NIETJOURNAL Winter 2011oFENGINEERING&TECHNOLOGY

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Analytical Study of TrafficBehaviour in a Networkon Chip Architecture

Vivek Srivastava'

IntroductionAbstract

A minimal model of computer network traffic has been

defined in simple as well as complex networks in

order to study the trade-off between topological-

based and traffic based routing strategies. The traffic

exhibits a phase transition from a low to high

congestion state measured in terms of average travel

time of packets as a function of packet creation rate in

network. This analysis results in a collective behaviour

of traffic which presents second-order as well as first-

order phases transition between a free-flow phase

and a congested phase. Global performance,

enlarging the free-flow region is improved by traffic

control in heterogeneous networks. Traffic control

also introduces non-linear effects, may trigger the

appearance of a congested phase in a discontinuous

manner. This paper presents an analytical study of the

traffic behaviour in a NoC architecture.

The task of designing cost effective networksthat provide the required quality of service undervaried traffic conditions demands a formalscientific basic. Such a basic is provided by"TRAFFIC ENGINEERING" or "TELETRAFFICTHEORY".

Network Traffic control is used for the bettermanagement of power consumed by networkedcomputational resources. As we know, in NoC[2] the energy consumption is often a majorconcern because the energy for globalcommunication does not scale down whereascomputational and storage energy greatlybenefits from device scaling (smaller gates andsmaller memory cells).On the contrary, globalcommunication on chip will require increasinglyhigher energy consumption as seen byprojections based on current delay optimizationtechniques for global wires. Hence,communication energy minimization will be agrowing concern in future technologies. Inintegrated circuit [1], interconnect wires accountfor a significant fraction (up to 50%) ofthe energyconsumed and this fraction is only expected togrow in future. In fact, it was projected that thedelay and energy consumption of globalinterconnect structures will prove to be a majorbottleneck for SoC design as technology scalesto the nanometer regime. With designersstriving to improve the lifetime of batteryoperated, personal computing devices,minimizing the energy consumed in on-chipinterconnects becomes crucial. Therequirements for this task are the use of a ~~~

'Department of ECE, NIET, Greater NoidaSrivastava. vivek050@gmail.com

structured, interconnect oriented, designmethodology at all layers of the hierarchy fromthe system-level down to physical design.

Observation of information flow densityfluctuationA whole new set of challenges has been posedon designers by interconnect oriented design.Also, the advent of deep sub-micron technologybrings several signal integrity issues to theforefront. Multi-billion transistors are going to beexpected with the next generation SoCs,ensuring efficient and reliable transport for datasignals becomes a daunting task indeed.Existing low power system designmethodologies are ill-equipped to tackle thisproblem and the reason is that the aim is toeliminate all noise related errors through fine-tuned circuit design while it follows an erroravoidance paradigm. Clearly, this will becomevery costly, if not impossible, given thecomplexity offuture SoCs. So the requirement isthat, after a moderate amount of design timeoptimization, the focus is on error resiliencetechno-quest to combat run time errors andensure correct system functionality and for thispurpose, the paradigm has to change to one oferror tolerance.An interdisciplinary new field of science [3] isgrowing with the growth of Internet Computerscientists; mathematicians and statisticalphysicists are now working on this emergingfield focusing especially on the fractal propertiesof the fluctuations of information traffic.In 1994, [3] Leland et al, reported a statistical self-similarity in the no fluctuation of packets in anEthernet cable inside a laboratory. In the sameyear Casbai independently discovered anotherself-similarity in the fluctuation of round trip timesof the "ping"-command which indirectly reflectthe level of congestion along a path in theInternet.

Computer network trafficThe packet delivery from source to destination iscompletely at random and this randomness isbut naturally, the function of traffic conditions onthe channel. Though channel utilization isincreased using the concept of virtual channel,the non-availability of virtual channels is also alimiting factor while dealing with the switches.

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With the increasing packet size, the delayincreases (almost linearly). Computer networktraffic can exhibit a phase transition from a low tohigh congestion state measured in terms ofaverage travel time of packets as a function ofpacket creation rate in network.Through simulations on a two-dimensionallattice model network, it has been found [3] thatthe phase transition point into the congestionphase depends on how each router chooses apath for the packets in its queue. In particular, anappropriate randomness in path selection canshift the onset of traffic congestion toaccommodate more packets in model network.Numerical simulation of packet traffic on anartificial network not only clarifies that the phasetransition is a continuous phase transitionaccompanied with critical behavior, but it alsodemonstrates that the critical point which istechnologically very important by informationcan be injected, while above the critical point thepossibility of loosing packets due to overflowincreases rapidly, namely the total flow rate is thelargest and reliability is high at the critical point.The dynamic properties of a collection of models[6] for communication processes, characterizedby a single parameter '€' representing therelation between information load of the nodesand its ability to deliver this information as:1-The critical transition to congestion reportedso far occurs only for '€' =1. This case is wellanalyzed for different network topologies.2-For '€' <1, no transition to congestion isobserved but it remains a crossover from a low-density state.3-For '€' >1, the transition to congestion isdiscontinuous and congestion nuclei arise.Now the complex networks are defined as theinteraction between the elements of social,technological, biological, chemical and physicalsystems. A lot of interest among the scientificcommunity has been generated with the study oftopological properties in such a network. Part ofthis interest comes from the attempts tounderstand the behavior of technology basedcommunication networks such as the Internet,the World Wide Web, e-mail networks, or phonecall networks. The study of communicationprocess is also of interest in other fields, notablyin the design of organizations. It is estimated that

NIETJOURNALoFENGINEERING&TECHNOLOGY

more than one-half of the US work force isdedicated to information processing, ratherthan to make or sell things in the narrow sense.The network architecture [4] considered in themodel consists of nodes placed as a two-dimensional lattice in Fig. 1 a. It is a square withN nodes routers on each side and N2 nodes as awhole. Packets are generated and destroyed onnodes on the boundary of the lattice squares inthe figure, but not on inner nodes circles. Innernodes only forward packets received fromneighbour nodes. A node on the boundarygenerates a packet according to the Poissonarrival with I and sends it to a destination nodeselected randomly from among the nodes onthe boundary including itself. Each node has areceiving queue of unlimited length throughwhich packets are forwarded to the destinationand then destroyed.The probabilistic routing strategy that wecompare with this deterministic routing is givenby introducing a particular form of routingprobability function. When we have multipleroutes A and B based on the destinationaddress, we assign the probability to choose aroute A or B by the following equation:

11

e -p,rz

P(B)= e p.l:'+e P,rB'

1=PI,Al+P(B), (3)

where b is a parameter. XA and XB are thenumber of packets the router has already sent inthe direction of A and B.

Phase transition in traffic network

In future, emphasis can be put on to find ageneralized trade off analysis between the areaand the performance while increasing thenumber of virtual channels. The net bandwidthcan be better utilized by increasing the numberof virtual channels; on the other hand it willincrease the cost while considering the chip areaa cost factor. A comparative analysis of variablepacket size and fixed packet size along with thegeneralized latency and throughput can be apoint of emphasis in future.The phenomenology [4] of the nature ofcomputer network traffic has commanded muchattention recently. Analysis, simulation and

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experiments based on such concepts as "phasetransitions" and "self-similarity" are activeresearch topics in physics as well as in computerscience. The approach is first to create a simplesimulation model for network traffic. Then aprobabilistic routing strategy is proposed thatcan shift the phase transition point. To gain moreinsight into this effect, the number of routers isvaried that take this probabilistic strategy. It wasfound that the effectiveness of model shows anonlinear response as a function of proportion ofprobabilistic routers.In order to observe fluctuations of informationflow in the internet [3] a personal computer isset as a host on an Ethernet cable that connectsthe gateway of Keo-university and WIDE internetbackbone that belongs to the public domain.The data link layer of campus backbone 20M bpsATM and a gateway is connected to the networkoperating centre of the WIDE backbone byEthernet of 10 Mbps. Our monitoring host isconnected to this segment via a non-intelligenthub.The recent enormous development of thecomputer network, the internet has beenattracting much attention not only by computerscientists but also physicists as a new target ofstatistical physics. The internet system has beenwidely spread in our daily life, exchanginginformation bye-mail, performing the operationsusing information services like www etc. Theinformation is sent from each local computer inthe form of packets in which the sender'saddress and the destination are recorded. Abigger unit of information is divided into a set ofmany packets.

Here the focus is [5] on an essential feature ofthe topological structure of the internet.Thousands of small local networks are linked toeach other by cables and technical joints suchas gateways to construct the Internet whichmakes topological hierarchical structure.Roughly speaking, a schematic view of theconnection is like a branching tree; terminals areon the very tip of network tree, and bunches ofcomputers are connected to a bunch of upperlevel groups are connected to still higher gradegroup, and so on. It can be approximated thatthe structure of the Internet with the Clayey-tree(or Bethe lattice) by ignoring loop structures,gateways and cables corresponding to sites andbonds, respectively because the gateways areplaying the role of bottlenecks in jammingprocesses.

A map analysis of information fluctuationIn this section we analysis the sort time corelation of information flow fluctuation by ••••.•..a....I1.II

introducing a map analysis that is a plot of An visXn + 1, where An denotes the flow density at timestep n.After summarizing the observation facts on therelation and vis Xn+1, we can assume thefollowing first- order autoregressive map with anexternal random force term, finals the simplestapproximation,

Xn+1 =g (An) +FNHere, the map function g(X) is empiricallyconstructed from the measured data byintroducing a piece wise linear function with twobending points for g(X);

{

ajX +hj for 0 <x <CI •

g(X) = X + b for ci ~X < C2 •

a2(X - 1.0) + h~ for c~~X ~ 1.0 .Where the maximum flow is normalized to1.0.The parameters, C1 & C2 indicate thebending point, b1 & b2 are the minimum andmaximum values of the mean values. Theparameter b is the most important parameter thatcontrols the mean flow density .For b<O thegenerated traffic has a low mean flow density fixpoint corresponding to the sparse phase and forb>O the generated traffic belongs to thecongested phase .The critical point by thecondition b=O which means that all the trafficpoints over the range of C1 <X<C2 are the fixedpoints ,thus the variance of the fluctuationbecomes very large .The values of at a2indicates the line slopes in the small and largeflow density range and are determined byrequiring the continuity of g(X) .As a best fit withthe observation set the parameters C1 =0.25,C2=0.75, b1 =0.1 & b2=0.9The generated fluctuations capture all the basicphase transition properties of the realfluctuations qualitatively as for the probabilitydensity shapes, the peak point shifts, the widthbroadening, the rapid increase of autocorrelation time and the power-law distributionof the interval of the successive high- densityflows. However, from the quantitative view pointthe critical exponents do not fit perfectly. Therecan be a rich variety of phase transitionbehaviors and it has been seen that the Internetcan be viewed as a huge composite of phasetransition elements. Due to buffer's non linerproperty, each router can show a phasetransition behavior microscopically. Due tocontagious propagation of congestion amongrouters there occurs another type of phasetransition macroscopically. By observinginformation flow density at a point we can findphase transition behavior from the fluctuations in

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the time sequential data. In order to confirm thevalidity of this data analysis method we performseveral other observations at differentobservation points .In any case [3] all the resultsare consistent .An interesting finding is that theestimated critical flow densities are about 60% ofthe maximum flow density in general. It istechnologically very important to estimate thecritical density because packet loss probabilitybecomes dominant at flow density higher thanthe critical point.The study of properties of Ethernet connectionby numerical simulation as the physicalmechanism of present phase transition is notelucidated yet.There is an interesting rule [3] of avoidingcollisions of information packets in the Ethernetcommunication called the back-off.The back-off rules are very complicated, but in arough sense the rules are given as follows; whentwo routers shearing an Ethernet cable are tryingto send information packets, the one that has justsent a packet successfully has a priority to emitthe next packet and the other router must wait.By this effect there occurs a new type of phasetransition between two phases; one phase is alow-density mixed flow phase and the other is ahigh-density oscillatory phase in which activerouter switches nearly periodically.

References1 Vijay Raghunathan, Mani B. Srivastava, and

Rajesh K. Gupta,"A Survey ofTechniques forEnergy Efficient On-Chip Communication"

2 Prabhat K. Sharma, "Study of network-on-chip & VHDL implementation of generic NoCrouter", Master of Technology Report,submitted to Department of Electronics andCommunication Engineering, MalaviyaNational Institute of Technology,Jaipur.2008-2009

3 Misako Takayasu, Kensuke Fukuda, HidekiTakayasu, "Application of statistical physicsto the internet traffic"

4 4-Toru Ohira and Ryusuke Sawatari, "PhaseTransition in a Computer network trafficmodel"

5 Misako Takayasu, Hideki Takayasu,Takamistu Sato, "Critical behaviour and 1/fnoise in information traffic"

6 Roger Guimera, Alex Arenas, Albert Diez-Guilera and Francesc Giralt,"Dynamicalproperties of model communicationnetworks"

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