EFFECT OF APPLICATION MAPPING ON NETWORK-ON-CHIP PERFORMANCE

Coşkun ÇELĐKDepartment of Electrical and Electronics

EngineeringGazi UniversityAnkara, TURKEY

Cüneyt F. BAZLAMAÇCIDepartment of Electrical and Electronics

EngineeringMiddle East Technical University

Ankara, TURKEY

Content

� Introduction

� Network on Chip (NoC)

� Application Mapping

� Self Similarity� Self Similarity in Network Traffics

� Self Similarity in On-Chip Networks

� Main study� Motivation

� Queuing Analysis under Self Similar Traffic

� Effect of Self Similarity Parameters

� Computational Work

� Observations on Results

� Introduction

� Network on Chip (NoC)

� Application Mapping

� Self Similarity

� Self Similarity in Network Traffics

� Self Similarity in On-Chip Networks

Network on Chip (NoC)

� System-on-Chip (SoC): integration of a number of different functional units into a single chip.

� SoC design problems;

� Implementation of functional units,

�Memory management,

� Power minimization,

� Clock synchronization between units,

�On chip communication

Network on Chip (NoC)

� Point-to-Point or Bus based methods do not scale well as the communication requirement of the chip increases

� A new on chip communication paradigm:

Network on Chip (NoC)

� NoC is a layered network architecture for on chip communication, composed of basic components;

� Network Interface

� Router

� Link

Main NoC Design Problems[3]

� Communication paradigm

� Routing protocol design

� Flow control & Congestion control mechanisms

� Communication Architecture Design� Topology design

� Router circuitry

� Application & Traffic Modeling� Traffic Modeling

� Application Scheduling (task-to-core mapping)

� Application Mapping (core-to-router mapping)

[3] R. Marculescu , U. Y. Ogras et.al. “Outstanding research problems in NoC design: system, microarchitecture, and circuit perspectives”, IEEE TCAD, 2009.

Application Mapping

� Definition: physical placement of IP cores onto NoC topology

Task Graph IP Core Graph

ApplicationScheduling

ApplicationMapping

IP Core Graph NoC Topology

Self Similarity

� A natural phenomenon where a certain property of an object is preserved with respect to scaling in space and/or time.

� Example for deterministic self similarity: 2D Cantor set;

Fern

Stochastic Self Similarity

� Self similarity in terms of second order statistic, like autocovariance or autocorrelation

� Second-order statistics are statistical properties that capture burstiness, variability or scale invariance

� Formal definition:� Consider a stationary discrete time stochastic process, X(t), which presents the traffic volume in packets, bytes or bits, at time instance

� Aggregate process X(p)

Stochastic Self Similarity

� Let autocovariance function of X(t) and X(p)(i) be C(k) and C(p)(k), respectively. Then

� X(t) is exactly second-order self-similar with Hurst parameter H, if

� X(t) is asymptotically second-order self-similar with Hurst parameter H, if

Self Similarity in Network Traffics

� In [5], authors analyze some real internet traffic traces;

� Aggregating the traces at different time scales (from a few milliseconds to minutes and hours) does not smooth the traffic, which is the case in Poisson process

� Self similar models are more accurate for modeling network traffics, than Poisson based models.

[5] W. Leland, M. Taqqu, W. Willinger, and D.V. Wilson. "On the self similar nature of Ethernet traffic" IEEE/ACM Trans. Networking, 1994.

Self Similarity in On-Chip Networks

� [6] shows the existence of self similarity in a typical MPEG-2 video application.

� In [8], the authors analyze the communication traces of processor IPs at a cycle-accurate level and show the presence of self similarity.

� [7] proposes a statistical traffic model for homogeneous on-chip networks and the bursty nature of traffic is represented by using self similarity concept.

[6] G. Varatkar and R. Marculescu. “On-chip traffic modeling and synthesis for MPEG-2 video applications”. IEEE Transactions of VLSI, 2004.[7] V. Soteriou, H. Wang, and L. Peh. “A statistical traffic model for on-chip interconnection networks.” IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS’06), 2006.[8] A. Scherrer, A. Fraboulet, and T. Risset. “Long-range dependence and on-chip processor traffic”, Microprocessors and Microsystems, 2008.

� Main study

�Motivation

�Queuing Analysis under Self Similar Traffic

� Effect of Self Similarity Parameters

� Computational Work

�Observations on Results

Motivation

� In literature, application mapping problem is generally considered as minimization of

� communication energy consumption� latency/delay

without considered network dynamics

� In most solutions in literature, an ideal underlying network is considered (no packet drop or blocking)

� Our main motivation to find a mapping which distributes network traffic fairly and avoids congested routers by using a priori traffic information

� This study aims to quantize the effect of application mapping and show the necessity of a new problem definition fed from this motivation

Queuing Analysis under Self Similar Traffic

� Mathematical modeling of self similarity is difficult� i.e. no simple, closed form formulas, such as Little’s theorem

� Some stochastic processes for modeling self similarity;� Fractional Gaussian Noise (FGN)

� Fractional Brownian Motion (FBM)

� On/Off Processes

� Wavelet-based Models

� FBM is used in [11] for analyzing a network buffer under self similar traffic

[11] I. Norros. "A storage model with self-similar input" Queueing Systems, 1994

� Let Z(t) be a FBM process with zero mean and variance of

E{Z2(t)}=|t|2H , then

is a self similar process with parameters;

� H: Hurst parameter

� m: mean input rate

� a: variance coefficient

� By using this model, lower bound for the probability of the queue length exceeds a certain buffer size

� By using this mathematical basis, we implemented a probability density function figure;

� Average number of packets in buffer can be obtained as;

Under infinite buffer assumption (b→∞)

� Similarly, packet loss rate on a queue of length b (under infinite buffer assumption) can be written as

Effect of Self Similarity Parameters

� For high input rates buffers enter congestion region (as expected)

� For higher values of H (i.e. self similarity is dominant) this effect is more obvious.

� Self similarity degenerates network performance

� For low values of input rate, short rate traffic (H=0.5) has better performance: resetting and truncating effect

Effect of Application Mapping on Network Performance under Self Similar Traffic

� In order to evaluate the effect of application mapping and assess our motivation, a brute-force computational study is performed.

� Six different core graph with various network density and traffic requirements and a 3x3 2D mesh topology are considered.

Test Case-2

� A mapping instance and the routing protocol specify the aggregated traffic that enters to a buffer.

� Self similar traffic aggregation;

� For each test case energy consumption and maximum/average loss rate are calculated for all possible mappings.

� Each mapping solution is labeled with both energy rank and loss rate rank

� Best 1% mappings with respect to energy is called “the short list” and considered as the near optimal solution of energy-only application mapping

� Loss rate ranks of this short list gives an idea about effect of application mapping on performance when network dynamics are not considered

� Following histograms present distribution of maximum/average loss rate ranks of solutions in our short list.

Observations

� Near optimal solutions of energy minimization problem can vary significantly with respect to loss rate behavior

Histogram of maximum loss rate for normal network with high traffic

Observations

� In dense network with high traffic, short list does not contain best 20% with respect to loss rate.

Histogram of average loss rate for dense network with high traffic

� Trade-off between nergy and loss rate.

Observations

� As expected, for sparse networks loss rate is not crucial. Near optimal solutions also have best loss rate behavior

Histogram of average loss rate for sparse network with low traffic

A new Application Mapping Problem Formulation

� Above disscussion shows degenerative effect of mapping function on network performance under self similar traffic assumption

� So, a cost function which contains both energy consumption and loss rate related terms is meaningful

� Given � an IP Core graph, a NoC topology, a routing policy and the traffic characteristics of the application

� Find � a mapping solution that minimizes both communication energy consumption and the buffer loss rates

� Such that � the energy and QoS requirements of the application are satisfied

A new Application Mapping Problem Formulation

� With such a formulation

� mappings that use network resources more fairly will be generated,

� variations of performance due to network dynamics will be minimized.

� Detailed formal definition of the problem and an evolutionary computing based solution will be presented in our next study..

Thank you