Dynamic Networks

CS 213, LECTURE 15L.N. Bhuyan

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What is Dynamic Network

• Dynamic Network is the network that can connect any input to any output by enabling or disabling some switches in the network

• Examples: - Shared Bus: The bus arbiter connects a

processor to a memory - Crossbar: Consists of a lot of switching

elements, which can be enabled to connect many inputs to many outputs simultaneously

- Multistage Network: Consists of several stages of switches that are enabled to get connections

- The nodes in static networks (like Mesh) also consist of dynamic crossbars

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Crossbar Switch Design

• Complexity O(N**2) for an NXN Crossbar

Cross-bar

InputBuffer

Control

OutputPorts

Input Receiver Transmiter

Ports

Routing, Scheduling

OutputBuffer

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How do you build a crossbar

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N**2 switches => Cost O(N**2)

Time taken by the arbiter = O(N**2)Multiplexors are controlled from the arbiter/controller/scheduler

From Control

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Crossbar Contd.

• An NXN Crossbar allows all N inputs to be connected simultaneously to all N outputs

• It allows all one-to-one mappings, called permutations. No. of permutations = N!

• When two or more inputs request the same output, it is called CONFLICT. Only one of them is connected and others are either dropped or buffered

• When processors access memories through crossbar, this situation is called memory access conflicts

• Given p as the probability of request by a processor per cycle and assuming that each of N processors’ request is uniformly directed to all N memories, the average number of connections allowed per cycle, called Bandwidth (BW) is

BW = N{1- (1-p/N)**N} – Derive this!!!

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Input buffered swtich

• Independent routing logic per input • Scheduler logic arbitrates each output - priority, FIFO, random• Head-of-line blocking problem – The head packet in a buffer cannot depart because the

output is busy with another packet. The second packet may be destined to an output that is free, but cannot depart due to blocking by the first packet => One solution is to create multiple input queues, one per output, called Virtual Output Queuing – adopted in most routers.

• Scheduler Design – How to ensure maximum simultaneous connections is a challenging research area.

Cross-bar

OutputPorts

Input Ports

Scheduling

R0

R1

R2

R3

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Problems with Input-Buffered Switch

• FIFO Input buffers give rise to Head of the Line (HOL) problem

• Current routers employ a separate input queue for each output, called virtual output queue (VOQ)

• Then how to schedule the packets from different VOQ’s for transmission?

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VOQ-based Input Buffered Switch

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Scheduling in Input Buffered Switch

• n independent arbitration problems?– static priority, random, round-robin

• simplifications due to routing algorithm?• general case is max bipartite matching – Iterative

algorithms – iSLIP in Cisco

Cross-bar

OutputPorts

R0

R1

R2

R3

O0

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O2

InputBuffers

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Output Buffered Switch

• How would you build a shared pool?

Control

OutputPorts

Input Ports

OutputPorts

OutputPorts

OutputPorts

R0

R1

R2

R3

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Output scheduling

• n independent arbitration problems?– static priority, random, round-robin

• simplifications due to routing algorithm?

• general case is max bipartite matching

Cross-bar

OutputPorts

R0

R1

R2

R3

O0

O1

O2

InputBuffers

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Multistage Interconnection Network (MIN)

Crossbar switch is not scalable. How about a network consisting of multiple stages of small crossbar switches? Has the following properties.

• NxN network for N=2n

• Consists of log2N stages of 2x2 switches

• Has N/2 2x2 switches per stage

• Cost O(N log n) instead of O(N2) for Crossbar

• For N= an, a MIN can be similarly designed with axa switches

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Multistage interconnection networks

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Complexity: Omega Network Complexity O(Nlog2N)Self Routing: The source node generates a tag, which is binary equivalent

Of the destination. At each switch, the corresponding tag bit is checked.If the bit is 0, the input is connected to the upper output. If it is 1, the

Input is connected to the lower output. If both inputs have either 0 or 1,It is a switch conflict. One of them is connected. The other one is rejected or

buffered at the switch (if it has buffer => buffered crossbar)

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What is Shuffle?

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(a) Perfect shuffle (b) Inverse perfect shuffle

shuffle interconnection

S(an-1 an-2 … a1 a0) = (an-2 an-3 … a0 an-1 )

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Omega Network

• Every stage of switches is preceded by a perfect shuffle interconnection

S(an-1 an-2 … a1 a0) = (an-2 an-3 … a0 an-1 )• An input can be connected to a straight or

exchange output in a 2x2 switch.

E(an-1 an-2 … a1 a0) = (an-1 an-2 … a1 ā0) • To route a message/packet in an Omega network,

the destination tag which is binary equivalent of the destination is used, (dn-1 dn-2 … d1 d0). The ith bit di is used to control the routing at the ith stage counted from the right with 0 <= i <= n-1. If di = 0, the input is connected to the upper output. If di = 1, it is connected to the lower output.

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Self Routing

• A processor generates a tag that is binary equivalent of the destination

• MSB controls the leftmost stage and the lsb controls the rightmost stage of the Omega network. A small controller inside the 2 x 2 switch senses this bit and enables the connection

• If bit ci = 0, the request is to the upper output; if it is 1, the request is to the lower output.

• Based on digit if switch size is greater than 2

• Network conflict - Select Round Robin

• Less Bandwidth than crossbar, but more cost effective

• What about QoS? Future research

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Theorem: The Omega network is self routing

Let source be (sn-1sn-2 … s2 … s1s0) and destination be (dn-1dn-2 … d2 … d1d0). Before Stage 1, the source is switched to the position (sn-2sn-3 … s1 … s0sn-1) due to perfect shuffle connection. After Stage 1 it is switched to (sn-2sn-3 … s1 … s0dn-

1) as per the (n-1)th of the destination.

Before 2nd stage of the switches, the source is connected to (sn-3 … s0dn-1sn-2) as after 2nd stage it becomes (sn-3 … s0dn-1dn-2)

If we continue like this for n stages, the source matches (dn-1dn-2 … di … d1d0) which is the destination.

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Switch Size axa

Let N = a**n

• The MIN will consist of n stages of axa crossbar switches with N/a switches per stage.

• The routing will be based on digit (a-1) <= I => 0 based on radix a

• Interconnection based on a-shuffle

Home Work: Prove self routing based on radix a. Draw a 16x16 MIN based

on 4x4 switches and explain its operation

Derive the BW of an Omega network with N=a**n with same input parameters as Crossbar (Slide 5)

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Example: SP

• 8-port switch, 40 MB/s per link, 8-bit phit, 16-bit flit, single 40 MHz clock

• packet sw, cut-through, no virtual channel, source-based routing

• variable packet <= 255 bytes, 31 byte fifo per input, 7 bytes per output, 16 phit links

P0P1P2P3 P15

E0E1E2E3 E15

Intra-Rack Host Ports

Inter-Rack External Switch Ports

16-node Rack

SwitchBoard

Multi-rack Configuration

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Example: IBM SP vulcan switch

• Many gigabit ethernet switches use similar design without the cut-through

FIFO

CRCcheck

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SGI SPIDER Chip

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SPIDER OPERATION

• The physical transmission layer for each port is based on a pair of Source Synchronous Drivers and Receivers (SSD and SSR), which transmit and receive 20 data bits and a data framing signal at 400 MBaud.

• The data link level guarantees reliable transmission using a CCITT-CRC code with a go-back-n sliding window protocol [1] retry mechanism, and is referred to as the Link Level Protocol (LLP).

• The message layer defines 4 virtual channels and a credit based flow control scheme to support arbitrary message lengths, as well as a header format to specify message destination, priority, and congestion control options.

• The receive buffers of a port maintain a separate linked list of messages for each of the 5 possible output ports for each virtual channel to avoid the ‘block at head of queue’ bottleneck.

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SPIDER Crossbar Arbitration

• To maximize bandwidth through the crossbar without using unreasonable buffering, each virtual channel buffer is organized as a set of linked lists. There is one linked list for each possible output port for each virtual channel. This solution avoids the block at head of queue problem. To maximize crossbar efficiency, each virtual channel from each port can request arbitration for every possible destination. Each arbitration cycle, the arbiter chooses up to 6 winners from as many as 120 arbitration candidates to maximize crossbar utilization.

• Messages accumulate a network age as they are routed, increasing their priority to avoid starvation and promote network fairness. In order to avoid starvation and encourage network fairness, the arbiter is rotated each arbitration cycle to favor the highest priority requestor. Priority is based on the age field of a message header.

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Arbitration Contd.

• After data is received by the SSR and synchronized, it enters the chip core and begins several operations in parallel. Table lookup and crossbar arbitration is normally serialized, as the exit port must be known before arbitration begins.

• To parallelize these operations, table lookup is pipelined across SPIDER chips. While arbitration progresses. the table lookup is performed for the next SPIDER chip, which depends on the destination ID and the direction field. This does increase table size, as a full table is required for each neighboring SPIDER chip, but it reduces latency by a full clock. Pipelined tables also add flexibility to possible routes, as different exit ports can be given depending on where a messages came from as well as where it is going.

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Summary

• Routing Algorithms restrict the set of routes within the topology

– simple mechanism selects turn at each hop

– arithmetic, selection, lookup

• Deadlock-free if channel dependence graph is acyclic– limit turns to eliminate dependences

– add separate channel resources to break dependences

– combination of topology, algorithm, and switch design

• Deterministic vs. adaptive routing

• Switch design issues– input/output/pooled buffering, routing logic, selection logic

• Flow control

• Real networks are a ‘package’ of design choices