not allowed to take East- North turn. Packets generated from any node at any odd column are not allowed to take North- West turn. (b) Packets generated from any node at any even

AHMED et al. Performance Analysis of Minimal Path Fault Tolerant Routing in NoC 589

column are not allowed to turn East- South. Packets generated from any node at any odd column are not allowed to take South-West turn. MinFT routing The MinFT provide shortest path routing between the source and destination pair with allowable turn constraint only within the quadrant of interest[11] defined as boundary region. With every source and destination as centre, the network is divided into quadrants referred to as a source quadrant and destination quadrants re-spectively. Any path a packet takes to the desti-nation is the Manhattan distance and has to follow only the allowed turns in the source destination overlapped quadrant to which the boundary is a subset as and hence the distance covered is always minimum.

III. Fault Tolerant Routing

Fault tolerant routing algorithms can either be fully or partially fault-tolerant. A fully fault-tol-erant routing finds a path between source and destination until faults do not partition the net-work. A partially adaptive fault-tolerant routing route packet around non-functional segments with a certain degree of tolerance to the number of faults in the network.

1. Fault tolerance technique

Faults can occur due to transient or permanent failures of links or router nodes anywhere in the network. Adaptive routing takes flexible path by reformations without impasse and minimal path from source to destination whereas a minimal path fault tolerance MinFT routing is constrained within boundary of identified region. Any faults ou-

tside a boundary are of no concern. The boundary for the source and destination pair is defined by the quadrant of interest for source and its corre-sponding quadrant of interest for destination. In-tersected area between the quadrant of interest for source and its corresponding quadrant of interest for destination defines the boundary as shown in Fig. 3. At any given node, there are four possible routes along directions {North, South, East, West}. In minimal path, at-most two directions can be chosen for next hop. Chosen directions are the ones that reduce distance to the destination. If destination is to North-East of current node, two directions are {North, East}. In minimal path routing, any intermediate node is always within bounding rectangle defined by coordinates of source and destination.

Let (XS,YS) and (XD,YD) are the coordinates for source and destination respectively. For any minimal path, number of steps in X and Y direction are given by D SX X| − | and D SY Y| − |, respectively. Then the total number of path available between source to destination can be states as

( )( )

!

! !D S D S

0D S D S

X X Y Y

X X Y YΓ

− + −=

− − (1)

Permitted directions denoted by 1 2, { , ,N S∇ ∇ ∈ , }E W and 1 2∇ ∇≠− are shown in Tab. 1. Number

of available minimal paths from S to D decrease as links begin to fail. The number of minimal paths are affected only if the failed link is within the boundary of ( , ), ( , ).S S D DX Y X Y We first consider simple case of single link failure and present how this analysis can be extended to multiple link failures.

Tab. 1 Virtual channels permitted directions for deadlock free routing

Relationship of coordinates > D CX X + D CX X= D CX X<

> D CY Y +

= D CY Y

D CY Y<

1 2,S E∇ ∇= =

1 2, NULLS∇ ∇= =

1 2,N E∇ ∇= =

1 2, NULLS∇ ∇= =

Core

1 2, NULLN∇ ∇= =

1 2,S W∇ ∇= =

1 2, NULLW∇ ∇= =

1 2,N W∇ ∇= = :+ Coordinates of core tile

Case I Single link failure We consider that link between Nodes A and B

fails. Following notations are used. LAB : Failed link lies between Nodes A and B. XA ,YA : Coordinates of Node A.

XB ,YB : Coordinates of Node B. Boundary Condition: {( , )s A B DX X X X= =

OR ( , )}s A B DX X X X= = AND {( ,S A BY Y Y= =)DY OR ( , )}.S A B DY Y Y Y= = Location of failed link in respect of source-


destination determines if number of available paths are affected or not. There are two possibilities.

(1) Boundary condition fails: Failed link lies outside boundary and its failure does not affect count of minimal paths available as paths using link

: :AB AB A BL L N N→ is zero. Total available paths remain 0.Γ

(2) Boundary condition is satisfied: Any routing path containing link ABL is not available and needs to be subtract from 0.Γ As can be inferred from Fig. 2, if the Link ABL in Fig. 2 fails in the network and satisfying the boundary area or region of of interest then the available path using link :AB A BL N N→ can be stated as

( )( )( )( )

1

!

! !

!

! !

A S A S

A S A S

D B D B

D B D B

X X Y Y

X X Y Y

X X Y Y

X X Y Y

Γ− + −

=− + −

− + −⋅

− + − (2)

and total path using the link ABL would be:

failure 0 1Γ Γ Γ= − (3)

Case II Multiple links failure In case of multiple link failure, while satisfying

the region of interest, the total number of paths available needed to be considered. If the k is the total number of faults inside the network then

{ }fault=

failure 0fault=1

path for consideration for K

KΓ Γ Γ= − ∪ (4)

Fig. 2 Link LAB fails between Nodes A and B in quadrant of interest for a given source and destination pair. If boundary con-dition is satisfied the available path from Node NA to Node NB can be calculated easily

Fig. 3 The boundary region for a source destination pair and faults in NoC

where path for consideration for kΓ is the total number of paths having k failure links. As the number of faults increase, the number of available minimal paths decrease.

Faults may be defined as: (1) Fault regions Where faults are in the

intermediary links of a boundary they are referred to as fault-regions.

(2) Fault chains Faults in the links of a boundary that are the axis of the destination node.

(3) Potentially faulty node Every node sharing one or more faults has local information about the fault. Such node is marked as “Poten-tially Faulty” (PF) node.

Fig. 3(a) illustrates region of interest for a source destination pair and Fig. 3(b) shows faulty region, faulty chain and PF nodes. Faulty link 9–14, 14–19 and 22–23, 23–24 constitute fault-chain as they lie on axis of destination.


2. Routing rules

Each adaptive routing has certain turn restric-tions (minimum two) to avoid deadlock condition. Adaptive routing takes a flexible path from source to destination by reformations without any dead-lock and minimal path. Whereas in MinFT, any path a packet takes to the destination is Manhat-tan distance and has to follow only the allowed turns in the source quadrant, where the boundary is a subset and hence the distance covered is always minimal.

Greedy approach is required to avoid faulty links and nodes. Routing decisions are considered from the adjacent routers in the permitted direc-tions only. Adaptive routing prohibits use of re-quires direction thus further decreasing in effi-ciency in terms of latency and throughput.

We take into account the following assumptions for path selection:

(1) If both neighbouring nodes are not PF nodes, the current router is free to choose any one for next-hop. If one of the nodes happen to lie on the axis of its destination quadrant, then that node is not chosen for next-hop. Intuitively, this is less likely to encounter fault chains and pushes the traffic toward the intermediary nodes of the boundary. Care is taken to avoid fault chains as it is impossible to route around them without violating routing rule. One of the solutions is to avoid all the boundary edges pushing the traffic to the inter-mediary nodes. This may increase congestion around the center of the boundary. To avoid con-gestion, only nodes lying on the axis of the desti-nation quadrant are avoided.

(2) If only one of the node (say Node A) is a PF node and if the other node (say Node B) does not lie on the axis of destination quadrant, then Node B is always chosen for next-hop. However, if the other node (Node B) lies on the axis of desti-nation node (refer Fig. 3), the PF node is chosen as the node for next-hop since fault-regions are much easier to handle in comparison to fault-chains.

(3) If both nodes are PF nodes, choose any one for next-hop. Credit lines can help us to choose wisely. However if one of the PF node lies on the axis of destination quadrant, choose the other PF

node for next-hop. Turn based routing are deadlock free and can

work without using any virtual channel. Only two Virtual Channels (VCs) are required for deadlock free routing[10] for MinFT routing algorithm. The assignment of virtual channels depends on the relative position of the source S and destination D. To break the cycle formed in channel dependency graph and preventing deadlock the following ap-proach is used.

(a) If destination D is towards East (West) of source S, packets use the first (second) virtual channel along Y direction.

(b) For X direction, any virtual channel can be used.

(c) If destination D is to the north or south of source S, any virtual channel can be used.

Fig. 4 Virtual channel assignment to prevent cycle formation and deadlock

IV. Simulation Framework and Ex-perimental Setup

NIRGAM, a NOC discrete event, cycle accurate simulator[12] is used for experimental analysis. We considered 7×7 Mesh topology, packet size of 20 bytes, fix 5 bytes buffer at each input port of switches. We applied synthetic data with Constant Bit Rate (CBR) and Bursty pattern with the burst length 3 and flit interval of 3.

For the first experiment, four source and des-tination pairs were chosen as shown in Fig. 6 with thirteen faults with one node failure. Under 100 percent load condition CBR traffic was applied. Non minimal path chosen by the fault tolerant adaptive routing West-First, North-Last, Negative- First are shown in Figs. 5(a), 5(b) and 5(c). Fig. 5(d) shows minimal path chosen by MinFT. Tab. 2 shows destination reached, overall average


Fig. 5 Path followed by the packet using fault tolerant routing algorithms

latency per clock cycle per flit, and average latency per clock cycle per packet of routing algorithms. Variation of path shows variation in latency as seen in the table.

Random and transpose pattern for all nodes in 7×7 Mesh have considered for exploring fault tol-erance and latency in second experiment. 14 links failure (3–4, 8–15, 9–16, 11–12, 11–18, 17–24, 23–24, 24–31, 24–25, 30–37, 32–39, 33–40, 36–37, 44–45 and one node failure (Node 24) have assigned for simulation under different load conditions ranging from 10 to 100 with CBR traffic injection pattern.


Tab. 2 Shows destination reached by the fault tolerant routing algorithms and latency

Routing algorithms Destination reached Overall average latency (in clock cycles per flit)

Average latency per channel (in clock cycles per packet)

MinFT 2 to 25, 36 to11 89.776 13.2642

FT Negative first 2 to 25, 36 to11 97.3307 12.6

FT North last 2 to 25, 11 to 29 92.609 12.859

FT West first 2 to 25, 17 to 20 81.776 14.2511

FT Odd even 2 to 25, 36 to 11 87.23 13.5238

Fig. 6 Average latency for the random and transpose traffic for Bursty and CBR data pattern in 7×7 Mesh NoC with 14 faults

V. Result Analysis Lower latency for random and transpose traffic

is achieved by MinFT compared with other routing algorithm as it always chooses minimal path for every source and destination pair. Fig. 6 shows overall average latency per cycle per flit for random and transpose traffic. Latency remains below 50 upto 60% of load and remains nearly same up to 60 per cycles per flit after increasing further load.

Similarly, Fig. 7 shows throughput for random and transpose traffic pattern. Figs. 7(a) and 7(c) show throughput for Bursty data for random and transpose traffic, and Figs. 7(b) and 7(d) shows throughput for CBR data for random and trans-pose traffic, respectively. Throughput of MinFT is comparable with FTOE and better than other routing algorithms. Throughput of 7.25 Gbps is observed with CBR data pattern at 50% of load compared to 10.6 Gbps in FTOE. 3% to 5% variation of throughput is observed with random traffic. 7.625 Gbps and 9.95 Gbps throughput is observed at 100% load injection in MinFT and


Fig. 7 Throughput for random and transpose traffic for Bursty and CBR data pattern in 7×7 Mesh NoC with 14 faults

FTOE respectively. Results that are more realistic with transpose traffic pattern. Throughput remain around 7.25 Gbps for MinFT and 7.035 Gbps in FTOE from 60% to 100% of load making MinFT better as compared to other routing algorithms.

This paper presents an approach to novel minimal path fault tolerant routing in NoC. A number of simulations were carried out to compare with other fault tolerant routing algorithms. MinFT tries to find the path from source to des-tination in the presence of faulty chains while maintaining the minimal path from source to des-tination. The MinFT survived in the network if it does not encounter the faulty chain in the network. The lower latency and higher throughput is ob-served in presence of multiple path compared with turn model routing algorithms.

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performance analysis of minimal path fault tolerant routing in noc

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