Vodafone Chair Mobile Communications Systems, Prof. Dr.-Ing. G. Fettweis
An Accurate and Scalable Analytic Model for Round-Robin
Arbitration in Network-on-Chip
Erik Fischer and Gerhard Fettweis
Speaker: Erik Fischer
7th International Symposium on Networks-on-Chip (NOCS) 2013
Outline
Motivation
System Model
Service Time Estimation
Performance Evaluation
TU Dresden
E. Fischer and G. Fettweis
Slide 2
Motivation
MPSoC Design Flow Today
Design of Future Many-Core SoC
Given
Future
applications
Application
Modeling &
Simulation
Automated Guidance
Concept
Designers Experience
Architecture
HW design
& chip
production
TU Dresden
???
E. Fischer and G. Fettweis
↑ computation
↑ reliability
Complex Design
Space
Needs fast models!
1000s of cores
on a single chip!
Slide 3
System Model
Assumptions on router level
•
•
•
.
.
.
Crossbar
Switch
...
𝑁𝑖 buffered inputs
𝑁𝑜 (unbuffered) outputs
Known mean arrival rates 𝜆𝑖
•
Known mean service rate 𝜇
(service incl. arbitration,
switching and forwarding)
•
Known forwarding probabilities 𝑓𝑖,𝑜
.
.
.
...
Input
FIFOs
Routing &
Arbitration
TU Dresden
•
Round-robin arbitration
E. Fischer and G. Fettweis
Slide 4
System Model
Depends on …
Topology
Routing
Decoupling of service time
and queueing model
Traffic
Advantages:
 Simplified queueing model
 More flexible to adapt for
other arbitration schemes
and service classes
Arbitration
Service Classes
Traffic / Service
Statistics
TU Dresden
E. Fischer and G. Fettweis
Slide 5
Service Time Estimation
Service Time Model
1. Contention Probability
Probability that contention
occurs when a packet is
requesting service to be routed
from input i to output o
2. Contention Resolution
Probability that a packet is
forced to wait under a given
contention situation
TU Dresden
E. Fischer and G. Fettweis
Slide 6
Service Time Estimation
Contention Probability
Path utilization from
input i to output o:
Auxiliary binary “truth table” matrix B:

Covers all possible collision
scenarios
e.g., for the case of 3 inputs:
TU Dresden
E. Fischer and G. Fettweis
Slide 7
Service Time Estimation
Contention Resolution

Decision probability:

Collision resolution distribution:
Number of contending
inputs for output o
TU Dresden
E. Fischer and G. Fettweis
Slide 8
Service Time Estimation

Waiting probability:
Contention Probability

Decision Probability
Service times:
 System of equations
TU Dresden
E. Fischer and G. Fettweis
Slide 9
Service Time Estimation
Iterative Service Time
Estimation Algorithm
Check: xi,o
converged?
true
Start
false
Precompute
B, λi,o
Finish
Exit w/ error
true
Initialize
xi,o=x
TU Dresden
Calculate
ρi,o, ρi
E. Fischer and G. Fettweis
Ǝ ρi>1
false
Update
xi,o
Calculate
NC, r, d, w
Slide 10
Comparison of service
times with:
Ref. model [1]
Setup:

Center router [4,4]
of 8x8 2D-mesh

Poisson inputs

Uniform network
traffic
Service Time

Cycle-accurate sim.
Service Time

Service Time
Performance Evaluation – Single Router
Northern router input
1.4
Sim
RRMod
RefMod
1.2
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.3
0.35
0.4
0.45
0.35
0.4
0.45
Eastern router input
1.2
Sim
RRMod
RefMod
1.1
1
0
0.05
0.1
0.15
0.2
0.25
Router input of module
1.4
Sim
RRMod
RefMod
1.2
1
0
0.05
0.1
0.15
0.2
0.25
0.3
Injection rate (flits/cycle/module)
[1] O. Lysne, “Towards a generic analytical model of wormhole routing networks,”
Microprocessors and Microsystems, vol. 21, no. 78, pp. 491 – 498, 1998.
TU Dresden
E. Fischer and G. Fettweis
Slide 11
Performance Evaluation – Network

Cycle-accurate sim.

Ref. models [2][3][1]
Setup:

8x8 2D-mesh

Det. XY routing

Flit based switching

Application specific
network traffic
50
Average packet latency [clock cycles]
Comparison of mean
packet latencies with:
45
40
35
Cycle-accurate Simulation
Round-Robin Model
Reference Model 1
Reference Model 2
Reference Model 3
30
25
20
15
10
5
5.5
6
6.5
7
Packet injection rate (pkt/cycle)
7.5
8
[2] U. Ogras, P. Bogdan, and R. Marculescu, “An analytical approach for network-on-chip performance analysis,” Computer-Aided
Design of Integrated Circuits and Systems, IEEE Transactions on, vol. 29, no. 12, pp. 2001 –2013, Dec. 2010
[3] E. Fischer, A. Fehske, and G. Fettweis, “A flexible analytic model for the design space exploration of many-core network-on-chips
based on queueing theory,” in Proc. of SIMUL, 2012
TU Dresden
E. Fischer and G. Fettweis
Slide 12
Conclusions
 Analytic model allows for fast NoC performance analysis in
an early stage of design space exploration
 Decoupling of service time and queueing model eases
arbiter model and makes it more flexible
 Round-robin service time model considers contention
probability as well as contentions resolution
 Iterative solution algorithm
Average packet latency [clock cycles]
50
45
40
35
Cycle-accurate Simulation
Round-Robin Model
Reference Model 1
Reference Model 2
Reference Model 3
30
25
20
15
10
5
5.5
7
6.5
6
Packet injection rate (pkt/cycle)
TU Dresden
7.5
8
 High accuracy of round-robin service time estimation
 Mean error <6% of packet latencies for analyzed case of
8x8 NoC
E. Fischer and G. Fettweis
Slide 13