lecture 5: deadlocks - itusharkrishna.ece.gatech.edu/.../2016/10/l05-deadlocks-i.pdf ·...

Lecture 5:Deadlocks - ITushar Krishna

Assistant ProfessorSchool of Electrical and Computer EngineeringGeorgia Institute of Technology

[email protected]

ECE 8823 A / CS 8803 - ICNInterconnection NetworksSpring 2017http://tusharkrishna.ece.gatech.edu/teaching/icn_s17/

Announcement: Lab 2

January 25, 2017ICN | Spring 2017 | L05: Deadlocks-I © Tushar Krishna, School of ECE, Georgia Tech

2

Link Weights:1 for X-direction links2 for Y-direction links

16-router NoCEach router connected to one CPU + one Directory(--num-cpus=16,--num-dirs=16)Just like Mesh_XY.py

DO NOT CONNECT 4 CPU/DIR to ONE ROUTER LIKE THE PAPER

Taxonomy of Routing Algorithms¡Classification I: path length¡Minimal: shortest paths¡ Example: Greedy over Ring, XY over Mesh

¡Non-minimal: non-shortest paths¡ Example: Random and Adaptive over Ring/Mesh


3

Taxonomy of Routing Algorithms¡ Classification II: path diversity (how to select between the

set of all possible paths Rxy from the source x to the dest y)¡ Deterministic: always choose the same route between x and y,

even if |Rxy| > 1¡ Example: Greedy over Ring, XY over Mesh¡ + Easy to Implement¡ - Inefficient use of bandwidth

¡ Oblivious: choose any of the routes in Rxy without considering any information about current network state (i.e., congestion)¡ Example: Random over Ring, O1Turn over Mesh¡ + More path diversity¡ - Can lead to deadlocks (this lecture)

¡ Adaptive: choose one of the routes in Rxy depending on the current network state (i.e., congestion)¡ Example: Adaptive over Ring/Mesh¡ + Best use of available bandwidth¡ - Need to track congestion, can lead to deadlocks


4

Taxonomy of Routing Algorithms¡Classification III – implementation¡Source Routing¡Node-Table Routing¡Combinational Circuits

¡To be discussed when we discuss router microarchitecture!


5

Recap: O1TURN Routing Algorithm


6

XY

SA

DC

DA DB

SB SC SBSA

DB

DC

DA

SC

YX

Randomly send over XY or YX

Minimal and Oblivious

Recap: Valiant’s Routing Algorithm¡ To route from s to d¡ Randomly choose intermediate

node d’¡ Route* from s to d’ (Phase I), and

d’ to d (Phase II)

¡ Pros¡ Randomizes any traffic pattern¡ All patterns appear uniform

random¡ Balances network-load¡ Higher throughput

¡ Cons¡ Non-minimal¡ Higher latency and energy

¡ Destroys locality


7

d’

s

d

Non-Minimal and *Oblivious

*can also be Adaptive

Deadlock§ A condition in which a set of agents wait indefinitely

trying to acquire a set of resources

§ Packet A holds buffer u (in 1) and wants buffer v (in 2)§ Packet B holds buffer v (in 2) and wants buffer w (in 3)§ Packet C holds buffer w (in 3) and wants buffer x (in 0)§ Packet D holds buffer x (in 0) and wants buffer u (in 1)


8

0 1

23

A

BC

Du

vw

x

Note: holding buffer u == holding Channel 01as no other packet can use channel 01 till buffer u becomes free

Classic Example: Dining Philosopher’s Problem


9

Agents: Philosophers

Resources: Forks

Resource Dependence


10

A B

u v w x

C D

Hold (i..e, wait for release)Wait to acquire

Agents

Resources

Resource A is dependent on resource B if it is possible for A to be held-byan agent X and it is also possible for X to wait-for B

u v w x

Resource Dependence Graph

Deadlock Condition¡Agents hold and do not release a resource

while waiting for access to another

¡A cycle exists between waiting agents such that there exists a set of agents A0, .. An-1, where agent Ai holds resource Ri, while waiting on resource R(i+i mod n), for i = 0, …, n-1

¡To avoid deadlock – resource dependence graph should not have any cycles


11

Dealing with Deadlocks¡Avoidance¡Guarantee that the network will never deadlock¡Almost all modern networks use deadlock avoidance

¡Recovery¡Detect deadlock and correct


12

Deadlock Avoidance¡Eliminate cycles in Resource Dependency Graph¡ Resource Ordering¡ Enforce a partial/total order on the resources, and insist

that an agent acquire the resources in ascending order¡ Deadlock avoided since a cycle must contain at least one

agent holding a higher numbered resource waiting for a lower-numbered resource which is not allowed by the ordering allocation

¡ Implementation¡ Restrict certain routes so that a higher numbered resource

cannot wait for a lower numbered resource¡ Partition the buffers at each node such that they belong to

different resource classes. A packet only any route can only acquire buffers in ascending order of resource class


13

Turn Model (Glass and Ni 1994) for Mesh

¡Deadlocks may occur if the turns taken form a cycle¡Removing some turns can make the routing algorithm

deadlock free


14

Dimension Ordered Routing


15

XY Model YX Model

O1Turn Deadlock!

Deadlock-free Oblivious/Adaptive Routing Algorithms


16

West-First Turn Model North-Last Turn Model

Negative-First Turn Model

Example 1


17

d

s

XY?

YX?

West-first?

North-last?

Example 2


18

s

d

XY?

YX?

West-first?

North-last?

Resource (channel) Ordering


19

0 1

2 3

4 5

7 6

9 8

11 10

12

13

14

15

16

17

19

18

21

20

23

22

10 17

11 18

12 19

1 0

3 2

5 4

6

7

13

14

20

21

9

8

16

15

23

22

XY Model West-First Turn Model

Can we eliminate any 2 turns?


20

Six turn model

Deadlock!Total Turn Models = 16Deadlock Free = 12Unique (non-symmetrical) = 3

Channel Dependency Graph (CDG)¡Vertices represent network links (channels)

¡Edges represent turns¡180o turns not allowed, e.g., AB à BA


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F

A B

E D

C

Cycles in the CDG


22

The channel dependency graph D derived from the network topology may contain many cycles

F

A B

E D

C

Flow routed through links AB, BE, EFFlow routed through links EF, FA, ABDeadlock!Edges in CDG = Turns in Networkè Disallow/Delete certain edges in CDG

Acyclic CDG


23

F

A B

E D

C

Acyclic CDG

Disable certain edges

FEED

DC CBBE EF FA

AFBA

EBDECDBCAB

Cyclic CDG

FEED

DC CBBE EF FA

AFBA

EBDECDBCAB

This is the West-first turn model!

CDG for arbitrary topology


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FC DA

CF AD

FEED

DC CBBE EF FA

AFBA

EBDECDBCAB

F

A B

E D

C

CDG for West-first turn model

Deadlock free?No

Deadlock-free Routing Algorithm


25

FC DA

CF AD

FEED

DC CBBE EF FA

AFBA

EBDECDBCAB

F

A B

E D

C

Suppose: Diagonal links should be traversed last (i.e., no edge from blue/green channel to black)

Deadlock-free Routing Algorithm


26

FC DA

CF AD

FEED

DC CBBE EF FA

AFBA

EBDECDBCAB

F

A B

E D

C

Suppose: Diagonal links should be traversed last (i.e., no edge from blue/green channel to black) Deadlock free?

Yes

What about a Ring?


27

F

A B

E D

C

Acyclic CDG for a Ring


28

F

A B

E D

C

FE

ED DC

CB

BAAF

CD

DE EF

FA

ABBC

Option 1

Problem?

Route from E to C disabled(E to D) and (D to C) allowed

Route from F to B disabled

No route from E/F to B/C

CDG



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F

A B

E D

C

FE

ED DC

CB

BAAF

CD

DE EF

FA

ABBC

Option 2

Problem?


Route from E to A disabled

No route from E to A/B/C

CDG



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F

A B

E D

C

FE

ED DC

CB

BAAF

CD

DE EF

FA

ABBC

Option 3

Problem?


Route from B to D disabled

Acceptable CDGE to C no longer minimal

CDG

Acyclic CDG for a Large Ring


31

H

C D

G F

E

I

B

J

A

G, H, I have to take non-minimal paths to reach E!

D, C, B have to take non-minimal paths to reach F

Problem?

Suppose two channels


32

F

A B

E D

C

FE0

ED0 DC0

CB0

BA0AF0

CD0

DE0 EF0

FA0

AB0BC0

ED1 DC1

FE1

AF1 BA1

CB1

DE1 EF1

CD1

AF1 BA1

FA1

Dateline

DatelineDateline

Need not be physical channels


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FE0

ED0 DC0

CB0

BA0AF0

CD0

DE0 EF0

FA0

AB0BC0

ED1 DC1

FE1

AF1 BA1

CB1

DE1 EF1

CD1

AF1 BA1

FA1

Dateline

DatelineDateline

Need at least 2 classes of buffers - called“Virtual Channels”Start in VC in Class0After Dateline, jump to VC in Class1

F

A B

E D

C

lecture 5: deadlocks - itusharkrishna.ece.gatech.edu/.../2016/10/l05-deadlocks-i.pdf ·...

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