Title: Switches with Input Buffers Cisco
1Switches with Input Buffers (Cisco)
2Packet Switches with Input Buffers
- Switching fabric
- Electronic chips (Mindspeed, AMCC, Vitesse)
- Space-wavelength selector (NEC, Alcatel)
- Fast tunable lasers (Lucent)
- Waveguide arrays (Chiaro)
- Scheduler
- Packets compete not only with the packets
destined for the same output but also with the
packets sourced by the same input. Scheduling
might become a bottleneck in a switch with
hundreds of ports and gigabit line bit-rates.
3Optical Packet Cross-bar (NEC,Alcatel)
- A 2.56 Tb/s multiwavelength and scalable
switch-fabric for fast packet-switching network,
PTL 1998,1999, NEC
4Optical Packet Cross-bar (Lucent)
- A fast 100 channel wavelength tunable transmitter
for optical packet switching, PTL 2001, Bell Labs
5Scheduling Algorithms for Packet Switches with
Input Buffers
- Each input sends request for its HOL packet to
the corresponding output. Each output grants one
input, and this input-output pair will be
connected in the next time slot. - Output utilization when inputs are fully loaded
is - U1-(1-1/N)N-1
6Scheduling Algorithms for Packet Switches with
Input Buffers
7Scheduling Algorithms for Packet Switches with
Input Buffers
- In parallel iterative matching (PIM), SLIP or
dual round-robin (DRR) inputs send requests to
outputs, outputs grant inputs, and inputs then
grant outputs in one iteration. It was proven
that PIM finds a maximal matching after log2N
4/3 steps on average. - Maximum weighted matching and maximum matching
algorithm maximize the weight of the connected
pairs, and achieve 100 for i.i.d. traffic but
have complexities O(N3log2N) and O(N2.5). - Sequential greedy scheduling is a maximal
matching algorithm that is simple to implement.
Maximal matching algorithm does not leave
input-output pair unmatched.
8Bandwidth ReservationsPacket Switches with Input
Buffers
- Anderson et al. Time is divided into frames of F
time slots. Schedule is calculated in each frame
Statistical matching algorithm. - Stiliadis and Varma Counters are loaded per
frame. Queues with positive counters are served
with priority according to parallel iterative
matching (PIM), their counters are then
decremented by 1. DRR proposed by Chao et al.
could be used as well. - Kam et al. Counter is incremented for the
negotiated bandwidth and decremented by 1 when
the queue is served. Maximal weighted matching
algorithm is applied. - Smiljanic Counters are loaded per frame. Queues
with positive counters are served with priority
according to the maximal matching algorithm
preferrably sequential greedy scheduling
algorithm (SGS), where inputs sequentially choose
outputs to transmit packets to.
9Maximum and Maximal Matching Algorithm
- It was shown that when packet arrivals are i.i.d
and traffic distribution is admissible then 100
can pass the cross-bar if the maximum or the
maximum weighted matching algorithms are applied.
- It was shown that when packet arrivals obey a
strong law of large numbers and traffic
distribution is admissible then 50 can pass the
cross-bar if the mximal matching algorithms are
applied.
10PIM, SLIP and DRR
- In PIM and SLIP each input sends requests to all
outputs for which it has packets, and in DRR only
to one chosen output. SLIP and DRR use
round-robin choices. - Theorem PIM finds a maximal matching after log2N
4/3 steps on average. - Proof Let n inputs request output Q, and let k
of these inputs receive no grants. With
probability k/n all requests are resolved, and
with probability 1-k/n at most k requests are
unresolved. The average number of requests is at
most (1-k/n)kn/4. So if there are N2 requests
at the beginning, the expected number of
unresolved requests after I iterations is N2/4i
11PIM, SLIP and DRR
- Proof (cont.) Let C be the last step on which
the last request is resolved. Then
12Typical Central Controllers (Cisco)
13SGS Implementation
- All inputs one after another choose outputs, SGS
is a maximal matching algorithm
14SGS Uses Pipelining
Ii -gt Tk Input i chooses output for time slot k
15Weighted Sequential Greedy Scheduling
- i1
- Input i chooses output j from Ok for which
it has packet to send
Remove i from Ik and j
from Ok - If iltN choose ii1 and
go to the previous step
16Weighted Sequential Greedy Scheduling
- If k1 mod F then cijaij
Ik1,...,N Ok1,...,N i1
- Input i chooses output j from Ok for which
it has packet to send such that cijgt0
Remove i from Ik and j from Ok cijcij-1 - If iltN choose ii1 and
go to the previous step
17Non-blocking Nature of WSGS
- Maximal matching algorithm does not leave input
or output unmatched if there is a packet to be
transmitted from the input to the output in
question. - It can be proven that all the traffic passes
through the cross-bar with the speedup of two
which is run by a maximal matching algorithm, as
long as the outputs are not overloaded.
18Performance of Maximal Matching Algorithm
Theorem The maximal matching protocol (and so
WSGS) ensures aij time slots per frame to
input-output pair (i,j), if
where Ti is the number of slots reserved for
input i, and Rj is the number of slots reserved
for output j.
Proof Note that
19Admission Control for Maximal Matching Algorithm
The maximal matching (and so WSGS) protocol
ensures aij time slots per frame to input-output
pair (i,j) if
F frame length Ti the number of slots reserved
for input i, Rj the number of slots reserved for
output j. ti, rj are normalized Ti, Rj.
20Analogy with Circuit Switches
- Inputs Switches in the first stage
- Time slots in a frame Switches in the middle
stage - Outputs Switches in the last stage
Non-blocking condition
Strictly non-blocking condition
21Rate and Delay Guranteed by Maximal Matching
Algorithm (and WSGS)
- Assume a coarse synchronization on a frame by
frame basis, where a frame is the policing
interval comprising F cell time slots of duration
Tc. - Then, the delay of D2FTc is provided for the
utilization of 50. Or, this delay and
utilization of 100 are provided for the fabric
with the speedup of 2. -
22Port Congestion Due to Multicasting
Solution Packets should be forwarded through
the switch by multicast destination ports.
23Forwarding Multicast Traffic
24Forwarding Multicast Traffic
25Forwarding Multicast Traffic
26Adding the Port to the Multicast Tree
27Removing the Port from the Multicast Tree
28Admission Control for Modified WSGS
where Ei is the number of forwarded packets per
frame
29Admission Control for Modified WSGS
for
30Admission Control for Modified WSGS
Modified WSGS protocol ensures negotiated
bandwidths to input-output pairs if for
I
II
F frame length, P forwarding fan-out
Ti the number of slots reserved for input i, Ri
the number of slots reserved for output i. ti,
ri are normalized Ti, Ri.
31Rate and Delay Guaranteed by Modified WSGS
- Assume again a coarse synchronization on a frame
by frame basis. - Then, the delay of D FTc is
provided for the utilization of 1/(P2), where P
is the forwarding fan-out. Or, this delay and
utilization of 100 are provided for the fabric
speedup of P2. -
32Quality of Service, P2, S4, B10Gb/s, Tc50ns
33References
- T. E. Anderson, S. S. Owicki, J. B. Saxe, and C.
P. Thacker, Highspeed switch scheduling for
local-area networks, ACM Transactions on
Computer Systems, vol. 11, no. 4, November 1993,
pp. 319-352. - N. McKeown et al., The Tiny Tera A packet
switch core, IEEE Micro, vol. 17, no. 1,
Jan.-Feb. 1997, pp. 26-33. - A. Smiljanic, Flexible bandwidth allocation in
high-capacity packet switches, IEEE/ACM
Transactions on Networking, April 2002, pp.
287-293.
34References
- A. Smiljanic, Scheduling of multicast trafc in
high-capacity packet switches, IEEE
Communication Magazine, November 2002, pp. 72-77.