COMP680E by M. Hamdi 1 Course Exam: Review April 17 (in-Class)

1COMP680E by M. Hamdi

Course Exam: ReviewApril 17 (in-Class)


Exam Format

• 5 questions – One general question (True or False) – or short

questions.– 4 Calculation-type questions

• Targeted towards topics that are extremely important in Targeted towards topics that are extremely important in the area of networkingthe area of networking


Question 2: Memory Bandwidth Limitations

• Understand the memory bandwidth requirement as a function of the queue placement

• Understand the relationship between queue placement and switch fabric speedup – Input-Queued Switches

– Output-Queued Switches

– Shared-Queued Switches

– Combined I/O Queued Switches

• Is a given architecture feasible for given configuration?


Question 3: Memory Bandwidth Limitations

• Memory-BW (IQ) = 2 R bits/sec

• Memory-BW (OQ) = (N + 1)xR bits/sec

• Memory-BW (SQ) = 2NR Bits/sec

• Memory-BW (CIOQ) = (S + 1)x R bits/sec

• Access time per packet = Packet size / Memory-BW


Example: A Comparison Memory speeds for 32x32 switch

Cell size = 64 bytes

Line Rate MemoryBW

Access TimePer cell

MemoryBW

Access Time

Shared-Memory Input-queued

100 Mb/s 6.4 Gb/s 80 ns 200 Mb/s 2.56 s

1 Gb/s 64 Gb/s 8 ns 2 Gb/s 256 ns

2.5 Gb/s 160 Gb/s 3.2 ns 5 Gb/s 102.4 ns

10 Gb/s 640 Gb/s 0.8 ns 20 Gb/s 25.6 ns


Question 3: Example

• Give you the access time using SRAM and DRAM• Give you a line rate• Give you an architecture and size of switch (e.g., OQ

or CIOQ switch of size 128x128)• Give you size of packets• Find the memory bandwidth required, and the access

time per packet• Can this be feasible using current technology


Question 4: VOQ Switch Scheduling/Arbitration

• The most practical scheduling algorithms are maximal matching algorithms – try to approximate maximum size matching

• These algorithms are based on Request-Grant-Accept scheme

• The Request-Grant-Accept scheme are based on pointer positions at the input and output arbiters

• Understand how iSLIP, FIRM, and RRM


RRM Maximum Size Matching Algorithm: Performance and Properties

• Round Robin Matching (RRM) is easier to implement that PIM (in terms of designing the I/O arbiters).

• The pointers of the arbiters move in straightforward way

• It iterates the following steps until no more requests can be accepted (or for a given number of iterations):

• Request. Each input sends a request to every output for which it has a queued cell.

• Grant. If an output receives any requests, it chooses the one that appears next in a fixed, round-robin schedule starting from the highest priority element. The output notifies each input whether or not its request was granted. The pointer gi to the highest priority element of the round-robin

schedule is incremented (modulo N) to one location beyond the granted input. If no request is received, the pointer stays unchanged.


RRM Maximum Size Matching Algorithm: Performance and Properties

• Accept. If an input receives a grant, it accepts the one that appears next in a fixed, round-robin schedule starting from the highest priority element. The pointer ai to the highest priority

element of the round-robin schedule is incremented (modulo N) to one location beyond the accepted output. If no grant is received, the pointer stays unchanged.


RRM Maximal Matching Algorithm (1)

0

1

2

3

0

1

2

3

Step 1: Request



0

1

2

3

0

1

2

3

Step 2: Grant

3 02 1

3 02 1



0 31 2

0

1

2

3

0

1

2

3

Step 3: Accept

3 02 1

3 02 1


iSLIP Maximum Size Matching Algorithm: Performance and Properties

• It is a scheduler used in most VOQ switches (e.g., Cisco).

• It is exactly like RRM algorithm with the following change:

• Grant. If an output receives any requests, it chooses the one that appears next in a fixed, round-robin schedule starting from the highest priority element. The output notifies each input whether or not its request was granted. The pointer gi to the highest priority element of

the round-robin schedule is incremented (modulo N) to one location beyond the granted input if and only if the grant is accepted in (Accept phase) .


1

2

3

4

1

2

3

4

Step 2: Grant

1

2

3

4

1

2

3

4Step 3: Accept

iSlip: 1st Iteration

4 13 2

4 13 2

1

2

3

4

1

2

3

4

Step 1: Request

1 42 3

4 13 2

Original pointerSelected oneUpdated pointer

iSLIP Maximum Size Matching Algorithm


1

2

3

4

1

2

3

4

Step 2: Grant

1

2

3

4

1

2

3

4Step 3: Accept

iSlip: 2nd Iteration

4 13 2

1

2

3

4

1

2

3

4

Step 1: Request

1 42 3

4 13 2

No change

Original pointerSelected oneUpdated pointer

iSLIP Maximum Size Matching Algorithm


Simple Iterative Algorithms: iSlip

0

1

2

3

0

1

2

3

Step 1: Request



0

1

2

3

0

1

2

3

Step 2: Grant

3 02 1

3 02 1


0 31 2

0

1

2

3

0

1

2

3

Step 3: Accept

3 02 1

3 02 1



FIRM Maximum Size Matching Algorithm: Performance and Properties

• It is exactly like iSLIP with a very small – yet significant modification.

• Grant (outputs): If an unmatched output receives a request, it grants the one that appears next in a fixed, round-robin schedule starting from the highest priority element. The output notifies each input whether or not its request is granted. The pointer to the highest priority element of the round-robin schedule is incremented beyond the granted input. If input does not accept the pointer is set at the granted one.


0

1

2

3

0

1

2

3

Step 3: Accept

3 02 1

3 02 1

Simple Iterative Algorithms: FIRM


Differences between RRM, iSlip & FIRM

RRM iSlip FIRM

Input Aribiters

No grant unchanged

Granted one location beyond the accepted one

Output

Arbiters

No request unchanged

Grant accepted

one location beyond the granted one

Grant not accepted

one location beyond the previously granted one

unchanged the granted one


Question 4 Example

• You will be given the status of the VOQs, and the position of the pointers, find the scheduling using iSLIP, FIRM or RRM in 2 to 3 time slots


Question 5: Output Scheduling Algorithms for QoS

• We looked at output scheduling algorithms for per flow queueing

• Understand the notion of fairness as defined by max-min fairness

• Understand Weighted Fair Queueing (WFQ) which is the most famous algorithm for fair queueing

– Bit-by-bit WFQ


Max-Min FairnessA common way to allocate flows

N flows share a link of rate C. Flow f wishes to send at rate W(f), and is allocated rate R(f).

1. Pick the flow, f, with the smallest requested rate.

2. If W(f) < C/N, then set R(f) = W(f).

3. If W(f) > C/N, then set R(f) = C/N.

4. Set N = N – 1. C = C – R(f).

5. If N>0 goto 1.


1W(f1) = 0.1

W(f3) = 10R1

C

W(f4) = 5

W(f2) = 0.5

Question 5 Example: Max-Min Fairness

Round 1: Set R(f1) = 0.1

Round 2: Set R(f2) = 0.9/3 = 0.3

Round 3: Set R(f4) = 0.6/2 = 0.3

Round 4: Set R(f3) = 0.3/1 = 0.3


Weighted Bit-by-Bit Fair Queueing

Flows can be allocated different rates by servicing a different number of bits for each flow during each round.

1R(f1) = 0.1

R(f3) = 0.3R1

C

R(f4) = 0.3

R(f2) = 0.3

Order of service for the four queues:… f1, f2, f2, f2, f3, f3, f3, f4, f4, f4, f1,…


Understanding bit by bit WFQ 4 queues, sharing 4 bits/sec of bandwidth, Weights 3:2:2:1

Weights : 3:2:2:1

3

2

2

1

6 5 4 3 2 1 0

B1 = 3

A1 = 4

D2 = 2 D1 = 1

C2 = 1 C1 = 1

Time

3

2

2

1

6 5 4 3 2 1 0

B1 = 3

A1 = 4

D2 = 2 D1 = 1

C2 = 1 C1 = 1

A1A1A1B1

A2 = 2

C3 = 2

Time

Weights : 3:2:2:1

Round 1

3

2

2

1

6 5 4 3 2 1 0

B1 = 3

A1 = 4

D2 = 2 D1 = 1

C2 = 1 C1 = 1

A1A1A1B1

A2 = 2

C3 = 2

D1, C2, C1 Depart at R=1Time

B1C1C2D1

Weights : 3:2:2:1

Round 1


Understanding bit by bit WFQ 4 queues, sharing 4 bits/sec of bandwidth, Weights 3:2:2:1

Weights : 3:2:2:1

3

2

2

1

6 5 4 3 2 1 0

B1 = 3

A1 = 4

D2 = 2 D1 = 1

C2 = 1 C1 = 1

A2 = 2

C3 = 2

B1, A2 A1 Depart at R=2Time

A1A1A1B1B1C1C2D1A1A2A2B1

Round 1Round 2

Weights : 3:2:2:1

3

2

2

1

6 5 4 3 2 1 0

B1 = 3

A1 = 4

D2 = 2 D1 = 1

C2 = 1 C1 = 1

A2 = 2

C3 = 2

D2, C3 Depart at R=2Time

A1A1A1B1B1C1C2D1A1A2A2B1C3C3D2D2

Round 1Round 23


Question 4 Example

• You are given a number of flows. What is the rate allocated for each flow using bit-by-bit WFQ.

• You are given packets in each flow. What is the order of the departure of packets using packet-by-packet WFQ.


RED (Random Early Detection)

• FIFO scheduling• Buffer management:

– Probabilistically discard packets

– Probability is computed as a function of average queue length

Discard Probability

AverageQueue Length

0

1

min_th max_th queue_len


Question 5: Random Early Detection(RED)


RED operationMin threshMax thresh

Average queuelength

minthresh maxthresh

MaxP

1.0

Avg length

P(drop)


Define Two Threshold Values

RED (Random Early Detection)

• FIFO scheduling

Min threshMax thresh

Average queuelength

Make Use of Average Queue LengthCase 1:

Average Queue Length < Min. Thresh ValueAdmit the New Packet


RED (Cont’d)

Min threshMax thresh

Average queuelength

Case 2: Average Queue Length betweenMin. and Max. Threshold Value

p

1-p

Admit the New Packet With Probability p…

p

1-p

Or Drop the New Packet With Probability 1-p


Random Early Detection Algorithm

• ave = (1 – wq)ave + wqq• P = max_P*(avg_len – min_th)/(max_th – min_th)

for each packet arrival: calculate the average queue size ave if ave ≤ minth

do nothing else if minth ≤ ave ≤ maxth

calculate drop probability p drop arriving packet with probability p else if maxth ≤ ave drop the arriving packetdarriving packetd


Question 5 Example

• You are given the status of a queue using RED, and all needed parameter (Max. threshold, Min. threshold, average queue length, etc.)

• For an arriving packet, determine whether the packet will accepted, dropped, or accepted with a certain probability.

COMP680E by M. Hamdi 1 Course Exam: Review April 17 (in-Class)

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