The Turn Model For Adaptive Routing

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The Turn Model for Adaptive The Turn Model for Adaptive RoutingRouting

Christopher J. Glass Christopher J. Glass Lionel M. NiLionel M. Ni

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SummarySummary

Introduction to Direct Networks.Introduction to Direct Networks.Deadlocks in Wormhole Routing.Deadlocks in Wormhole Routing.System Model.System Model.Partially Adaptive Routing Algorithms inPartially Adaptive Routing Algorithms in

2D Meshes.2D Meshes. p-cube routing in Hypercube p-cube routing in Hypercube Analysis.Analysis. Conclusion and Future Work.Conclusion and Future Work.

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What is Direct Network?What is Direct Network?

Each node has a point-to-point, or direct, connection to Each node has a point-to-point, or direct, connection to some number of other nodes.some number of other nodes.

Offers massive parallelism and scalability.Offers massive parallelism and scalability.

Popular architecture for constructing massively parallel Popular architecture for constructing massively parallel computers.computers.

Communicates by passing messagesCommunicates by passing messages

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Generic ArchitectureGeneric Architecture

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Evaluation of Direct NetworkEvaluation of Direct Network

Communication latency:Communication latency: Start-up latency + Network latency + Blocking timeStart-up latency + Network latency + Blocking time Start-up latency:Start-up latency:

It is the time to handle the packet at source & destination nodes.It is the time to handle the packet at source & destination nodes. Network latency:Network latency:

It is the time between a packet leaving the source and arriving at It is the time between a packet leaving the source and arriving at the destination.the destination.

Blocking timeBlocking timeAll possible delays encountered during the life-time of packet.All possible delays encountered during the life-time of packet.

Communication latency depends on the type of Communication latency depends on the type of switching technique → Wormhole routingswitching technique → Wormhole routing

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Switching TechniqueSwitching Technique

Switching Technique

Circuit Switching

Virtual Cut Through

Packet Switching

Wormhole Switching

Switching Technique

Virtual Cut Through

04/10/2304/10/23

Packet RoutingPacket Routing

There are two basic approaches to routing There are two basic approaches to routing packets, based on what a switch does with packets, based on what a switch does with a packet as its flits begin to arrive.a packet as its flits begin to arrive.

1)1) Store-and-forwardStore-and-forward

2)2) Cut-throughCut-through Virtual cut-throughVirtual cut-through WormholeWormhole

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Wormhole SwitchingWormhole Switching

A packet is divided into a number of flitsA packet is divided into a number of flitsThe header flit of a packet governs the routeThe header flit of a packet governs the routeThe remaining flits following in a pipelineThe remaining flits following in a pipeline

fashionfashionThus a message resembles worm borrowing Thus a message resembles worm borrowing

through the networkthrough the network

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TransmissionTransmission

Packet is transmitted from a node as Packet is transmitted from a node as flit( smallest unit on which flow control flit( smallest unit on which flow control can be performed).can be performed).

Two kinds of Flits Header flit and Data Two kinds of Flits Header flit and Data flit.flit.

Header Flit tries to get the another Header Flit tries to get the another channel while the data flits are channel while the data flits are transmitted through the already transmitted through the already obtained channels. obtained channels.

A channel is released only when the A channel is released only when the last flit of the message is passed last flit of the message is passed though it.though it.

Flits of two messages cannot be Flits of two messages cannot be interleaved.interleaved.

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Wormhole RoutingWormhole Routing

Based on cut-through conceptBased on cut-through concept Relatively independent of path lengthRelatively independent of path length

Overcome: Overcome: Store-and-forward and Virtual cut-through Store-and-forward and Virtual cut-through

’s buffer size problem ’s buffer size problem Circuit switching ’s channel reservation and Circuit switching ’s channel reservation and

release problemrelease problem

Two positive effect:Two positive effect: The absence of network contention makes The absence of network contention makes

the network latency relatively insensitive to the network latency relatively insensitive to path lengthpath length

Large packet buffers at each intermediate Large packet buffers at each intermediate node are obviatednode are obviated

1111

S

D

C om m and

Address

Payload

Flit

Flit

Flit

Wormhole RoutingWormhole Routing

Advantages: Advantages:

reduced bufferingreduced buffering

Flit (routing info)

Flit

Flit

Low latencyLow latency

Wormhole Packet:

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Characteristics of Routing Characteristics of Routing AlgorithmsAlgorithms

A good routing algorithm:A good routing algorithm:

Reduce the network latencyReduce the network latency

Easily implemented in hardwareEasily implemented in hardware

High network throughputHigh network throughput

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DeadlockDeadlock

Packets are allowed Packets are allowed to hold a resource to hold a resource (channel) while (channel) while waiting for another waiting for another resource resource

Deadlock free routing Deadlock free routing algorithmalgorithm

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Deadlocks in Wormhole SwitchingDeadlocks in Wormhole Switching

Header Flit contains all the routing Header Flit contains all the routing information that is required to move data information that is required to move data flits across the network. If the header flit flits across the network. If the header flit cannot move any further then there will a cannot move any further then there will a congestion which causes a chained block congestion which causes a chained block in the network which leads to Deadlocks.in the network which leads to Deadlocks.

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The Turn ModelThe Turn Model

Basis: Basis: Analyze directions in which packets Analyze directions in which packets cancan turn in the turn in the

networknetwork Determine the cycles that such turns can formDetermine the cycles that such turns can form Prohibit Prohibit just enoughjust enough turns to break turns to break all all cycle cycle

Resulting routing algorithms are:Resulting routing algorithms are: Deadlock and livelock freeDeadlock and livelock free Minimal/Non-minimalMinimal/Non-minimal Highly Adaptive.Highly Adaptive.

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The Turn model (contd..)The Turn model (contd..)

Deadlock freeDeadlock freeLivelock freeLivelock free

livelock occurs when the routing of a packet never leadlivelock occurs when the routing of a packet never lead it to its destination.it to its destination.

Adaptive Adaptive from A to B determines the path based on the Network load.from A to B determines the path based on the Network load.

Minimal Minimal restricts packets to shortest paths.restricts packets to shortest paths.

Non-minimal Non-minimal Although minimal routing may initially sound more promising, non-minimal Although minimal routing may initially sound more promising, non-minimal

routing provides more choices.routing provides more choices.

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The Turn Model (contd…)The Turn Model (contd…)

Classify channels according to the direction in which they route packets.

Identify the turns that occur between one direction and another, omitting 0-degree and 180-degree turns.

Identify the simple cycles these turns can form.

Prohibit one turn in each cycle.

In the case of k-ary n-cubes, incorporate as many turns as possible that involve wraparound channels.

Add 180-degree and 0-degree turns if there are multiple channels in the same direction.

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The Turn Model (contd.)The Turn Model (contd.)

Simple Illustration:Simple Illustration:

-The possible turns and simple cycles in a two-dimensional mesh.

-The four turns allowed by the xy routing algorithm.

-Six turns that complete the cycles and allows deadlock.

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Turn Model (contd.)Turn Model (contd.)

West-First Routing AlgorithmWest-First Routing Algorithm

Prohibited turns are theProhibited turns are the

two to the west.two to the west.

Route a packet first west if Route a packet first west if necessary, and then adaptively necessary, and then adaptively south , east, and north.south , east, and north.

Both minimal and non-minimal Both minimal and non-minimal paths are shown.paths are shown.

[Dally and Seitz] proof show that a [Dally and Seitz] proof show that a routing algorithm is deadlock free if routing algorithm is deadlock free if the channels in the interconnection the channels in the interconnection network can be numbered so that network can be numbered so that the algorithm routes every packet the algorithm routes every packet along channels with strictly along channels with strictly decreasing numbers.decreasing numbers.

2020

S

D

Deadlock Free RoutingDeadlock Free Routing

West First Algorithm

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S

D



2222

D S



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North-Last Routing AlgorithmNorth-Last Routing Algorithm

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D S


North Last Algorithm

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Turn Model (contd.)Turn Model (contd.)Negative-First Routing AlgorithmNegative-First Routing Algorithm

If the packet in +ve direction If the packet in +ve direction

it will never turn –ve.it will never turn –ve.

+y

-x

-y

+x

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n – Dimensional meshesn – Dimensional meshes Prohibit n(n-1) 90 degree turns to prevent deadlock.Prohibit n(n-1) 90 degree turns to prevent deadlock. One half of all possible 180 degree turns must be prohibitedOne half of all possible 180 degree turns must be prohibited Resulting algorithms:Resulting algorithms:

All-but-one-negative-firstAll-but-one-negative-firstAll-but-one-positive-lastAll-but-one-positive-lastNegative-firstNegative-first

k-ary n-cubesk-ary n-cubesAllows to use the wraparound channelsAllows to use the wraparound channelsAssigns the wraparound channels a number.Assigns the wraparound channels a number.

Negative first algorithmNegative first algorithmClassify wraparound channel according to the direction in which it Classify wraparound channel according to the direction in which it routes packetsroutes packetsApply the algorithmApply the algorithm

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p-cube Routing in Hypercubesp-cube Routing in Hypercubes

Hypercubea are special case of both Hypercubea are special case of both n-dimensional meshes and k-ary n-n-dimensional meshes and k-ary n-cube.cube.

S =the binary address of the source S =the binary address of the source node for a packetnode for a packet

C=binary address of the node the C=binary address of the node the header flits currently occupyheader flits currently occupy

D=binary address of the destination D=binary address of the destination node.node.

Two Phase:Two Phase:Phase 1: route packets along a Phase 1: route packets along a

dimension i for which ci=1 and dimension i for which ci=1 and di=0 in minimal di=0 in minimal

Phase Phase 2:when no such dimension2:when no such dimension then , route packet along i such then , route packet along i such that ci=0 and di=1 in minimal.that ci=0 and di=1 in minimal.

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The minimal The minimal pp-cube ….-cube ….Example : 10-cube S=1011010100 D=0010111001

h0=3 and h1=3 so h=6 36 possible shortest paths.

Phase 1: C=1011010100 = C9 C8 C7 C6 C5 C4 C3 C2 C1 C0

C=1011010100 ;( ci=1 and di=0)

‘D=1101000110

^ ------------------------------

R = 1001000100 ( 3 choices) dimension taken d2

C= 1011010000

‘D= 1101000110

------------------------------

R= 1001000000 (2 Choices) dim. taken d9

C= 0011010000

‘D=1101000110

------------------------------

R= 0001000000 (1 choice) dim d6

C= 0010010000

‘D=1101000110

-----------------------

R= 000000000

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The minimal The minimal pp-cube ….-cube ….Example : 10-cube S=1011010100 D=0010111001

h0=3 and h1=3 so h=6 36 possible shortest paths.

Phase 2: C= 0010010000 D=0010111001

‘C=1101101111

D=0010111001

------------------------

R=0000101001 Choices = 3 Dim=d5

C=0010110000 ( 0 to 1)

‘C=1101001111

D=0010111001

------------------------

R= 0000001001 choices= 2 Dim=d0

C= 0010110001

‘C= 1101001110

D= 0010111001

---------------------------

R= 0000001000 Choice=1 Dim =d3

C=0010111001 = D

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The nonminimal The nonminimal p-p-cube algo.cube algo.

It is desired , because of It is desired , because of its increased adaptive its increased adaptive nessness

The first phase can route The first phase can route the packet along any the packet along any dimension i for which ci=1 dimension i for which ci=1 and di=1.and di=1.

pp : last hop was in the : last hop was in the

+ve direction.+ve direction.

Expect more choicesExpect more choices

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The nonminimal The nonminimal p-p-cube algocube algo

(0,0,0) (1,0,0)

(0,0,1)

(0,1,1)(1,1,1)

(1,0,1)

(1,1,0)

The meaning of the algorithm's steps are with Dr. Pfeiffer’s help (example):

2- if last hop from +ve . Take the +ve only.

If S=011 , D=111

One choice 011→ 111

3- else if last hop was –ve and if destination not any more –ve go –ve or +ve.

S=011 , D=111

Choice 1 : 011→ 111

Choice 2: 011 → 001

Choice 3: 011 → 010

4- else going -ve

(0,1,0)

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Simulation ExperimentsSimulation Experiments

• Comparison of the partially adaptive with a non adaptive routing algorithms

• Simulation of a 16x16 mesh and a binary 8-cube for three different traffic patterns

• Each of these contains 256 nodes

• Bandwidth is equal to 20 flits/microsec

• For uniform traffic in the mesh and the hypercube the nonadaptive routing algorithms have lower latencies at high throughputs than the partially adaptive algorithms

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Simulation experiments (contd.)Simulation experiments (contd.)

• At low throughputs ,the algorithms performs about the same.

•For the non-uniform traffic patterns the partially adaptive routing algorithms have lower latencies at high throughputs

•For the negative-first algo.The degree of adaptive ness higher than the other . According to the hamming distance or if we measure S( algo.)/S( fully adaptive).

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ConclusionConclusion

The turn model produces The turn model produces deadlock free, livelock free, deadlock free, livelock free, minimal or non-minimal and minimal or non-minimal and maximally adaptive algorithms.maximally adaptive algorithms.

These algorithms perform These algorithms perform better than nonadaptive better than nonadaptive algorithms for nonuniform algorithms for nonuniform patterns of message traffic.patterns of message traffic.

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A Peek into the Future A Peek into the Future

To investigate the effects of different input and output To investigate the effects of different input and output selection policies on network performance.selection policies on network performance.

To illustrate the application of the turn model to To illustrate the application of the turn model to networks that include extra physical or virtual channel.networks that include extra physical or virtual channel.

To apply the turn model to other topologies, such as, To apply the turn model to other topologies, such as, hexagonal, octagonal and cube connected cycle hexagonal, octagonal and cube connected cycle networks.networks.

Identification of realistic workload distributions.Identification of realistic workload distributions.

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ReferencesReferences

The Turn Model for adaptive routingThe Turn Model for adaptive routing

Wormhole Routing in Parallel ComputersWormhole Routing in Parallel Computers

A processor architecture for A processor architecture for multiprocessing multiprocessormultiprocessing multiprocessor

The Turn Model For Adaptive Routing

Technology

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