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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