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IQ switch scheduling
Pag. 1
Input Queued routers/switches
Andrea BiancoTelecommunication Network Group
QoS Issues in Telecommunication Networks - 1Andrea Bianco – TNG group - Politecnico di Torino
Telecommunication Network [email protected]
http://www.telematica.polito.it/
The Internet is a mesh of routers
core router
QoS Issues in Telecommunication Networks - 2Andrea Bianco – TNG group - Politecnico di Torino
access router
enterprise router
IQ switch scheduling
Pag. 2
The Internet is a mesh of routers• Access router:
– high number of ports at low speed (kbps/Mbps)– several access protocols (modem ADSL cable)several access protocols (modem, ADSL, cable)
• Enterprise router:– medium number of ports at high speed (Mbps)– several services (IP classification, filtering)
C t
QoS Issues in Telecommunication Networks - 3Andrea Bianco – TNG group - Politecnico di Torino
• Core router:– moderate number of ports at very high speed
(Mbps/Gbps)– very high throughput
Faster and faster• Need for high performance routers
– to accommodate the bandwidth demands for new users and new services
– to support QoS– to reduce costs
• Moore’s law (electronic packet processing power) is too slow with respect to the increase
QoS Issues in Telecommunication Networks - 4Andrea Bianco – TNG group - Politecnico di Torino
power) is too slow with respect to the increase in link speed
• The bottleneck is memory speed
IQ switch scheduling
Pag. 3
Single packet processing
• The time to process one packet is becoming shorter and shortershorter and shorter
• Worst case: 40-Byte packets (ACKs)• 3.2 µs at 100 Mbps• 320 ns at 1 Gps• 32 ns at 10 Gps• 3 2 ns at 100 Gbps
QoS Issues in Telecommunication Networks - 5Andrea Bianco – TNG group - Politecnico di Torino
• 3.2 ns at 100 Gbps• 320 ps at 1Tbps
CP CP
Hardware architecture
S F
LC
LC
LC
LC
CP
S F
IP
IP
IP
IP
CP
OP
OP
OP
OP
QoS Issues in Telecommunication Networks - 6Andrea Bianco – TNG group - Politecnico di Torino
O
physical structure logical structure
IQ switch scheduling
Pag. 4
Hardware architecture: main elements
• Line cards– support input/output transmissions– store packets– adapt packets to the internal format of the switching fabric– support data link protocols– classify packets– schedule packets
t it
QoS Issues in Telecommunication Networks - 7Andrea Bianco – TNG group - Politecnico di Torino
– support security • Switching fabric
– transfers packets from input ports to output ports
Hardware architecture: main elements
• Control processor/network processor– runs routing protocolsg p– computes routing tables– manages the overall system
• Forwarding engines
QoS Issues in Telecommunication Networks - 8Andrea Bianco – TNG group - Politecnico di Torino
– compute the packet destination (lookup)– inspect packet headers– rewrite packet headers
IQ switch scheduling
Pag. 5
control forwarding forwarding
Interconnections among main elements - I
switching fabric
processor engine engine
QoS Issues in Telecommunication Networks - 9Andrea Bianco – TNG group - Politecnico di Torino
line card line card1 N
Interconnections among main elements - II
control
processor
switching fabric
processor
QoS Issues in Telecommunication Networks - 10Andrea Bianco – TNG group - Politecnico di Torino
line card &forwarding engine
1
line card &forwarding engine
N
IQ switch scheduling
Pag. 6
Cell switch (fabric) ORM1ISMpackets cells cells packets
Cell-based synchronous routers
ORMN
1
N
ISM
QoS Issues in Telecommunication Networks - 11Andrea Bianco – TNG group - Politecnico di Torino
• ISM: Input-Segmentation Module
• ORM: Output-Reassembly Module
• Packet: variable-size data unit
• Cell: fixed-size data unit
Switching fabric• Our assumptions:
– Bufferless• to reduce internal hardware complexity
– Non-blocking• it is always possible to transfer in parallel from input to
output ports any non-conflicting set of cells
QoS Issues in Telecommunication Networks - 12Andrea Bianco – TNG group - Politecnico di Torino
IQ switch scheduling
Pag. 7
Switching fabric• Examples:
– BusesSh d
123pu
ts
– Shared memory – Crossbar – Multi-stage
• rearrangeable Clos network • Benes network • Batcher-Banyan network (self-routing)
Buffered cross bars (not considered)
34
1 2 3 4outputs
inp
QoS Issues in Telecommunication Networks - 13Andrea Bianco – TNG group - Politecnico di Torino
– Buffered cross-bars (not considered)• Switching constraints
– at most one cell for each input and for each output can be transferred
Generic switching architecture
Output 1
switching fabricInput 1
Input N Output N
Sin
Sin
Sout
Sout
QoS Issues in Telecommunication Networks - 14Andrea Bianco – TNG group - Politecnico di Torino
input queues output queues
IQ switch scheduling
Pag. 8
Speedup• The speedup (increase in speed with respect
to line speed) determines switch performance:p ) p– Sin = reading speed from input queues– Sout = writing speed to output queues
• The speedup is also a technological constraint
QoS Issues in Telecommunication Networks - 15Andrea Bianco – TNG group - Politecnico di Torino
• Maximum speedup factor:– S = max(Sin, Sout)
Switches with queues at outputs• OQ (Output Queued)• The switching fabric is able
to transfer to any output all 1 1Nλto transfer to any output all cells received in one time slot
• 100% throughput • Optimal average delay• Speedup N with respect to
line speed is required in NxNN N
λi λo=Nλi
Nλi
QoS Issues in Telecommunication Networks - 16Andrea Bianco – TNG group - Politecnico di Torino
p qswitching fabric speed and in output port memory access
IQ switch scheduling
Pag. 9
Switches with queues at inputs• IQ (Input Queued) • Advantages: 1 1
– Switching fabrics and memories less costly
• No speedup required in the switching fabric
• Memory access speed equal to line speedS d 1
1 1
N N
QoS Issues in Telecommunication Networks - 17Andrea Bianco – TNG group - Politecnico di Torino
• Speedup=1
– Only viable solution for very high speed devices
NxNN
1 1
IQ switches• Two problems:
– Define scheduling algorithms to avoid output 1 1
N N
algorithms to avoid output contention
• Select in each time slot data to be transmitted from inputs to outputs
• Constraint: in each time slot– At most 1 data from each
input (no speeedup in reading)
QoS Issues in Telecommunication Networks - 18Andrea Bianco – TNG group - Politecnico di Torino
NxNN Nreading)
– At most 1 data to each output (no speedup in writing because no memory is available)
IQ switch scheduling
Pag. 10
IQ switches• Two problems:
– Memory architecture:• If using FIFO queues, HoL
(Head of the Line) blocking• If choosing cyan packet from
queue N, the red packet in queue 1 is blocked by the cyan packet which is at the head of queue 1 even if red
t t t N i f
1 1
N
QoS Issues in Telecommunication Networks - 19Andrea Bianco – TNG group - Politecnico di Torino
output port N is free• For uniform unicast traffic
throughput limited to 58.6%NxN
N N
Memory architecture
• To avoid HoL blocking phenomenum, a more complex memory architecture is needed
• Two possible solutions:– p-window queueing
VOQ (Vi t l O t t Q i )
QoS Issues in Telecommunication Networks - 20Andrea Bianco – TNG group - Politecnico di Torino
– VOQ (Virtual Output Queueing)
IQ switch scheduling
Pag. 11
p=3
Memory architecture• p-window queueing:
– p is the window size1 1
N
– The first p cells of each queue are considered for scheduling
– Higher complexity• Scheduler deals with pN
cells
QoS Issues in Telecommunication Networks - 21Andrea Bianco – TNG group - Politecnico di Torino
NxNN N• Non FIFO queues
– HoL blocking reduced, completely eliminated only for P→∞
1
Memory architecture• VOQ (virtual output
queueing)1 1
N
N
1
– At each input data are stored in separate queues according to data destination (N queues for each input)
– N2 queues in total
QoS Issues in Telecommunication Networks - 22Andrea Bianco – TNG group - Politecnico di Torino
NxNN N
N
– Eliminates HoL blocking and it permits to achieve 100% throughput with a proper scheduling algorithm
IQ switch scheduling
Pag. 12
Scheduling problem modelling• Problem to be solved
by the scheduling can be represented using a
• An edge i→j exist if there is at least a data at input i willing to reach
1
2
1
2
be represented using a bipartite graph
at input i willing to reach output j
• Edges may be weighted• Weight
– Binary– Queue length
QoS Issues in Telecommunication Networks - 23Andrea Bianco – TNG group - Politecnico di Torino
3
N
3
N
g– HoL cell age or waiting
time– Other metrics
Scheduling problem modeling• The scheduling algorithm tries to determine, in each
time slot, a matching over the bipartite graphs.
1
2
1
2
1
2
1
2
• Select at most N edges with constraints– At most one edge for each input– At most one edge for each output
QoS Issues in Telecommunication Networks - 24Andrea Bianco – TNG group - Politecnico di Torino
3
N
3
N
3
N
3
N
Graph G Matching M
IQ switch scheduling
Pag. 13
• Another possible representation is based on a (Request Matrix RM), which stores the information related to data transfer request
Scheduling problem modeling
transfer request
INPU
0: no data from input to output
1: at least one data from inputto output (may be weighted)
QoS Issues in Telecommunication Networks - 25Andrea Bianco – TNG group - Politecnico di Torino
• Matching it is a permutation matrix i.e., a matrix such that the row and column sum is at most equal to 1
T
OUTPUT
to output (may be weighted)
Scheduling in IQ switches• Request Matrix • Permutation matrix
3 5 0 02 0 0 44 5 0 00 0 8 2
0 1 0 00 0 0 11 0 0 00 0 1 0
QoS Issues in Telecommunication Networks - 26Andrea Bianco – TNG group - Politecnico di Torino
IQ switch scheduling
Pag. 14
Traffic description• Aij(n) = 1 if a packet arrives at time n at input i,
with destination reachable through output jg p j• λij = E[Aij(n)]• An arrival process is admissible if:
– ∑i λij < 1– ∑j λij < 1
QoS Issues in Telecommunication Networks - 27Andrea Bianco – TNG group - Politecnico di Torino
∑j λij• no input and no output are overloaded on average• OQ switches exhibit finite delays only for admissible traffic
• Traffic matrix: Λ = [λij ]
Traffic scenarios• Uniform traffic
– Bernoulli i.i.d. arrivalsl t tb d i th ⎥
⎥⎤
⎢⎢⎡
11111111
ρ– usual testbed in the literature
• “easy to schedule”
• Diagonal traffic– Bernoulli i.i.d arrivals
⎥⎤
⎢⎡ 0012
⎥⎥⎥
⎦⎢⎢⎢
⎣
=Λ
111111111111
Nρ
QoS Issues in Telecommunication Networks - 28Andrea Bianco – TNG group - Politecnico di Torino
– critical to schedule, since only two matchings are good
⎥⎥⎥⎥
⎦⎢⎢⎢⎢
⎣
=Λ
200112000120
3ρ
IQ switch scheduling
Pag. 15
Traffic scenarios• LogDiagonal traffic
– Bernoulli i.i.d. arrivals ⎥⎥⎤
⎢⎢⎡
24811248
ρ– more critical than
uniform, less than diagonal traffic
⎥⎥⎥
⎦⎢⎢⎢
⎣
−=Λ
8124481212 N
ρ
QoS Issues in Telecommunication Networks - 29Andrea Bianco – TNG group - Politecnico di Torino
Scheduling policies: objective• Let us consider a NxN IQ• Denote by i the input port index and by j the output port
index• Goal: assuming infinite buffer size, transfer any admissible
traffic pattern with no losses• Solutions are known
– If traffic pattern is known in advance• TDM of Birkhoff von Neumann algorithm
– For admissible unknown traffic patterMaximum Weight Matching
QoS Issues in Telecommunication Networks - 30Andrea Bianco – TNG group - Politecnico di Torino
• Maximum Weight Matching• Maximum Size Matching
• Several heuristics are proposed for unknown traffic pattern– iSLIP, iLQF, iOCF, 2DRR (WFA), MUCS, RPA, and many others
IQ switch scheduling
Pag. 16
Scheduling uniform known traffic
• A number of algorithms give 100% throughput when traffic is uniform – For example:
• TDM and a few variants• iSLIP (see later)
Example of a TDM schedule for a 4x4 switch
QoS Issues in Telecommunication Networks - 31Andrea Bianco – TNG group - Politecnico di Torino
Example of a TDM schedule for a 4x4 switch
Birkhoff - von Neumann theorem• Any doubly stochastic matrix Λ can be
expressed as convex combination of t ti t ipermutation matrices πn:
Λ = ∑n an πn
with
QoS Issues in Telecommunication Networks - 32Andrea Bianco – TNG group - Politecnico di Torino
• with– an≥0– ∑n an =1
IQ switch scheduling
Pag. 17
Scheduling non-uniform known traffic
• Thanks to the Birkhoff - von Neumann theorem
• If the traffic is known and admissible, 100% throughput can be achieved by a TDM scheme using:– for a fraction of time a1 matching M1 (π1)
QoS Issues in Telecommunication Networks - 33Andrea Bianco – TNG group - Politecnico di Torino
for a fraction of time a1 matching M1 (π1)– for a fraction of time a2 matching M2 (π2)– for a fraction of time ak matching Mk (π3)
MSM: Maximum Size Matching• MSM maximizes the number of data
transferred in a single time slot, i.e. select the i b f dmaximum number of edges
– Instantaneous throughput maximization.• Asymptotic computational complexity is
O(N2.5)• Non optimal algorithm
QoS Issues in Telecommunication Networks - 34Andrea Bianco – TNG group - Politecnico di Torino
Non optimal algorithm– Some admissible traffic pattern cannot be
scheduled, i.e. it does not always achieve 100% throughput.
IQ switch scheduling
Pag. 18
MSM: exampleO1 O2 O3
I1 λ 0 0I 0 λ 0
I1
I2
O1
O2I2 0 λ 0
I3 λ λ 0 λ=0.5
I2
I3
O2
O3
I1 O1 I1 O1 I1 O1
Three MSM are possible in overload, i.e. when all queues are full
QoS Issues in Telecommunication Networks - 35Andrea Bianco – TNG group - Politecnico di Torino
I2
I3
O2
O3
I2
I3
O2
O3
I2
I3
O2
O3
When the first matching is chosen, the maximum throughput cannot be achieved
MWM: Maximum Weight Matching• A weight is associated with each edge• The MWM, among all possible N! matchings,
selects the one with the highest weight (sum of edge metrics)
I1 O1 I1 O1 I1 O11
20
MWMMSM
QoS Issues in Telecommunication Networks - 36Andrea Bianco – TNG group - Politecnico di Torino
I2
I3
O2
O3
I2
I3
O2
O3
I2
I3
O2
O3
1
1
IQ switch scheduling
Pag. 19
MWM: Maximum Weight Matching• MWM does not maximize instantaneous throughput (worse
than MSM)It was demonstrated that a MWM algorithm• It was demonstrated that a MWM algorithm– in IQ switches with VOQ architecture– under admissible traffic– with infinite queue size– when using as weight either the queue length or the age of the HoL
data
achieves100% throughput
QoS Issues in Telecommunication Networks - 37Andrea Bianco – TNG group - Politecnico di Torino
achieves100% throughput • Asymptotic computational complexity O(N3)• With finite queue size, it behaves similarly to MSM• Problems with delays and possible starvation
MSM algorithm• Start from the bipartite graph• Add a source and a sink node, respectivelyAdd a source and a sink node, respectively
connected to all inputs and all outputs• Execute a flow maximization algorithm
– Flow augmentation path
I1 O1
QoS Issues in Telecommunication Networks - 38Andrea Bianco – TNG group - Politecnico di Torino
I1
I2
I3
O1
O2
O3
source sink
IQ switch scheduling
Pag. 20
MSM algorithm• Operates on the residual capacity graph• Select at random a path connecting source
to sink
source sink Flow 1
QoS Issues in Telecommunication Networks - 39Andrea Bianco – TNG group - Politecnico di Torino
• Residue graph:
source sink
MSM algorithm
• Residue graph:
source sink Flow 2
QoS Issues in Telecommunication Networks - 40Andrea Bianco – TNG group - Politecnico di Torino
source sink
IQ switch scheduling
Pag. 21
MSM algorithm
so rce sink Flow 3
• Residue graph:
source sink Flow 3
QoS Issues in Telecommunication Networks - 41Andrea Bianco – TNG group - Politecnico di Torino
• Algorithm terminates when there are no more admissible paths among source and sink
source sink
MSM algorithm• Final solution obtained by summing the flows
obtained ineach step
• Algorithms never backtracks to modify a choice
source sink
QoS Issues in Telecommunication Networks - 42Andrea Bianco – TNG group - Politecnico di Torino
choice• Problems:
– Successive iterations cannot be made parallell– Not suitable to hardware implementation
IQ switch scheduling
Pag. 22
Uniform traffic• MWM and MSM behave almost identically
100Uniform Traffic
MWM
10
Mea
n de
lay
MWM MSM
QoS Issues in Telecommunication Networks - 43Andrea Bianco – TNG group - Politecnico di Torino
10.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
M
Normalized Load
Diagonal traffic• MSM yields much longer delays than MWM at medium/high loads
1000Diagonal Traffic
MWM
100
Mea
n de
lay
MWM MSM
QoS Issues in Telecommunication Networks - 44Andrea Bianco – TNG group - Politecnico di Torino
1
10
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
M
Normalized Load
IQ switch scheduling
Pag. 23
Practical solutions• Need to define heuristics
– with reasonable complexity– that can be implemented in hardware
• Any scheduling algorithm defines three aspects:– A method to compute the weights to be associated with
each edge (metric):• Approximate MSM
– Binary (queue occupancy)
QoS Issues in Telecommunication Networks - 45Andrea Bianco – TNG group - Politecnico di Torino
Binary (queue occupancy)• Approximate MWM
– Queue length (it is an indication of the fact that the queue, which is associated with an input/output pair, is suffering)
– Age of HoL data– Interface load– Ad hoc metrics to select critical edges/nodes
Practical solutions– ...– A heuristic algorithm to determine a matching– A contention resolution algorithm among edges
with the same metric:• round-robin (initial choice state dependent)• sequential search (initial choice non state dependent)• random
QoS Issues in Telecommunication Networks - 46Andrea Bianco – TNG group - Politecnico di Torino
IQ switch scheduling
Pag. 24
i-SLIP• Iterative algorithm• It defines a heuristic algorithm which g
determines, with a proper number of iterations, a maximal size matching (i.e., a matching that cannot be further extended with other edges selection)Metric is the queue occupancy
QoS Issues in Telecommunication Networks - 47Andrea Bianco – TNG group - Politecnico di Torino
• Metric is the queue occupancy• To solve contentions, it exploits an arbiter for
each input and for each output
i-SLIP• In each iteration, three phases can be
identified:– Request: each unmatched input sends a request– Request: each unmatched input sends a request
to every output for which it has a cell– Grant: each unmatched output that has received
requests, sends a grant to one of the requesting inputs.
• Contentions solved by a round robin mechanism
QoS Issues in Telecommunication Networks - 48Andrea Bianco – TNG group - Politecnico di Torino
Contentions solved by a round robin mechanism.– Accept: if an unmatched input receives grants, it
selects an output and becomes matched to it • Contentions solved by a round robin mechanism
IQ switch scheduling
Pag. 25
i-SLIP: counters• Each input (output) has a pointer associated with
to solve contentions• The output pointer is incremented, modulo N, by
one unit beyond the index of the input to which the grant was issued
• The input pointer is incremented, modulo N, by one unit beyond the index of the output from
QoS Issues in Telecommunication Networks - 49Andrea Bianco – TNG group - Politecnico di Torino
one unit beyond the index of the output from which an accept was received
i-SLIP: properties• For uniform overload the bipartite graph is
a full mesh the higher the number of alternatives the easier is to determine aalternatives, the easier is to determine a good matching. iSLlP degenerates to a TDM scheme ES:
I
I1
O
O11,2,3,4 1,2,3,4
• All outputs grant
QoS Issues in Telecommunication Networks - 50Andrea Bianco – TNG group - Politecnico di Torino
I2
I3
I4
O2
O3
O4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
p ginput 1
• Input 1 accepts output 1
IQ switch scheduling
Pag. 26
i-SLIP: properties
I
I1
O
O1• IT 1
For one iteration unsatisfactoryI2
I3
I4
O2
O3
O4
y
I1 O1
• IT 2I1 O11,2,3,4 1,2,3,4
QoS Issues in Telecommunication Networks - 51Andrea Bianco – TNG group - Politecnico di Torino
I4 O4
I2I3
O2
O3
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
I2
I3
I4
O2
O3
O4
i-SLIP: properties• At the end:
• IT N
I O4
I2
I1
I3
O2
O1
O3
1,2,3,4
1,2,3,4
1 2 3 4
1,2,3,4
1,2,3,4
1 2 3 4
• IT N
I2
I1
I3
I
O2
O1
O3
O
1,2,3,41,2,3,4
QoS Issues in Telecommunication Networks - 52Andrea Bianco – TNG group - Politecnico di Torino
• A maximum (implies maximal) matching is obtained after N iterations
I4 O41,2,3,4 1,2,3,4 I4 O4
IQ switch scheduling
Pag. 27
i-SLIP: propertiesIn the following steps, pointers are staggered one iteration is enough to obtain a maximum matching
I O1 2 3 4• Step 2
I O
I2
I1
I3I4
O2
O1
O3
O4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
I2
I1
I3I4
O2
O1
O3
O4• Step 3
QoS Issues in Telecommunication Networks - 53Andrea Bianco – TNG group - Politecnico di Torino
I2
I1
I3I4
O2
O1
O3
O4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
I2
I1
I3I4
O2
O1
O3
O4
1,2,3,4
1,2,3,4
1,2,3,4
1,2,3,4
i-SLIP: properties• Each iteration has a computational complexity of O(N2),
but it can be easily made parallel• Worst case in one iteration: 1 edge is selected• Worst case in one iteration: 1 edge is selected• When executing N iterations, the matching is maximal
(depends on the choice made but cannot be extended) however, the computational complexity is O(N3)
• Experimental results show that log2N iterations are in general enough to obtain good performance
QoS Issues in Telecommunication Networks - 54Andrea Bianco – TNG group - Politecnico di Torino
g g g p• Performance drops if pointers are badly synchronized• iSLIP was implemented on a single chip in the Cisco
12000 router
IQ switch scheduling
Pag. 28
iSLIP: extensions• Use the same heuristic algorithm (3-phase) but with
different metrics– Queue length iLQFQueue length iLQF– HoL cell age iOCF
• Input send requests containing the weight • Contentions are solved using the weight first, only
for equal weights the choice is random• Does not exploit pointer synchronization to obtain
good performance rather the edge weight
QoS Issues in Telecommunication Networks - 55Andrea Bianco – TNG group - Politecnico di Torino
good performance, rather the edge weight • OCF has better delay properties (never starves
data), but the increase in complexity is significant and makes the algorithm practically unfeasible
2DRR: Two Dimensional Round Robin
• Operates on the request matrix• Extension of the WFA (Wave Front Arbiter), very
easily implementable in hardwareeasily implementable in hardware• Definitions
– Generalized diagonal is a set of N elements of a matrix NxN such that two elements do not belong to the same row or column
• A set of N diagonal is said to be covering if each element of the matrix belongs to one and only one
QoS Issues in Telecommunication Networks - 56Andrea Bianco – TNG group - Politecnico di Torino
g ydiagonal
• In each time slot, the algorithm goes through N iterations
IQ switch scheduling
Pag. 29
2DRR: Two Dimensional Round Robin
• At the beginning, all links (input-output connections) are enabledAt h it ti i li d di l i• At each iteration, a given generalized diagonal is chosen– Only enabled links may be selected if the are covered by
the elements belonging to the chosen diagonal • If a link from input i to output j is selected, all
requests issued by i or sent to j are disabled for the
QoS Issues in Telecommunication Networks - 57Andrea Bianco – TNG group - Politecnico di Torino
current time slot (cannot be chosen in the matching)• In N iterations, all N generalized diagonal are
considered and the request matrix is fully covered
2DRR: example
1 0 1 10 1 0 1 1010
1101IT 1
10101101
IT 2
0 1 0 11 1 0 10 0 1 0
0001
010010111010
1101IT 3
010010111010
IT 41101
RM=
QoS Issues in Telecommunication Networks - 58Andrea Bianco – TNG group - Politecnico di Torino
010010000010
010010111010
010010111010
IQ switch scheduling
Pag. 30
2DRR: Two Dimensional Round Robin
• At each time slot, a different covering set of generalized diagonal is chosen, to improve fairness– Indeed, edges covered to the first diagonal chosen are
more likely selected– Round robin over different sets of covering diagonal and
round robin on each element in the set• Emulates a MSM
Not easy to extend to other metrics
QoS Issues in Telecommunication Networks - 59Andrea Bianco – TNG group - Politecnico di Torino
• Not easy to extend to other metrics• Asymptotic computational complexity O(N2)
MUCS: Matrics Unit Cell Scheduler• Information on queue status are concentrated
on a request matrix A (NxN)q ( )• Starting from A, the weight matrix W is
computed• The matching is computed on the basis of W• Elements aij of A are non-negative integers
QoS Issues in Telecommunication Networks - 60Andrea Bianco – TNG group - Politecnico di Torino
jthat indicate the priority to be assigned to the edge connecting input i to output j
IQ switch scheduling
Pag. 31
MUCS: Matrics Unit Cell Scheduler
• 3 possible values can be associated with each aij:ij– QoS priority: aij is inversely proportional to the
minimum Maximum Cell Transfer Delay in queue storing packets from i to j
– Binary priority: aij=1 if there is at least a packet in the queue storing packets from i to jQ l th i it i th f th
QoS Issues in Telecommunication Networks - 61Andrea Bianco – TNG group - Politecnico di Torino
– Queue length priority: aij is the occupancy of the queueu storing packets from i to j
• Weights wij are computed starting from aij
MUCS: Matrics Unit Cell Scheduler• At step n, the reduced request matrix An is defined,
whose size Mn is decreasing (Mn+1< Mn)At each iteration the follo ing steps are e ec ted• At each iteration, the following steps are executed:– Compute the weight matrix from matrix An:
⎪
⎪⎨
⎧ ≠+ aifwca
wra
w ijij
ij
ij
ij
ij
0
QoS Issues in Telecommunication Networks - 62Andrea Bianco – TNG group - Politecnico di Torino
⎪⎩ otherwisej
0
∑=
=nM
jijij awr
1∑=
=nM
iijij awc
1
IQ switch scheduling
Pag. 32
MUCS: Matrics Unit Cell Scheduler– Select the edge i→j associated with the largest value of wij
Once edges are selected, the reduced matrix An+1 is computed taking into account all elements in A belongingcomputed, taking into account all elements in A belonging to rows and columns not selected in previous iterations
– the algorithm ends when all elements in A were considered
• It is a greedy algorithm• Asymptotic computational complexity is O(N3)
QoS Issues in Telecommunication Networks - 63Andrea Bianco – TNG group - Politecnico di Torino
• Asymptotic computational complexity is O(N3)• Good performance, but implemented using analog
components
RPA: Reservation with Preemption and Acknowledgment
• It is a heuristic algorithm based on two phases:– Reservation (possibly preemptive) – Acknowledgment
• Inputs keep an urgency metric Xij associated with each queue
• Inputs operate on a reservation vector RES which stores reservations made by inputs in each time slot
• Reservation vector RES has N elements; each element refers to a different output port and contains– Urgency
QoS Issues in Telecommunication Networks - 64Andrea Bianco – TNG group - Politecnico di Torino
g y– Input port index
• Initially, at each round: Urgj = 0, ∀ j
Urg1,In1 Urg2,In2 Urg3,In3 UrgN,InN
Out 1 Out 2 Out 3 Out N
RES
IQ switch scheduling
Pag. 33
RPA: reservation phase• Input ports access vector RES sequentially, according to a
pre-defined order• The first input makes a greedy selection, choosing the output g y g
corresponding to the maximum urgency • The input following in the pre-defined order chooses the
output that maximizes the difference among queue urgency and RES vector urgencies– Input i computes Wj = Xij – Urgj for all j– finds j* such that Wj* = max{ Wj }– if Wj* > 0,
⇒ reserve output j* and set Urg =X possibly overwriting the previous
QoS Issues in Telecommunication Networks - 65Andrea Bianco – TNG group - Politecnico di Torino
⇒ reserve output j and set Urgj*=Xij*, possibly overwriting the previous reservation
– It may pre-empt an already existing request if this choice maximizes the global urgency (may not select its maximum urgency)
• The reservation phase ends when all ports made their reservation
RPA: acknowledgment phase• Reservation vector RES is again processed by all
inputs, in the same order followed during the reservation phase
• Each input checks if its reservation was cancelled :– If NOT: input gets access to the reserved output– If YES: the input cannot gain access to the previously
reserved output; however, it may select another output among available (not reserved) outputs Note that since
QoS Issues in Telecommunication Networks - 66Andrea Bianco – TNG group - Politecnico di Torino
among available (not reserved) outputs. Note that, since the number of inputs is normally equal to the number of outputs, if some reservations were cancelled, some outputs are surely available
IQ switch scheduling
Pag. 34
RPA features• Good performance
– Sum of the weights selected is at least half of the weights transferred by MWMtransferred by MWM
• Different urgency metrics may be chosen, making the algorithm very flexible– Strict priority among multiple classes may be enforced– Standard urgency is queue length
• No iterations are required
QoS Issues in Telecommunication Networks - 67Andrea Bianco – TNG group - Politecnico di Torino
q• Asymptotic computational complexity O(N2)• Cannot be made parallel, since a sequential access
is fundamental
Uniform traffic• Comparison between MWM, iSLIP, iLQF, RPA
1000Uniform Traffic
100
1000
ean
dela
y
MWMiSLIP iLQF RPA
QoS Issues in Telecommunication Networks - 68Andrea Bianco – TNG group - Politecnico di Torino
1
10
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
M
Normalized Load
IQ switch scheduling
Pag. 35
LogDiagonal traffic• iSLIP saturates close to 84% throughput
100000LogDiagonal Traffic
1000
10000
100000
ean
dela
y
MWMiSLIP iLQFRPA
QoS Issues in Telecommunication Networks - 69Andrea Bianco – TNG group - Politecnico di Torino
1
10
100
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Me
Normalized Load
Diagonal traffic• RPA achieves 98% throughput, iLQF 87%, iSLIP 83%
100000Diagonal Traffic
100
1000
10000
100000
ean
dela
y
MWMiSLIP iLQF RPA
QoS Issues in Telecommunication Networks - 70Andrea Bianco – TNG group - Politecnico di Torino
1
10
100
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Me
Normalized Load
IQ switch scheduling
Pag. 36
Issues in IQ switches• Signalling:
– Signalling bandwidth required to transfer weights from i h ll b i ifi i hinputs to the controller may be significant with respect to the available bandwidth in the switching fabric
– The more complex the adopted metric, the larger the signalling bandwidth required
– Differential signalling may be adopted• Multiple classes:
QoS Issues in Telecommunication Networks - 71Andrea Bianco – TNG group - Politecnico di Torino
Multiple classes:– Given K classes, first the VOQ architecture must be
extended, by using KN queues at each input– Scheduling algorithms must be extended to support
priorities
Issues in IQ switches• QoS (fair queueing):
– Scheduling for QoS (need to serve the most urgent k ) h diffi l i i i h h h d lipacket) has a difficult interaction with the scheduling to
transfer data from inputs to outputs– Need to balance performance and fairness– No ideal optimal solution known
• Frame scheduling:Operate on a frame of length F slot and compute a
QoS Issues in Telecommunication Networks - 72Andrea Bianco – TNG group - Politecnico di Torino
– Operate on a frame of length F slot, and compute a schedule on the frame and not on a slot by slot basis
– Scheduling algorithm executes only at frame boundaries– Relatively easy to provide QoS guarantees for each input-
output pair– Delay increases at low loads
IQ switch scheduling
Pag. 37
Issues in IQ switches• Variable packet length support
– May introduce packet scheduling instead of cell y p gscheduling
• Packets transferred as trains of cells– An edge is selected when the first cell of a packet arrives
and is kept in all the following matchings until the last cell of the packet is transferred
– It avoids reassembly machines at outputs
QoS Issues in Telecommunication Networks - 73Andrea Bianco – TNG group - Politecnico di Torino
It avoids reassembly machines at outputs– Same throughput guarantees– Packet delay may be larger or shorter
• Depends on packet length distribution
Issues in IQ switches• Multicast:
– 2N possible different multicast flows– May be treated as unicast through input port replicationMay be treated as unicast through input port replication
(often named multicopy) • At each input a number of copies equal to the packet fanout are
created, for the proper outputs, and inserted in the proper VOQ– Speedup required– Increases the instantaneous input load– May lead to low throuhgput (unable to sustain a single broadcast
flow)– Scheduling for multicast must be defined to exploit
QoS Issues in Telecommunication Networks - 74Andrea Bianco – TNG group - Politecnico di Torino
Scheduling for multicast must be defined to exploit switching fabric multicast capabilities
• Balance fanout splitting and no-fanout splitting• Often a single FIFO for multicast is proposed (HoL blocking, less
critical with respect to unicast)• Critical traffic patterns when few inputs are active
IQ switch scheduling
Pag. 38
Example of a critical traffic pattern
QoS Issues in Telecommunication Networks - 75Andrea Bianco – TNG group - Politecnico di Torino
Issues in IQ switches– MC-VOQ architecture
• 2N separate queues at each input• Best possible solution (no HoL blocking)• Best possible solution (no HoL blocking)
– An optimal scheduling was defined (only theoretically)– Implies re-enqueueing and out-of-sequence
• However, admissible traffic pattern exist that cannot be scheduled in an IQ switch regardless of the queue architecture and of the scheduling algorithm
• Scalability problemN b f
QoS Issues in Telecommunication Networks - 76Andrea Bianco – TNG group - Politecnico di Torino
– Number of queues– Scheduling algorithm
– Manage a finite number of queues• CIOQ switches (a moderate speedup helps a lot)
IQ switch scheduling
Pag. 39
ReferencesKarol M., Hluchyj M., Morgan S., ``Input versus output queueing on a space division switch'', IEEE Transactions on Communications, vol.35, n.12, Dec.1987McKeown N., Anantharam V., Walrand J.,``Achieving 100% throughput in an input-queued switch'',IEEE INFOCOM'96, vol.1, San Francisco, CA, Mar.1996, pp.296-302McKeown N.,``iSLIP: a scheduling algorithm for input-queued switches'', IEEE Transactions on Networking, vol.7, n.2, Apr.1999, pp.188-201Tamir Y., Chi H.-C., ``Symmetric crossbar arbiters for VLSI communication switches'', IEEE Transaction on Parallel and Distributed Systems, vol.4, no.1, Jan.1993, pp.13 –27, , ppAnderson T., Owicki S., Saxe J., Thacker C.,``High speed switch scheduling for local area networks'', ACM Transactions on Computer Systems, vol.11, n.4, Nov.1993 LaMaire R.O., Serpanos D.N., ``Two dimensional round-robin schedulers for packet switches with multiple input queues'', IEEE/ACM Transaction on Networking, vol.2, n.5, Oct.1994, p.471-482Duan H., Lockwood J.W., Kang S.M., Will J.D., ``A high performance OC12/OC48 queue design prototype for input buffered ATM switches'', IEEE INFOCOM'97, vol.1, 1997, pp.20-8, Los Alamitos, CAAjmone Marsan M., Bianco A., Leonardi E., Milia L., ``RPA: a flexible scheduling algorithm for input buffered switches'', IEEE Transactions on Communications, vol.47, n.12, Dec.1999, pp.1921-1933 Ajmone Marsan M., Bianco A., Giaccone P., Leonardi E., Neri F., ``Packet scheduling in input-queued cell-based switches'', IEEE Trans. on Networking, Oct.2002
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Kim C.K., Lee T.T., Call scheduling algorithm in multicast switching systems , IEEE Transactions on Communications, vol.40, n.3, Mar.1992, pp.625635
• Prabhakar B., McKeown N., Ahuja R., ``Multicast scheduling for input-queued switches'', IEEE Journal on Selected Areas in Communications, vol.15, n.5, Jun.1997, pp.855-866
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• Liu Z., Righter R., ``Scheduling multicast input-queued switches'', Journal of Scheduling, John Wiley & Sons, May 1999• Ajmone Marsan M., Bianco A., Giaccone P., Leonardi E., Neri F., ``On the throughput of input-queued cell-based switches with multicast traffic'', IEEE
INFOCOM'01, Anchorage Alaska, Apr.2001• Smiljanic A., “Flexible bandwidth allocation in high-capacity packet switches”, IEEE/ACM Transactions on Networking, vol.10, n.2, pp.287-293,
Apr.2002 Chang C.S., Lee D.S., Jou Y.S., ``Load balanced Birkhoff-von Neumann switches'', 2001 IEEE HPSR, 2001, pp.276-280.