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On the Self-Similar Nature of Ethernet Traffic (Extended Version

On the Self-Similar Nature of Ethernet Traf?c Will E.Leland?Murad S.Taqqu§

wel@https://www.doczj.com/doc/f213905565.html, murad@https://www.doczj.com/doc/f213905565.html,

Walter Willinger?Daniel V.Wilson?

walter@https://www.doczj.com/doc/f213905565.html, dvw@https://www.doczj.com/doc/f213905565.html,

?Bellcore§Department of Mathematics

445South Street Boston University

Morristown,NJ07960-6438Boston,MA02215

Abstract

We demonstrate that Ethernet local area network(LAN)traf?c is statistically self-similar,that none of the commonly used traf?c models is able to capture this fractal behavior,and that such behavior has serious implications for the design,control, and analysis of high-speed,cell-based networks.Intuitively,the critical characteristic of this self-similar traf?c is that there is no natural length of a"burst":at every time scale ranging from a few milliseconds to minutes and hours,similar-looking traf?c bursts are evident;we?nd that aggregating streams of such traf?c typically intensi?es the self-similarity("burstiness") instead of smoothing it.

Our conclusions are supported by a rigorous statistical analysis of hundreds of millions of high quality Ethernet traf?c measurements collected between1989and1992,coupled with a discussion of the underlying mathematical and statistical properties of self-similarity and their relationship with actual network behavior.We also consider some implications for congestion control in high-bandwidth networks and present traf?c models based on self-similar stochastic processes that are simple,accurate,and realistic for aggregate traf?c.

1.INTRODUCTION

The main objectives of this paper are(i)to establish in a statistically rigorous manner the self-similarity characteristic or, to use a more popular notion,the fractal nature of the high time-resolution Ethernet traf?c measurements of Leland and Wilson(1991),(ii)to illustrate some of the most striking differences between self-similar models and the standard models for packet traf?c currently considered in the literature,and(iii) to demonstrate some of the serious implications of self-similar network traf?c for the design,control,and performance analysis of high-speed,cell-based communications systems. Intuitively,self-similar phenomena display structural similarities across all(or at least a very wide range of)time scales.In the case of Ethernet LAN traf?c,self-similarity is manifested in the absence of a natural length of a"burst";at every time scale ranging from a few milliseconds to minutes and hours,bursts consist of bursty subperiods separated by less bursty subperiods. We also show that the degree of self-similarity(de?ned via the Hurst parameter)typically depends on the utilization level of the Ethernet and can be used to measure"burstiness"of LAN traf?c.The term"self-similar"was formally de?ned by Mandelbrot.For applications and references on the theory of self-similar processes,see Mandelbrot(1983)and the extensive bibliography by Taqqu(1985).For an early application of the self-similarity concept to communications systems,see the seminal paper by Mandelbrot(1965).

In this paper,we use very high quality,high time-resolution LAN traf?c data collected between August1989and February 1992on several Ethernet LANs at the Bellcore Morristown Research and Engineering Center(MRE).Leland and Wilson (1991)present a preliminary statistical analysis of this unique high-quality data and comment in detail on the presence of "burstiness"across an extremely wide range of time scales: traf?c"spikes"ride on longer-term"ripples",that in turn ride on still longer term"swells",etc.This self-similar or apparently fractal-like behavior of aggregate Ethernet LAN traf?c is very different both from conventional telephone traf?c and from currently considered formal models for packet traf?c(e.g.,pure Poisson or Poisson-related models such as Poisson-batch or Markov-Modulated Poisson processes(Heffes and Lucantoni (1986)),packet-train models(Jain and Routhier(1986)),and ?uid?ow models(Anick et al.(1982)),etc.).These differences require a new look at modeling the traf?c and performance of broadband networks.For example,our analysis of the Ethernet data shows that the generally accepted argument for the "Poisson-like"nature of aggregate traf?c,namely,that aggregate traf?c becomes smoother(less bursty)as the number of traf?c sources increases,has very little to do with reality.In fact,the burstiness(degree of self-similarity)of LAN traf?c typically intensi?es as the number of active traf?c sources increases, contrary to commonly held views.

Because of the growing market for LAN interconnection services,LAN traf?c is rapidly becoming one of the major potential traf?c contributors for high speed networks of the future such as B-ISDN.Another expected major contributor is variable-bit-rate(VBR)video service.Since VBR video traf?c has recently been shown to display the same self-similarity property as LAN traf?c(see Beran et al.(1992)),self-similar models provide simple,accurate,and realistic descriptions of traf?c scenarios to be encountered during high-bandwidth network deployment.

In light of this new understanding of the nature of broadband traf?c,we also address some of the serious implications of self-similar traf?c for issues related to the design,control,and performance analysis of high-speed,cell-based networks.As one speci?c example,we consider the area of congestion management and show that the nature of congestion produced

Presented at ACM SIGComm′93,San Francisco,CA,USA,September1993.

On the Self-Similar Nature of Ethernet Traf?c2

by self-similar traf?c differs drastically from that predicted by traf?c models currently considered in the literature and is far more complex than has been typically assumed in the past.As a result,proposed congestion control schemes that work well assuming conventional traf?c models typically perform less than satisfactorily in a self-similar traf?c environment.Finally,we mention two approaches for modeling self-similar network traf?c.

The paper is organized as follows.In Section2,we?rst brie?y describe the available Ethernet traf?c measurements and comment on the changes of the Ethernet environment during the measurement period from August1989to February1992.In Section3,we give the mathematical de?nition of self-similarity, identify classes of stochastic models which are capable of accurately describing the self-similar behavior of the traf?c measurements at hand,and present statistical techniques for dealing with self-similar data.Section4describes our statistical analysis of the Ethernet data,with emphasis on testing for self-similarity.We illustrate our statistical methods with a variety of different sets of Ethernet traf?c data,taken at different times during the measurement period,with quite different user populations and gross traf?c rates.We typically deal with time series with hundreds of thousands of observations and are, therefore,in the unique situation to rely on statistical results known to hold asymptotically in the number of observations. Finally,in Section5we discuss the signi?cance of self-similarity for traf?c engineering,and for operation,design,and control of B-ISDN environments.Among the implications discussed are(i)in?nite variance source models for individual Ethernet users,(ii)inadequacies of commonly used notions of "burstiness",and(iii)better understanding of the nature of congestion for broadband network traf?c.We conclude with a brief discussion of two different approaches for modeling self-similar network traf?c.

2.TRAFFIC MEASUREMENTS

The monitoring system used to collect the data for the present study is custom built,records all packets seen on the Ethernet under study with accurate timestamps,and will do so for very long runs without interruption.The monitoring system is designed so that traf?c analysts need make no a priori decisions as to what they are searching for when the data is taken other than how much of each packet is to be saved.The monitor was custom-built in1987/88and has been in use to the present day with one upgrade.The original version is described at length, including extensive testing of its capacity and accuracy,in Leland and Wilson(1991).There is only one major difference between the two versions:the updated version records timestamps accurate to20μs versus the original version’s accuracy of100μs.

2.1BELLCORE’S NETWORK ENVIRONMENT

The MRE environment is probably typical of a research or software development environment where workstations are the primary machines on people’s desks.Table1gives a summary description of the traf?c data analyzed later in the paper.We consider4sets of traf?c measurements,each one representing between20and40consecutive hours of Ethernet traf?c and each one consisting of tens of millions of Ethernet packets.The data were collected on different intracompany LAN networks at different periods in time over the course of approximately4 years(August’89,October’89,January’90,and February’92). The traf?c was mostly from services that used the Internet Protocol(IP)suite for such capabilities as remote login or electronic mail,and the Network File System?(NFS)protocol for?le service from servers to workstations.While it is not our intent to provide here a detailed description of the particular MRE network segments under study,some words about the network environment from which each data set was taken are appropriate.

The?rst two data sets were collected from a typical workgroup or laboratory network which was isolated from the rest of the Bellcore network by a router.At the time of collection of the ?rst(August’89)data set,the laboratory consisted of about140 people,most of whom had diskless Sun-3?-class workstations on their desks.The network in the laboratory consisted of two cable segments separated by a bridge,implying that not all traf?c within the laboratory could be seen by the monitor.The hosts on this network consisted of workstations,their?le servers,and a pair of DEC8650?-class minicomputers.Only a small number of hosts were reduced instruction set(RISC) based.However,by the time the second data set(October’89) was collected,a massive upgrade of the Sun-3class machines to RISC-based SPARCstation1?and DEC3100-class machines had taken place on this network,along with a small increase in the number of hosts(from about120who spoke up during the ?rst collection to about140in the second set).This extensive upgrade is the reason for the large increase in traf?c volume seen between the?rst two data sets.Note,for example,that the "busy hour"from this October’89data set is indeed busy: 30.7%utilization as compared to15.1%during the August’89 busy hour;similar increases can also be observed for the low and normal hours.Less than5%of the total traf?c observed in these two data sets was from conversations with hosts in the rest of Bellcore or the outside world;during the busy periods this ?gure was more typically1-2%of the total traf?c observed. The third data set,taken in January1990(row3in Table1), came from an Ethernet cable that linked the two wings of the MRE facility that were occupied by a second laboratory.At the time the data set was collected,this second laboratory comprised about160people engaged in work similar to the?rst laboratory. This particular Ethernet segment was unique in that it was also the segment serving Bellcore’s link to the outside Internet world.Thus the traf?c on this cable was from several sources: (i)two very active?le servers(Sun4/490?’s)directly connected to the segment;(ii)traf?c(?le service and remote login)between the two wings of this laboratory,(iii)traf?c between the laboratory and the rest of Bellcore,and(iv)traf?c between Bellcore as a whole and the larger Internet world.This Ethernet segment was speci?cally monitored to capture this last type of traf?c,which we term external traf?c.We studied both the aggregate and external traf?c from this and the last data set, but as we shall see in Section4the external traf?c was no different from internal traf?c as far as our analysis is concerned. This segment was separated from both the Bellcore internet and the two wings of the laboratory by bridges,and from the outside world by a vendor-controlled router programmed to pass anything with a Bellcore address as source or destination.In contrast to the two earlier data sets,over1200hosts spoke up during the40hour monitoring period on this segment.

The last data set,taken in February1992(row4in Table1)was taken from the Ethernet"backbone"in the MRE facility. Because of rising concern about network security,Bellcore’s connection to the Internet world was moved to a Bellcore-controlled"?rewall"security router directly connected to the building backbone.Many major workgroups and laboratories also inserted routers between their networks and the backbone; previously they had been either directly connected or bridged. The traf?c on this backbone cable therefore consisted of(i) traf?c between workgroups and laboratories within the MRE facility,including traf?c between the two laboratories

Presented at ACM SIGComm′93,San Francisco,CA,USA,September1993.

On the Self-Similar Nature of Ethernet Traf?c3

Traces of Ethernet Traf?c Measurements

Measurement Period data set total number total number Ethernet

of bytes of packets utilization

AUGUST1989total(27.45hours)11,448,753,13427,901,9849.3%

Start of trace:low hour AUG89.LB224,315,439 5.0%

Aug.29,11:25am(6:25am-7:25am)AUG89.LP652,909

End of trace:normal hour AUG89.MB380,889,4048.5%

Aug.30,3:10pm(2:25pm-3:25pm)AUG89.MP968,631

busy hour AUG89.HB677,715,38115.1%

(4:25pm-5:25pm)AUG89.HP1,404,444

OCTOBER1989total(20.86hours)14,774,694,23627,915,37615.7%

Start of trace:low hour OCT89.LB468,355,00610.4%

Oct.5,11:00am(2:00am-3:00am)OCT89.LP978,911

End of trace:normal hour OCT89.MB827,287,17418.4%

Oct.6,7:51am(5:00pm-6:00pm)OCT89.MP1,359,656

busy hour OCT89.HB1,382,483,55130.7%

(11:00am-12:00am)OCT89.HP2,141,245

JANUARY1990total(40.16hours)7,122,417,58927,954,961 3.9%

Start of trace:low hour(Jan.11,JAN90.LB87,299,639 1.9%

Jan.10,6:07am8:32pm-9:32pm)JAN90.LP310,038

End of trace:normal hour(Jan.10,JAN90.MB182,636,845 4.1%

Jan.11,10:17pm9:32am-10:32am)JAN90.MP643,451

busy hour(Jan.11,JAN90.HB711,529,37015.8%

10:32am-11:32am)JAN90.HP1,391,718

FEBRUARY1992total(47.91hours)6,585,355,73127,674,814 3.1%

Start of trace:low hour(Feb.20,FEB92.LB56,811,435 1.3%

Feb.18,5:22am1:21am-2:21am)FEB92.LP231,823

End of trace:normal hour(Feb.18,FEB92.MB154,626,159 3.4%

Feb.20,5:16am8:21pm-9:21pm)FEB92.MP524,458

busy hour(Feb.18,FEB92.HB225,066,741 5.0%

11:21am-12:21am)FEB92.HP947,662

Table1.Qualitative description of the sets of Ethernet traf?c measurements used in the analysis in Section4.

previously discussed,(ii)traf?c from some individual hosts still directly connected to the backbone,(iii)traf?c from MRE to other Bellcore locations via a mesh of bridged interlocation links,and?nally(iv)external traf?c from Bellcore to the outside Internet world.Because there is very little workstation to ?leserver traf?c on this cable,the overall load on this cable is the lowest of any of the three data collection points considered. The most radical difference between this data set and the others is that the traf?c is primarily router to router rather than host to host.About600hosts spoke up during this measurement period (down from about1200active hosts during the January’90 measurement period),and the?ve most active hosts were routers.The updated version of the monitor was used to collect this data set.Overall,the4data sets cover a wide range of network utilizations and host populations over a4year period.

3.SELF-SIMILAR STOCHASTIC PROCESSES

The presentation below of the mathematical and statistical properties of self-similar processes closely follows Cox(1984) and Beran et al.(1992).3.1SELF-SIMILARITY BY PICTURE

For27consecutive hours of monitored Ethernet traf?c from the August1989measurements(?rst row in Table1),Figure1 depicts a sequence of simple plots of the packet counts(i.e., number of packets per time unit)for5different choices of time units.Starting with a time unit of100seconds(a),each subsequent plot is obtained from the previous one by increasing the time resolution by a factor of10and by concentrating on a randomly chosen subinterval(as indicated by the darker shade). Recall that the time unit corresponding to the?nest time scale is 10milliseconds(e).Observe that all plots look intuitively very "similar"to one another(in a distributional sense)and are distinctively different from white noise(i.e.,an independent and identically distributed sequence of random variables).Notice also the scaling property(y-axis)and the absence of a natural length of a"burst":at every time scale ranging from milliseconds to minutes and hours,bursts consist of bursty subperiods separated by less bursty subperiods.This scale-invariant or"self-similar"feature of Ethernet traf?c is drastically different from both conventional telephone traf?c and

Presented at ACM SIGComm′93,San Francisco,CA,USA,September1993.

On the Self-Similar Nature of Ethernet Traf?c 4

100

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Figure 1(a)—(e).Pictorial "proof"of self-similarity:Ethernet traf?c (packets per time unit for the August ’89trace)on 5different time scales.(Different gray levels are used to identify the same segments of traf?c on the different time scales.)

from stochastic models for packet traf?c currently considered in the literature.The latter typically produce plots of packet counts which are indistinguishable from white noise after aggregating over a few hundred milliseconds.This pictorial "proof"of the

self-similar nature of Ethernet packet traf?c suggests that Ethernet traf?c on one time scale is statistically identical (at least with respect to its second-order statistical properties)to Ethernet traf?c on a different time scale and,thus,motivates the use of self-similar stochastic processes for traf?c modeling purposes.

3.2THE MATHEMATICS OF SELF-SIMILARITY The notion of self-similarity is not merely an intuitive description,but a precise concept captured by the following rigorous mathematical de?nition.Let X =(X t :t =0,1,2,...)be a covariance stationary (sometimes called wide-sense stationary )stochastic process;that is,a process with constant mean μ=E [X t ],?nite variance σ2=E [(X t ?μ)2],and an autocorrelation function r (k )=E [(X t ?μ)(X t +k ?μ)]

/E [(X t ?μ)2

](k =0,1,2,...)that depends only on k .In particular,we assume that X has an autocorrelation function of the form

r (k )～a 1k ?β,

as k →∞,(3.2.1)

where 0<β<1(here and below,a 1,a 2,...denote ?nite positive constants).For each m =1,2,3,...,let X (m )=(X k (m )

:k =1,2,3,...)denote a new time series obtained by averaging the original series X over non-overlapping blocks of size m .That is,for each m =1,2,3,...,X (m )is given by X k (m )=1/m (X km ?m +1+...+X km ),(k ≥1).Note that for each m ,the aggregated time series X (m )de?nes a covariance stationary process;let r (m )denote the corresponding autocorrelation function.

The process X is called exactly (second-order)self-similar with self-similarity parameter H =1?β/2if the corresponding aggregated processes X (m )have the same correlation structure as X ,i.e.,r (m )(k )=r (k ),for all m =1,2,...(k =1,2,3,...).In other words,X is exactly self-similar if the aggregated processes X (m )are indistinguishable from X —at least with respect to their second order statistical properties.An example of an exactly self-similar process with self-similarity parameter H is fractional Gaussian noise (FGN)with parameter 1/2

Intuitively,the most striking feature of (exactly or asymptotically)self-similar processes is that their aggregated processes X (m )possess a nondegenerate correlation structure as m →∞.This behavior is precisely the intuition illustrated with the sequence of plots in Figure 1;if the original time series X represents the number of Ethernet packets per 10milliseconds (plot (e)),then plots (a)to (d)depict segments of the aggregated time series X (10000),X (1000),X (100),and X (10),respectively.All of the plots look "similar",suggesting a nearly identical autocorrelation function for all of the aggregated processes.Mathematically,self-similarity manifests itself in a number of equivalent ways (see Cox (1984)):(i)the variance of the sample mean decreases more slowly than the reciprocal of the sample size (slowly decaying variances ),i.e.,var (X (m ))～a 2m ?β,as m →∞,with 0<β<1;(ii)the autocorrelations decay hyperbolically rather than exponentially fast,implying a non-

Presented at ACM SIGComm ′93,San Francisco,CA,USA,September 1993.

On the Self-Similar Nature of Ethernet Traf?c 5

summable autocorrelation function Σk r (k )=∞(long-range dependence ),i.e.,r (k )satis?es relation (3.2.1);and (iii)the spectral density f (.)obeys a power-law behavior near the origin (1/f-noise ),i.e.,f (λ)～a 3λ?γ,as λ→0,with 0<γ<1and γ=1?β.

The existence of a nondegenerate correlation structure for the aggregated processes X (m )as m →∞is in stark contrast to typical packet traf?c models currently considered in the literature,all of which have the property that their aggregated processes X (m )tend to second order pure noise,i.e.,r (m )(k )→0,as m →∞(k =1,2,...).Equivalently (see Cox(1984)),they can be characterized by (i)a variance of the sample mean that decreases like the reciprocal of the sample mean,(ii)an autocorrelation function that decreases exponentially fast,implying a summable autocorrelation function Σk r (k )<∞(short-range dependence ),or (iii)a spectral density that is bounded at the origin.

Historically,the importance of self-similar processes lies in the fact that they provide an elegant explanation and interpretation of an empirical law that is commonly referred to as Hurst’s law or the Hurst effect .Brie?y,for a given set of observations (X k :k =1,2,...,n )with sample mean X (n )and sample variance S 2(n ),the rescaled adjusted range or the R/S statistic is given by R (n )/S (n )=1/S (n )[max(0,W 1,W 2,...,W n )?min(0,W 1,W 2,...,W n )],with W k =(X 1+X 2+...+X k )?kX

(n ),k =1,2,...,n .Hurst (1955)found that many naturally occurring time series appear to be well represented by the relation E [R (n )/S (n )]～a 4n H ,as n →∞,with Hurst parameter H "typically"about 0.73.On the other hand,if the observations X k come from a short-range dependent model,then Mandelbrot and Van Ness (1968)showed that

E [R (n )/S (n )]～a 5n 0.5

,as n →∞.This discrepancy is generally referred to as the Hurst effect or Hurst phenomenon .Finally,for an attempt to explain self-similarity in terms of representing some underlying physical process,we refer to a construction originally introduced by Mandelbrot (1969)(see also Taqqu and Levy (1986))of self-similar processes based on aggregating many simple renewal reward processes exhibiting inter-renewal times with in?nite variances (i.e.,"heavy-tails").That is,the distribution of the inter-renewal times U satis?es P [U ≥u ]～a 6u ?α,as u →∞,1<α<2(e.g.,stable (Pareto)distributions with parameter 1<α<2).Producing self-similarity by aggregating more and more i.i.d.copies of elementary renewal reward processes relies crucially on this "heavy-tail property"of the inter-renewal times and provides an intuitive explanation for the occurrence of self-similarity in high-speed network traf?c (see Section 5).3.3THE STATISTICS OF SELF-SIMILARITY

Since slowly decaying variances,long-range dependence,and a spectral density obeying a power-law behavior are different manifestations of one and the same property of the underlying covariance stationary process X ,namely that X is (asymptotically or exactly)self-similar,we can approach the problem of testing for and estimating the degree of self-similarity from three different angles:(1)time-domain analysis based on the R/S-statistic,(2)analysis of the variances of the aggregated processes X (m ),and (3)periodogram-based analysis in the frequency-domain.This subsection provides a brief discussion of the graphical R/S analysis and brie?y mentions methods (2)and (3).We will illustrate the use of these methods in our analysis of the Ethernet data in Section 4below.

The objective of the R/S analysis of an empirical record is to infer the degree of self-similarity H (Hurst parameter)in relation

(3.1.6)for the self-similar process that presumably generated the record under consideration.In practice,R/S analysis is based on a heuristic graphical approach (originally described in detail in Mandelbrot and Wallis (1969))that tries to exploit as fully as possible the information in a given record.The following graphical method has been used extensively in the past.Given a sample of N observations (X k :k =1,2,3,...,N ),one subdivides the whole sample into K non-overlapping blocks and computes the rescaled adjusted range R (t i ,n )/S (t i ,n )for each of the new "starting points"t 1=1,t 2=N /K +1,t 3=2N /K +1,...which satisfy (t i ?1)+n ≤N .Here,the R/S-statistic R (t i ,n )/S (t i ,n )is de?ned as above with W k replaced by W t i +k ?W t i and S 2(t i ,n )is the sample variance of X t i +1,X t i +2,...,X t i +n .Thus,for a given value ("lag")of n ,one obtains many samples of R/S,as many as K for small n and as few as one when n is close to the total sample size N .Next,one takes logarithmically spaced values of n ,starting with n ～～10.Plotting log (R (t i ,n )/S (t i ,n ))versus log (n )results in the rescaled adjusted range plot (also called the pox diagram of R/S ).When the parameter H is well de?ned,a typical rescaled adjusted range plot starts with a transient zone representing the nature of short-range dependence in the sample,but eventually settles down and ?uctuates in a straight "street"of a certain slope.Graphical R/S analysis is used to determine whether such asymptotic behavior appears supported by the data.In the

af?rmative,an estimate H

?of the self-similarity parameter H is given by the street’s asymptotic slope (typically obtained by a simple least squares ?t)which can take any value between 1/2and 1.For practical purposes,the most useful and attractive feature of the R/S analysis is its relative robustness against changes of the marginal distribution.This feature allows for practically separate investigations of the self-similarity property of a given empirical record and of its distributional characteristics.

We have observed that for self-similar processes,the variances of the aggregated processes X (m )(m =1,2,3,...)decrease linearly (for large m )in log-log plots against m with slopes arbitrarily ?atter than ?1.The so-called variance-time plots are obtained by plotting log(var(X (m )))against log(m )("time")and by ?tting a simple least squares line through the resulting points in the plane,ignoring the small values for m .Values of the

estimate β

?of the asymptotic slope between ?1and 0suggest self-similarity,and an estimate for the degree of self-similarity

is given by H

?=1?β?/2.The absence of any limit law results for the statistics

corresponding to the R/S analysis or the variance-time plot makes them inadequate for a more re?ned data analysis (e.g.,requiring con?dence intervals for the degree of self-similarity H ,model selection criteria,and goodness of ?t tests).In contrast,a more re?ned data analysis is possible for maximum likelihood type estimates (MLE)and related methods based on the periodogram and its distributional properties.In particular,for Gaussian processes,Whittle’s approximate MLE has been studied extensively and has been shown to have desirable statistical properties (Fox and Taqqu (1986),and Dahlhaus (1989)).Combined,Whittle’s approximate MLE approach and the aggregation method discussed earlier give rise to the following operational procedure for obtaining con?dence intervals for the self-similarity parameter H .For a given time series,consider the corresponding aggregated processes X (m )with m =100,200,300,...,where the largest m -value is chosen such that the sample size of the corresponding series X (m )is not less than about 100.For each of the aggregated series,estimate the self-similarity parameter H via the Whittle estimate.This procedure results in estimates H ?(m )of H and

Presented at ACM SIGComm ′93,San Francisco,CA,USA,September 1993.

On the Self-Similar Nature of Ethernet Traf?c6 corresponding,say,95%-con?dence intervals of the form

H?(m)±1.96σ?H,whereσ?H2is given by a known central limit

theorem result(see Dahlhaus(1989)).Finally,we plot the

estimates H?(m)of H together with their95%-con?dence

intervals versus m.Such plots will typically vary widely for

small aggregation levels,but will stabilize after a while and

?uctuate around a constant value,our?nal estimate of the self-

similarity parameter H.

4.THE SELF-SIMILAR NATURE OF ETHERNET

TRAFFIC

In this section,we establish in a statistically rigorous manner

(using the graphical and statistical tools described in the

previous section)the self-similar nature of(internal)Ethernet

traf?c and of some of its major components(e.g.,external traf?c

and external TCP traf?c).For each of the4measurement

periods described in Table1,we identi?ed what are considered

"typical"low-,medium-,and high-activity hours.With the

resulting data sets,we are able to investigate features of the

observed traf?c(e.g.,self-similarity)that persist across the

network as well as across time,irrespective of the utilization

level of the Ethernet.

4.1ETHERNET TRAFFIC OVER A1-DAY PERIOD

We?rst consider the August’89snapshot of Ethernet traf?c

(row1in Table1)and analyze the3subsets AUG89.LB,

AUG89.MB,and AUG89.HB.Each sequence contains360000

observations,and each observation represents the number of

bytes sent over the Ethernet every10milliseconds.

Figure2depicts the pox plot of R/S(a),the variance-time curve

(b),and the periodogram plot(c)corresponding to the sequence

AUG89.MB.The pox plot of R/S(Figure2(a))show an

asymptotic slope that is distinctly different from0.5(lower

dotted line)and1.0(upper dotted line)and is easily estimated

(using the points)to be about0.79.The variance-time curve

(Figure2(b)),which has been normalized by the corresponding

sample variance,shows an asymptotic slope that is clearly

different from-1(dotted line)and is easily estimated to be about

-0.40,resulting in a practically identical estimate of the Hurst

parameter H of about0.80.Finally,looking at the periodogram

plot corresponding to the time series AUG89.MB,we observe

that although there are some pronounced peaks in the high-

frequency domain of the periodogram,the low-frequency part is

characteristic for a power-law behavior of the spectral density

around zero.In fact,by?tting a simple least-squares line using

only the lowest10%of all frequencies,we obtain a slope estimateγ?～～0.64which results in a Hurst parameter estimate of about0.82.Thus,together the3graphical methods suggest that

the sequence AUG89.MB is self-similar with self-similarity

parameter H～～0.80.Moreover,Figure2(d)indicates that the normal hour Ethernet traf?c of the August’89data is(exactly)

self-similar rather than asymptotically self-similar(see Section

3.2).Figure2(d)shows the estimates of the Hurst parameter H

for selected aggregated time series derived from the sequence

AUG89.MB,as a function of the aggregation level m.For

aggregation levels m=1,5,10,50,100,500,1000,we plot the Hurst parameter estimate H?(m)(based on the pox plots of R/S("?"),the variance-time curves(" "),and the periodogram plots(" "))for the aggregated time series X(m)against the logarithm of the aggregation level m.Notice that the estimates are extremely stable and practically constant over the depicted range of aggregation levels1≤m≤1000.Thus,in terms of their second-order statistical properties,the aggregated series X(m)(m≥1)can be considered to be identical and produce, therefore,realizations that have similar overall structure and

(a)

log10(d)

(

)

012345 0

(b)

log10(m)

(

)

012345 0

....

...

....

...

....

.....

...

....

...

.....

...

....

...

(c)

log10(frequency)

(

)

-4-3-2-10 0

0123

0.5

0.6

0.7

0.8

0.9

1.0

(d)

log10(m)

Figure2(a)—(d).Graphical methods for checking

for self-similarity of the sequence AUG89.MB.((a)

pox plot of R/S,(b)variance-time plot,(c)

periodogram plot,and(d)Hurst parameter estimates

as a function of the aggregation level m(?is method

(a), is method(b),and is method(c).)

look very much alike.

In addition to the sequence AUG89.MB,we also analyzed the sequences AUG89.LB and AUG89.HB.While both series behave very much like the sequence AUG89.MB,the resulting Hurst parameter estimates H?differ slightly;H?～～0.75for AUG89.LB,and H?～～0.85for AUG89.HB.This difference suggests that although Ethernet traf?c over approximately a24-

Presented at ACM SIGComm′93,San Francisco,CA,USA,September1993.

On the Self-Similar Nature of Ethernet Traf?c7 hour period is self-similar,the degree of self-similarity depends

on the utilization level of the Ethernet and increases as the

utilization increases.Finally,we also analyzed the sequences

AUG89.LP,AUG89.MP,and AUG89.HP,i.e.,the time series

representing the total number of Ethernet packets rather than the

total number of bytes in every10millisecond interval.Not

surprisingly,the packet traf?c is also self-similar,but with

slightly larger H-values than the corresponding bytes/time unit

data.For a more detailed analysis of Ethernet traf?c at the

packet level,see Section4.2below.

4.2ETHERNET TRAFFIC OVER A4-YEAR PERIOD

As discussed in Section2,Ethernet LANs are generally known to change signi?cantly during the course of a few years.By analyzing additional data sets(see Table1),similar to the August’89ones but taken at different points in time and at different physical locations within the network,we show below that Ethernet traf?c is self-similar,irrespective of when and where the data were collected in the Bellcore Morristown network during the4-year period August’89—February’92.

In contrast to Section4.1,our analysis below results in point estimates of the self-similarity parameter H together with their respective95%-con?dence intervals.As discussed in Section

3.3,such a re?ned analysis resulting in con?dence intervals for

H is possible if maximum likelihood type estimates(MLE)or related estimates based on the periodogram are used instead of the mostly heuristic graphical estimation methods illustrated in the previous section.Plots(a)—(d)of Figure3show the result of the MLE-based estimation method when combined with the method of aggregation.For each of the4sets of traf?c measurements described in Table1,we use the time series representing the packet counts during normal traf?c conditions (i.e.,AUG89.MP in(a),OCT89.MP in(b),JAN90.MP in(c), and FEB92.MP in(d)),and consider the corresponding aggregated time series X(m)with m=100,200,300, (1900)

2000(representing the packet counts per1,2,...,20seconds, respectively).We plot the Hurst parameter estimates H?(m)of H obtained from the aggregated series X(m),together with their 95%-con?dence intervals,against the aggregation level m. Figure3shows that for the packet counts during normal traf?c loads(irrespective of the measurement period),the values of H?(m)are quite stable and?uctuate only slightly in the0.85to 0.95range throughout the aggregation levels considered.The same holds for the95%-con?dence interval bands,indicating strong statistical evidence for self-similarity of these4time series with degrees of self-similarity ranging from about0.85to about0.95.The relatively stable behavior of the Hurst parameter estimates H?(m)for the different aggregation levels m also con?rms our earlier?nding that Ethernet traf?c during normal traf?c hours can be considered to be exactly self-similar rather than asymptotically self-similar.Plots(a)—(d)of Figure 3suggest that this property holds irrespective of when and where the Ethernet was monitored.For exactly self-similar time series,determining a single point estimate for H and the corresponding95%-con?dence interval is straightforward and can be done by visual inspection of plots such as the ones in Figure3(see below).Notice that in each of the four plots in Figure3,we added two lines corresponding to the Hurst parameter estimates obtained from the pox diagrams of R/S and the variance-time plots,respectively.Typically,these lines fall well within the95%-con?dence interval bands which shows that for these long time series considered here,graphical estimation methods based on R/S or variance-time plots can be expected to be very accurate.

In addition to the4normal hour packet data time series,we also applied the combined MLE/aggregation method to the other

(a)

Aggregation Level m

500100015002000 0

(b)

Aggregation Level m

500100015002000 0

(c)

Aggregation Level m

500100015002000 0

(d)

Aggregation Level m

500100015002000 0

Figure3(a)—(d).Periodogram-based MLE estimate

H?(m)of H(solid line)and95%-con?dence intervals

(dotted lines),as a function of the aggregation level m,

for sequences AUG89.MP(a),OCT89.MP(b),

JAN90.MP(c),and FEB92.MP(d).For example,plot

(a)shows that m～～300is an appropriate aggregation

level for sequence AUG89.MP,yielding a point

estimate H?=H?(300)=0.90and a95%-con?dence

interval[0.85,0.95].For comparison,we also added to

each plot the estimate of H based on the variance-time

plot(?.?.?)and the R/S-based estimate of H

(???).

traf?c data sets described in Table1.Figure4(a)depicts all Hurst parameter estimates(together with the95%-con?dence interval corresponding to the choice of m discussed earlier)for each of the12packet data time series,while Figure4(b) summarizes the same information for the time series

Presented at ACM SIGComm′93,San Francisco,CA,USA,September1993.

On the Self-Similar Nature of Ethernet Traf?c 8

(a)

Measurement Period

H u r s t P a r a m e t e r E s t i m a t e s a n d 95%-C I

AUG89OCT89JAN90FEB92

0.5

0.6 0.7 0.8 0.9

1.0 (b)

Measurement Period

H u r s t P a r a m e t e r E s t i m a t e s a n d 95%-C I

AUG89OCT89JAN90FEB92

0.5

0.6 0.7 0.8 0.9

1.0 Figure 4(a)—(b).Summary plot of estimates of the Hurst parameter H for all data sets (representing the number of packets (a)and the number of bytes (b))in Table 1.( denotes the periodogram-based MLE estimate and corresponding 95%-con?dence interval, the point estimate of H based on the asymptotic slope of the variance-time plot,and ?the point estimate of H based on the asymptotic slope of the pox plot of R/S.)

representing the number of bytes per 10milliseconds during a typical low,normal,and busy hour for each of the four measurement periods.We also included in these summary plots the Hurst parameter estimates obtained via the R/S analysis ("?")and variance-time plots (" ")in order to indicate the accuracy of these "graphical"estimators when compared to the statistically more rigorous Whittle estimator (" ").Concentrating ?rst on the packet data,i.e.,Figure 4(a),we see that despite the transition from mostly host-to-host workgroup traf?c during the August ’89and October ’89measurement periods,to a mixture of host-to-host and router-to-router traf?c during the January ’90measurement period,to the predominantly router-to-router traf?c of the February ’92data set,the Hurst parameter corresponding to the typical normal and busy hours,respectively,are comparable,with slightly higher H -values for the busy hours than for the normal traf?c hours.This latter observation might be surprising in light of conventional traf?c modeling where it is commonly assumed that as the number of sources (Ethernet users)increases,the resulting aggregate traf?c becomes smoother.In contrast to this generally accepted argument for the "Poisson-like"nature of

aggregate traf?c,our analysis of the Ethernet data shows that,in fact,the aggregate traf?c tends to become less smooth (or,more bursty)as the number of active sources increases (see also our discussion in Section 5).In fact,while there were about 120hosts that spoke up during the August ’89or October ’89busy hour,we heard from about 1200hosts during the January ’90high traf?c hour;the comparable number of active hosts during the February ’92busy hour was around 600.The major difference between the early (pre-1990)measurements and the the later ones (post-1990,i.e.,January ’90and February ’92)can be seen during the low traf?c hours.Intuitively,low period router-to-router traf?c consists mostly of machine-generated packets which tend to form a much smoother arrival process than low period host-to-host traf?c,which is typically produced by a smaller than average number of actual Ethernet users,i.e.,researchers working late hours.

Next,turning our attention to Figure 4(b),i.e.,the Hurst parameter estimates for the bit rates,we observe that as in the case of the packet data,the degree of self-similarity H increases as we move from low to normal to high traf?c hours.Moreover,while there is practically no difference between the two post-1990data sets,the two pre-1990sets clearly differ from one another but follow a similar pattern as the post-1990ones.The difference between the August ’89and October ’89measurements can be explained by the transition from diskless to "dataless"workstations (workstations with the operating system on a local disk but all user ?les on a remote ?leserver)that occurred during the latter part of 1989(see Section 2).Except during the low hours,the increased computing power of many of the Ethernet hosts causes the Hurst parameter to increase and gives rise to a bit rate that nearly matches the self-similar feature of the corresponding packet process.Also note that the 95%-con?dence intervals corresponding to the Hurst parameter estimates for the low traf?c hours are typically wider than those corresponding to the estimates of H for the normal and high traf?c hours.This widening indicates that Ethernet traf?c during low traf?c periods is asymptotically self-similar rather than exactly self-similar.

The Ethernet traf?c analyzed in Section 4.2is called internal traf?c and consists of all packets on a LAN.In addition to this internal traf?c,we also analyzed external or remote Ethernet traf?c,and external TCP traf?c,the portion of external traf?c using the Transmission Control Protocol (TCP)and IP.Repeating the same laborious statistical analysis for these important components of internal Ethernet traf?c,we ?nd that in terms of its self-similar nature,external traf?c and external TCP traf?c do not differ from the internal traf?c studied earlier,and that our ?ndings for the internal traf?c apply directly.5.SIGNIFICANCE OF SELF-SIMILARITY FOR TRAFFIC ENGINEERING

Our measured data show dramatically different statistical properties than those predicted by the stochastic models currently considered in the literature.Almost all these models are characterized by an exponentially decaying autocorrelation function.As a result,they give rise to a Hurst parameter

estimate of H

?=.50,producing variance-time curves,R/S plots,and frequency domain behavior strongly disagreeing with the self-similar behavior of actual traf?c (see Section 4).In terms of the aggregation procedure described above,the theoretical models have the property that typically,after aggregating over non-overlapping blocks of about 10-100observations,the aggregated series become indistinguishable from second-order pure noise.The fact that one can distinguish clearly—with respect to second-order statistical properties—between the

Presented at ACM SIGComm ′93,San Francisco,CA,USA,September 1993.

On the Self-Similar Nature of Ethernet Traf?c9

existing models for Ethernet traf?c and our measured data is surprising and clearly questions some of the modeling assumptions that have been made in the past.Potential traf?c engineering implications of this distinction are currently under intense scrutiny.In this section,we emphasize three direct implications of the self-similar nature of packet traf?c for traf?c engineering purposes:modeling individual Ethernet sources, inadequacy of conventional notions of"burstiness",and effects on congestion management for packet networks.We conclude with some guidelines toward modeling self-similar traf?c and suggest some open problems.

5.1ON THE NATURE OF TRAFFIC GENERATED BY

AN INDIVIDUAL ETHERNET USER

In Section4,we showed that irrespective of when and where the Ethernet measurements were collected,the traf?c is self-similar, with different degrees of self-similarity depending on the load on the network.We did so without?rst studying and modeling the behavior of individual Ethernet users(sources).Although historically,accurate source modeling has been considered an absolute necessity for successful modeling of aggregate traf?c, we show here that in the case of self-similar packet traf?c, knowledge of fundamental characteristics of the aggregate traf?c can provide new insight into the nature of traf?c generated by an individual user.To this end,we recall Mandelbrot’s construction of self-similar processes(see Mandelbrot(1969))by aggregating many simple renewal reward processes,which provides a physical explanation for the visually obvious(see Figure1)and statistically signi?cant(see Figure4) self-similarity property of Ethernet LAN traf?c in terms of the behavior of individual Ethernet users.In fact,the renewal rewards for one such process represent the amount of traf?c(in bytes or packets)generated by a single user during successive time intervals whose lengths obey the"heavy-tail"property discussed in Section3.2.If bytes are the preferred units,the renewal reward process source model resembles the popular class of?uid models(see Anick et al.(1982)).On the other hand,if we think of packets as the underlying unit of information,the renewal reward process is basically a packet train model in the sense of Jain and Routhier(1986).For simplicity,one can restrict the"rewards"to the values0and1, where0means that the corresponding source is inactive and1 means that it is active(and generating traf?c at a?xed rate). Note that the crucial property that distinguishes this model from ?uid models and packet train models is that the lengths of the inactive/active periods are heavy-tailed in the sense of Section 3.2.Intuitively,this property means that there is no characteristic length of a busy period or packet train:individual inactive/active periods can be arbitrarily long with signi?cant probability(for evidence in support of this"heavy-tail behavior" in related traf?c studies,see the recent work by Meier-Hellstern et al.(1991)).Mandelbrot(1969)and Taqqu and Levy(1986) showed that aggregating the traf?c of many such source models produces a self-similar superposition process with self-similarity parameter H=(3?α)/2,whereαis the parameter that characterizes the"thickness"of the tail of the distribution.

5.2SELF-SIMILARITY AND SOME COMMONLY USED

NOTIONS OF BURSTINESS

Section4has shown that data sets with higher self-similarity H satisfy intuitive notions of higher"burstiness".Similarly,the greater the variability(smallerα)of the inactive/active periods in our individual source model,the higher the H and the burstier the aggregate traf?c.The fact that the self-similarity parameter H captures the intuitive notion of burstiness in a mathematically rigorous manner can be contrasted with the behavior of many commonly used measures of"burstiness",including the index of dispersion,the peak-to-mean ratio,and the coef?cient of variation.The index of dispersion(for counts)has recently attracted considerable attention(e.g.,Heffes and Lucantoni (1986))as a measure for capturing the variability of traf?c over different time scales.For a given time interval of length L,the index of dispersion for counts(IDC)is given by the variance of the number of arrivals during the interval of length L divided by the expected value of that same quantity.

0.010.10 1.0010.0

500

(a)

L (in Seconds)

0.010.10 1.0010.0

500

(b)

L (in Seconds)

Figure5(a)—(b).Index of dispersion for counts

(IDC)as a function of the length L of the time interval

over which IDC is calculated,for the January’90busy

hour(a)and the February’92busy hour(b).The solid

lines are the IDC curves for the sequences JAN90.HP

and FEB92.HP(internal traf?c)and the dashed lines

depict the IDC curves for the corresponding hours of

external traf?c.The dotted lines are the IDC curves

predicted by a self-similar model?tted to the time

series JAN90.HP and FEB92.HP,respectively.Note

that the asymptotic slopes of the solid lines agree with

the slopes of the dotted lines.

the IDC increases monotonically throughout a time span that covers nearly5orders of magnitude(Figure5),in stark contrast to conventional traf?c models where the IDC is either constant or converges to a?xed value rapidly.Simple self-similar traf?c models with parameter H are easily shown to produce a monotonically increasing IDC proportional to L2H?1,exactly matching the straight-line appearance of the log-log plot of the actual data.For self-similar traf?c,both the peak-to-mean ratio and the coef?cient of variation are unsatisfactory measures: essentially any peak-to-mean ratio is possible,depending on the length of the interval over which the peak is determined,and essentially any ratio of the standard deviation of interarrival times to the expected value is possible,depending on the sample size.

5.3CONGESTION MANAGEMENT IN THE PRESENCE

OF SELF-SIMILAR TRAFFIC

In order to illustrate the effect of self-similar traf?c on basic architectural issues concerning high-speed,high-bandwidth communications systems of the future,we revisit some aspects of congestion management?rst explored using simulation by Fowler and Leland(1991)and Leland and Wilson(1991).

Presented at ACM SIGComm′93,San Francisco,CA,USA,September1993.

On the Self-Similar Nature of Ethernet Traf?c10

Because of the statistical groundwork established in Section4, their conclusions about the nature of congestion and the task of congestion management for B-ISDN provide convincing evidence for the signi?cance of self-similar network traf?c for engineering future integrated high-speed networks.In light of the same self-similar behavior of VBR video traf?c(see Beran et al.(1992)),their conclusions are likely to also apply to more heterogeneous B-ISDN traf?c.

Leland and Wilson(1991)consider the access control scheme proposed for Switched Multimegabit Data Service(SMDS)on public B-ISDN.SMDS is a connectionless data service where packets arriving from a LAN are buffered at the interface and delivered to the cell-based network at some maximum rate, subject to traf?c shaping intended to reduce the burstiness of the submitted LAN traf?c.Simple conventional models based on the observed external LAN traf?c suggest that proposed SMDS quality of service requirements can readily be met.However, packet loss and delay behaviors differ radically between trace-driven simulations based on the actual traf?c measurements and those based on these formal traf?c models.In particular,overall packet loss decreases very slowly with increasing buffer capacity,in sharp contrast to Poisson-based models where losses decrease exponentially fast with increasing buffer size. Moreover,packet delay always increases with buffer capacity, again in contrast to the formal models where delay does not exceed a?xed limit regardless of buffer size.This distinctive loss and delay behavior can be precisely explained in terms of the frequency domain manifestation of self-similarity(see Section 3.2).Because both low and high frequencies are signi?cant,heavy losses and long delays occur during long time-frame bursts(due to the presence of low frequencies)and can,therefore,not be dealt with effectively by larger buffers. This observation is also backed by a recent analytic study by Norros(1992)who studies a model for connectionless traf?c based on fractional Brownian motion.The mathematical properties of self-similarity also explain the results of Fowler and Leland(1991),who also observed the ineffectiveness of buffering to manage congestion and went on to observe that when congestion occurs,losses are severely concentrated and are far greater than the background loss rate.While many formal standard network traf?c models provably show that congestion control"works"(e.g.,large buffers provide protection against congestion and average loss rates are a sensible quality of service measure)self-similar traf?c models reveal a far more challenging picture for broadband congestion management.

5.4PARSIMONIOUS MODELS FOR SELF-SIMILAR

TRAFFIC

Self-similarity is often explained as being equivalent to the existence of a multilevel hierarchy of underlying mechanisms. For packet traf?c,it is practically impossible to demonstrate why such mechanisms should result,for example,in an asymptotic power law for the autocorrelations of the form (3.2.1).Even if their physical reality could be established,the resulting models for packet traf?c are likely to have a large number of parameters.Similarly,conventional modeling approaches that stress the importance of source modeling produce highly overparameterized models for aggregate traf?c. Two alternative approaches are far more parsimonious for self-similar traf?c,yielding models with a small number of parameters where every parameter can be given a physically meaningful interpretation.

As we have noted in Section4,self-similar stochastic models?t Ethernet traf?c very well using very few parameters.For example,FGN is characterized by just3parameters(meanμ,varianceσ2,and H),each with a natural physical interpretation. Parameter estimation techniques are known for FGN and fractional ARIMA models,but often turn out to be computationally too intensive for large data sets.However, Section4illustrates how to estimate the parameter H for large data sets,and methods to adapt the existing parameter estimation techniques to long time series are currently being studied.Another promising approach to modeling packet traf?c uses deterministic chaotic maps(Erramilli and Singh(1990)). Generating a packet stream using this approach is appealingly easy;however,the problem of deriving an appropriate nonlinear chaotic map based on a set of actual traf?c measurements currently requires considerable experimenting.Developing more rigorous statistical estimation methods for dynamical systems has recently attracted considerable attention in the statistics literature(e.g.Berliner(1992)and references therein).Both approaches offer a simple description of the complex packet traf?c generation process,and each yield a single parameter that describes the fractal-like nature of traf?c(H and the fractal dimension,respectively).While traditional performance modeling favors the use of stochastic input models,studying arrival streams to queues that are generated by non-linear chaotic maps may well provide new insight into the performance of queueing systems where the arrival processes exhibit fractal-like properties.

6.CONCLUSIONS

Understanding the nature of traf?c in high-speed,high-bandwidth communications systems such as B-ISDN is essential for engineering,operations,and performance evaluation of these networks.In a?rst step toward this goal,it is important to know the traf?c behavior of some of the expected major contributors to future high-speed network traf?c.In this paper,we analyze LAN traf?c offered to a high-speed public network supporting LAN interconnection,an important and rapidly growing B-ISDN service.The main?ndings of our statistical analysis of a few hundred million high quality,high time-resolution Ethernet LAN traf?c measurements are that(i)Ethernet LAN traf?c is statistically self-similar,irrespective of when during the4-year data collection period1989-1992the data were collected and where they were collected in the network,(ii)the degree of self-similarity measured in terms of the Hurst parameter H is typically a function of the overall utilization of the Ethernet and can be used for measuring the"burstiness"of the traf?c (namely,the burstier the traf?c the higher H),and(iii)major components of Ethernet LAN traf?c such as external LAN traf?c or external TCP traf?c share the same self-similar characteristics as the overall LAN traf?c.

An important implication of the self-similarity of LAN traf?c is that aggregating streams of such traf?c typically does not produce a smooth("Poisson-like")superposition process but instead,intensi?es the burstiness(i.e.,the degree of self-similarity)of the aggregation process.Thus,self-similarity is both ubiquitous in our data and unavoidable in future,more highly aggregated,traf?c.However,none of the currently common formal models for LAN traf?c is able to capture the self-similar nature of real traf?c.We brie?y mention two novel methods for modeling self-similar LAN traf?c,based on stochastic self-similar processes and deterministic nonlinear chaotic maps,that provide accurate and parsimonious models. Implications of the self-similar nature of packet traf?c for engineering,operations,and performance evaluation of high-speed networks are ample:(i)source models for individual Ethernet users are expected to show extreme variability in terms of interarrival times of packets(the in?nite variance syndrome),

Presented at ACM SIGComm′93,San Francisco,CA,USA,September1993.

On the Self-Similar Nature of Ethernet Traf?c11

(ii)the Hurst parameter provides a more satisfactory measure of "burstiness"for self-similar traf?c than such commonly used measures as the index of dispersion,the peak-to-mean-ratio,or the coef?cient of variation(which become ill-de?ned for self-similar traf?c),and(iii)the nature of congestion produced by self-similar network traf?c models differs drastically from that predicted by standard formal models and displays a far more complicated picture than has been typically assumed in the past. Finally,in light of the same self-similar behavior recently observed in VBR video traf?c—another major contributor to future high-speed network traf?c—the more complicated nature of congestion due to the self-similar traf?c behavior can be expected to persist even when we move toward a more heterogeneous B-ISDN environment.Thus,we believe based on our measured traf?c data that the success or failure of,for example,a proposed congestion control scheme for B-ISDN will depend on how well it performs under a self-similar rather than under one of the standard formal traf?c scenarios. ACKNOWLEDGEMENTS

This work could not have been done without the help of J.Beran and R.Sherman who provided the S-functions that made the statistical analysis of an abundance of data possible.We also acknowledge many helpful discussions with A.Erramilli about his dynamical systems approach to packet traf?c modeling.M. S.Taqqu was supported,at Boston University,by ONR grant N00014-90-J-1287.

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Communication Systems and the Concept of Conditional Stationarity",IEEE https://www.doczj.com/doc/f213905565.html,munications Technology COM-13,71-90,1965.

17. B.B.Mandelbrot,"Long-Run Linearity,Locally Gaussian

Processes,H-Spectra and In?nite Variances",Intern.

Econom.Rev.10,82-113,1969.

18. B. B.Mandelbrot,The Fractal Geometry of Nature,

Freeman,New York,1983.

19. B.B.Mandelbrot,J.W.Van Ness,"Fractional Brownian

Motions,Fractional Noises and Applications",SIAM Review10,422-437,1968.

20. B. B.Mandelbrot,J.R.Wallis,"Some Long-Run

Properties of Geophysical Records",Water Resources Research5,321-340,1969.

21.K.Meier-Hellstern,P.E.Wirth.Y-L Yan,D.A.Hoe?in,

"Traf?c Models for ISDN Data Users:Of?ce Automation Application",in:Teletraf?c and Datatraf?c in a Period of Change(Proc.13th ITC,Copenhagen,1991),A.Jensen, V.B.Iversen(Eds.),North Holland,167-172,1991.

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Based on Fractional Brownian Motion", COST24TD(92)041,1992.

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Processes and Long-Range Dependence",in:Dependence in Probability and Statistics,E.Eberlein and M.S.Taqqu (Eds.),Birkhauser,Basel,137-165,1985.

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Generate Long-Range Dependence and High Variability", in:Dependence in Probability and Statistics,E.Eberlein and M.S.Taqqu(Eds.),Progress in Prob.and Stat.Vol.

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Presented at ACM SIGComm′93,San Francisco,CA,USA,September1993.

on the contrary的解析

On the contrary Onthecontrary, I have not yet begun. 正好相反，我还没有开始。 https://www.doczj.com/doc/f213905565.html, Onthecontrary, the instructions have been damaged. 反之，则说明已经损坏。 https://www.doczj.com/doc/f213905565.html, Onthecontrary, I understand all too well. 恰恰相反，我很清楚 https://www.doczj.com/doc/f213905565.html, Onthecontrary, I think this is good. ⑴我反而觉得这是好事。 https://www.doczj.com/doc/f213905565.html, Onthecontrary, I have tons of things to do 正相反，我有一大堆事要做 Provided by jukuu Is likely onthecontrary I in works for you 反倒像是我在为你们工作 https://www.doczj.com/doc/f213905565.html, Onthecontrary, or to buy the first good. 反之还是先买的好。 https://www.doczj.com/doc/f213905565.html, Onthecontrary, it is typically american. 相反，这正是典型的美国风格。 222.35.143.196 Onthecontrary, very exciting.

恰恰相反，非常刺激。 https://www.doczj.com/doc/f213905565.html, But onthecontrary, lazy. 却恰恰相反，懒洋洋的。 https://www.doczj.com/doc/f213905565.html, Onthecontrary, I hate it! 恰恰相反，我不喜欢！ https://www.doczj.com/doc/f213905565.html, Onthecontrary, the club gathers every month. 相反，俱乐部每个月都聚会。 https://www.doczj.com/doc/f213905565.html, Onthecontrary, I'm going to work harder. 我反而将更努力工作。 https://www.doczj.com/doc/f213905565.html, Onthecontrary, his demeanor is easy and nonchalant. 相反，他的举止轻松而无动于衷。 https://www.doczj.com/doc/f213905565.html, Too much nutrition onthecontrary can not be absorbed through skin. 太过营养了反而皮肤吸收不了. https://www.doczj.com/doc/f213905565.html, Onthecontrary, I would wish for it no other way. 正相反，我正希望这样 Provided by jukuu Onthecontrary most likely pathological. 反之很有可能是病理性的。 https://www.doczj.com/doc/f213905565.html, Onthecontrary, it will appear clumsy. 反之，就会显得粗笨。 https://www.doczj.com/doc/f213905565.html,

黄自艺术歌曲钢琴伴奏及艺术成就

【摘要】黄自先生是我国杰出的音乐家，他以艺术歌曲的创作最为代表。而黄自先生特别强调了钢琴伴奏对于艺术歌曲组成的重要性。本文是以黄自先生创作的具有爱国主义和人道主义的艺术歌曲《天伦歌》为研究对象，通过对作品分析，归纳钢琴伴奏的弹奏方法与特点，并总结黄自先生的艺术成就与贡献。【关键词】艺术歌曲；和声；伴奏织体；弹奏技巧一、黄自艺术歌曲《天伦歌》的分析（一）《天伦歌》的人文及创作背景。黄自的艺术歌曲《天伦歌》是一首具有教育意义和人道主义精神的作品。同时，它也具有民族性的特点。这首作品是根据联华公司的影片《天伦》而创作的主题曲，也是我国近代音乐史上第一首为电影谱写的艺术歌曲。作品创作于我国政治动荡、经济不稳定的30年代，这个时期，这种文化思潮冲击着我国各个领域，连音乐艺术领域也未幸免――以《毛毛雨》为代表的黄色歌曲流传广泛，对人民大众，尤其是青少年的不良影响极其深刻，黄自为此担忧，创作了大量艺术修养和文化水平较高的艺术歌曲。《天伦歌》就是在这样的历史背景下创作的，作品以孤儿失去亲人的苦痛为起点，发展到人民的发愤图强，最后升华到博爱、奋起的民族志向，对青少年的爱国主义教育有着重要的影响。（二）《天伦歌》曲式与和声。《天伦歌》是并列三部曲式，为a+b+c，最后扩充并达到全曲的高潮。作品中引子和coda所使用的音乐材料相同，前后呼应，合头合尾。这首艺术歌曲结构规整，乐句进行的较为清晰，所使用的节拍韵律符合歌词的特点，如三连音紧密连接，为突出歌词中号召的力量等。和声上，充分体现了中西方作曲技法融合的创作特性。使用了很多七和弦。其中，一部分是西方的和声，一部分是将我国传统的五声调式中的五个音纵向的结合，构成五声性和弦。与前两首作品相比，《天伦歌》的民族性因素增强，这也与它本身的歌词内容和要弘扬的爱国主义精神相对应。（三）《天伦歌》的伴奏织体分析。《天伦歌》的前奏使用了a段进唱的旋律发展而来的，具有五声调性特点，增添了民族性的色彩。在作品的第10小节转调入近关系调，调性的转换使歌曲增添抒情的情绪。这时的伴奏加强和弦力度，采用切分节奏，节拍重音突出，与a段形成强弱的明显对比，突出悲壮情绪。 c段的伴奏采用进行曲的风格，右手以和弦为主，表现铿锵有力的进行。右手为上行进行，把全曲推向最高潮。左手仍以柱式和弦为主，保持节奏稳定。在作品的扩展乐段，左手的节拍低音上行与右手的八度和弦与音程对应，推动音乐朝向宏伟、壮丽的方向进行。coda 处，与引子材料相同，首尾呼应。二、《天伦歌》实践研究《天伦歌》是具有很强民族性因素的作品。所谓民族性，体现在所使用的五声性和声、传统歌词韵律以及歌曲段落发展等方面上。作品的整个发展过程可以用伤感――悲壮――兴奋――宏达四个过程来表述。在钢琴伴奏弹奏的时候，要以演唱者的歌唱状态为中心，选择合适的伴奏音量、音色和音质来配合，做到对演唱者的演唱同步，并起到连接、补充、修饰等辅助作用。作品分为三段，即a+b+c+扩充段落。第一段以五声音阶的进行为主，表现儿童失去父母的悲伤和痛苦，前奏进入时要弹奏的使用稍凄楚的音色，左手低音重复进行，在弹奏完第一个低音后，要迅速的找到下一个跨音区的音符；右手弹奏的要有棱角，在前奏结束的时候第四小节的t方向的延音处，要给演唱者留有准备。演唱者进入后，左手整体的踏板使用的要连贯。随着作品发展，伴奏与旋律声部出现轮唱的形式，要弹奏的流动性强，稍突出一些。后以mf力度出现的具有转调性质的琶音奏法，要弹奏的如流水般连贯。在重复段落，即“小

英语造句

一般过去式时间状语：yesterday just now (刚刚) the day before three days ag0 a week ago in 1880 last month last year 1. I was in the classroom yesterday. I was not in the classroom yesterday. Were you in the classroom yesterday. 2. They went to see the film the day before. Did they go to see the film the day before. They did go to see the film the day before. 3. The man beat his wife yesterday. The man didn’t beat his wife yesterday. 4. I was a high student three years ago. 5. She became a teacher in 2009. 6. They began to study english a week ago 7. My mother brought a book from Canada last year. 8.My parents build a house to me four years ago . 9.He was husband ago. She was a cooker last mouth. My father was in the Xinjiang half a year ago. 10.My grandfather was a famer six years ago. 11.He burned in 1991

我国艺术歌曲钢琴伴奏-精

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写作中，不可忽略的是钢琴伴奏织体的作用，因此作曲家们通常都以丰富的伴奏织体来烘托歌曲的意境，铺垫音乐背景，增强音乐感染力。和声织体，复调织体都在许多作品中使用，较为常见的是综合织体。这些不同的伴奏织体的歌曲，极大限度的发挥了钢琴的艺术表现力，起到了渲染歌曲氛围，揭示内心情感，塑造歌曲背景的重要作用。钢琴伴奏成为整体乐思不可缺少的部分。优秀的钢琴伴奏织体，对发掘歌曲内涵，表现音乐形象，构架诗词与音乐之间的桥梁等方面具有很大的意义。在不断发展和探索中，也将许多伴奏织体使用得非常娴熟精确。二、青主艺术歌曲《我住长江头》中钢琴伴奏的特点《我住长江头》原词模仿民歌风格，抒写一个女子怀念其爱人的深情。青主以清新悠远的音乐体现了原词的意境，而又别有寄寓。歌调悠长，但有别于民间的山歌小曲；句尾经常出现下行或向上的拖腔，听起来更接近于吟哦古诗的意味，却又比吟诗更具激情。钢琴伴奏以江水般流动的音型贯穿全曲，衬托着气息宽广的歌唱，象征着绵绵不断的情思。由于运用了自然调式的旋律与和声，显得自由舒畅，富于浪漫气息，并具有民族风味。最有新意的是，歌曲突破了“卜算子”词牌双调上、下两阕一般应取平行反复结构的惯例，而把下阕单独反复了三次，并且一次比一次激动，最后在全曲的高音区以ff结束。这样的处理突出了思念之情的真切和执著，并具有单纯的情歌所没有的昂奋力量。这是因为作者当年是大革命的参加者，正被反动派通缉，才不得不以破格的音乐处理，假借古代的

学生造句--Unit 1

●I wonder if it’s because I have been at school for so long that I’ve grown so crazy about going home. ●It is because she wasn’t well that she fell far behind her classmates this semester. ●I can well remember that there was a time when I took it for granted that friends should do everything for me. ●In order to make a difference to society, they spent almost all of their spare time in raising money for the charity. ●It’s no pleasure eating at school any longer because the food is not so tasty as that at home. ●He happened to be hit by a new idea when he was walking along the riverbank. ●I wonder if I can cope with stressful situations in life independently. ●It is because I take things for granted that I make so many mistakes. ●The treasure is so rare that a growing number of people are looking for it. ●He picks on the weak mn in order that we may pay attention to him. ●It’s no pleasure being disturbed whena I settle down to my work. ●I can well remember that when I was a child, I always made mistakes on purpose for fun. ●It’s no pleasure accompany her hanging out on the street on such a rainy day. ●I can well remember that there was a time when I threw my whole self into study in order to live up to my parents’ expectation and enter my dream university. ●I can well remember that she stuck with me all the time and helped me regain my confidence during my tough time five years ago. ●It is because he makes it a priority to study that he always gets good grades. ●I wonder if we should abandon this idea because there is no point in doing so. ●I wonder if it was because I ate ice-cream that I had an upset student this morning. ●It is because she refused to die that she became incredibly successful. ●She is so considerate that many of us turn to her for comfort. ●I can well remember that once I underestimated the power of words and hurt my friend. ●He works extremely hard in order to live up to his expectations. ●I happened to see a butterfly settle on the beautiful flower. ●It’s no pleasure making fun of others. ●It was the first time in the new semester that I had burned the midnight oil to study. ●It’s no pleasure taking everything into account when you long to have the relaxing life. ●I wonder if it was because he abandoned himself to despair that he was killed in a car accident when he was driving. ●Jack is always picking on younger children in order to show off his power. ●It is because he always burns the midnight oil that he oversleeps sometimes. ●I happened to find some pictures to do with my grandfather when I was going through the drawer. ●It was because I didn’t dare look at the failure face to face that I failed again. ●I tell my friend that failure is not scary in order that she can rebound from failure. ●I throw my whole self to study in order to pass the final exam. ●It was the first time that I had made a speech in public and enjoyed the thunder of applause. ●Alice happened to be on the street when a UFO landed right in front of her. ●It was the first time that I had kept myself open and talked sincerely with my parents. ●It was a beautiful sunny day. The weather was so comfortable that I settled myself into the

英语句子结构和造句

高中英语~词性~句子成分~语法构成第一章节：英语句子中的词性 1.名词：n. 名词是指事物的名称，在句子中主要作主语.宾语.表语.同位语。 2.形容词;adj. 形容词是指对名词进行修饰~限定~描述~的成份，主要作定语.表语.。形容词在汉语中是（的）.其标志是: ous. Al .ful .ive。. 3.动词：vt. 动词是指主语发出的一个动作，一般用来作谓语。 4.副词：adv. 副词是指表示动作发生的地点. 时间. 条件. 方式. 原因. 目的. 结果.伴随让步. 一般用来修饰动词. 形容词。副词在汉语中是（地）.其标志是：ly。 5.代词：pron. 代词是指用来代替名词的词，名词所能担任的作用，代词也同样.代词主要用来作主语. 宾语. 表语. 同位语。 6.介词：prep.介词是指表示动词和名次关系的词，例如：in on at of about with for to。其特征：

介词后的动词要用—ing形式。介词加代词时，代词要用宾格。例如：give up her（him）这种形式是正确的，而give up she（he）这种形式是错误的。 7.冠词：冠词是指修饰名词，表名词泛指或特指。冠词有a an the 。 8.叹词：叹词表示一种语气。例如：OH. Ya 等 9.连词：连词是指连接两个并列的成分，这两个并列的成分可以是两个词也可以是两个句子。例如：and but or so 。 10.数词：数词是指表示数量关系词，一般分为基数词和序数词第二章节：英语句子成分主语：动作的发出者，一般放在动词前或句首。由名词. 代词. 数词. 不定时. 动名词. 或从句充当。谓语：指主语发出来的动作，只能由动词充当，一般紧跟在主语后面。宾语：指动作的承受着，一般由代词. 名词. 数词. 不定时. 动名词. 或从句充当. 介词后面的成分也叫介词宾语。定语：只对名词起限定修饰的成分，一般由形容

六级单词解析造句记忆MNO

M A: Has the case been closed yet? B: No, the magistrate still needs to decide the outcome. magistrate n.地方行政官，地方法官，治安官 A: I am unable to read the small print in the book. B: It seems you need to magnify it. magnify vt.１．放大，扩大；２．夸大，夸张 A: That was a terrible storm. B: Indeed, but it is too early to determine the magnitude of the damage. magnitude n.１．重要性，重大；２．巨大，广大 A: A young fair maiden like you shouldn’t be single. B: That is because I am a young fair independent maiden. maiden n.少女，年轻姑娘，未婚女子 a.首次的，初次的 A: You look majestic sitting on that high chair. B: Yes, I am pretending to be the king! majestic a.雄伟的，壮丽的，庄严的，高贵的 A: Please cook me dinner now. B: Yes, your majesty, I’m at your service. majesty n.１．［Ｍ－］陛下（对帝王，王后的尊称）；２．雄伟，壮丽，庄严 A: Doctor, I traveled to Africa and I think I caught malaria. B: Did you take any medicine as a precaution? malaria n.疟疾 A: I hate you! B: Why are you so full of malice? malice n.恶意，怨恨 A: I’m afraid that the test results have come back and your lump is malignant. B: That means it’s serious, doesn’t it, doctor? malignant a.１．恶性的，致命的；２．恶意的，恶毒的 A: I’m going shopping in the mall this afternoon, want to join me? B: No, thanks, I have plans already. mall n.（由许多商店组成的）购物中心 A: That child looks very unhealthy. B: Yes, he does not have enough to eat. He is suffering from malnutrition.

奈达翻译理论初探

第27卷第3期唐山师范学院学报2005年5月Vol. 27 No.3 Journal of Tangshan Teachers College May 2005 奈达翻译理论初探尹训凤1，王丽君2 （1.泰山学院外语系，山东泰安 271000；2.唐山师范学院教务处，河北唐山 063000）摘要：奈达的翻译理论对于翻译实践有很强的指导作用：从语法分析角度来讲，相同的语法结构可能具有完全不同的含义；词与词之间的关系可以通过逆转换将表层形式转化为相应的核心句结构；翻译含义是翻译成败的关键所在。关键词：奈达；分析；转换；重组；核心句中图分类号：H315.9 文献标识码：A 文章编号：1009-9115（2005）03-0034-03 尤金?奈达是美国当代著名翻译理论家，也是西方语言学派翻译理论的主要代表，被誉为西方“现代翻译理论之父”。他与塔伯合著的《翻译理论与实践》对翻译界影响颇深。此书说明了中国与西方译界人士思维方式的巨大差别：前者是静的，崇尚“信、达、雅”，讲究“神似”，追求“化境”；后者是动的，将语言学、符号学、交际理论运用到翻译研究当中，提倡“动态对等”，注重读者反应。中国译论多概括，可操作性不强；西方译论较具体，往往从点出发。他在该书中提到了动态对等，详细地描述了翻译过程的三个阶段：分析、转换和重组，对于翻译实践的作用是不言而喻的。笔者拟结合具体实例，从以下角度来分析其理论独到之处。一一般来说，结构相同的词组、句子，其语法意义是相同或相近的。然而奈达提出，同样的语法结构在许多情况下可以有不同的含义。“名词+of+名词”这一语法结构可以对此作最好的阐释。如下例：（1）the plays of Shakespeare/ the city of New York/ the members of the team/ the man of ability/ the lover of music/ the order of obedience/ the arrival of the delegation 在以上各个词组中，假设字母A和B分别代表一个名词或代词，它们之间存在着不同的关系。在the plays of Shakespeare 中，Shakespeare是施事，plays是受事，用公式表示就是“B writes A”；在the city of New York中，city和New York是同位关系，用公式表示就是“A is B”；the members of the team中，members和team是所属关系，即“A is in the B”；在the man of ability中，“B is A’s characteristic”；在the lover of music中，lover表示的是活动，即动作，music是它的受事，因此可以理解为（he/she）loves the music, 用公式表示就是“X does A to B”（X施A于B）或“B is the goal of A”（B为A的受事）；在the order of obedience中，obedience表示的是活动，order是它的受事，因此用公式表示就是“X does B to A”（X施B于A）或“A is the goal of B”（A为B的受事）；在the arrival of the delegation中，arrival表示动作，而delegation是动作的发出者，所以是“B does A”。因此它们的结构关系如下所示： the plays of Shakespeare——Shakespeare wrote the plays. the city of New York——The city is New York. the members of the team——The members are in the team. the man of ability——The man is able. the lover of music——(He/She) loves the music. the order of obedience——(People) obey the order. the arrival of the delegation——The delegation arrives. ────────── 收稿日期：2004-06-10 作者简介：尹训凤（1976-），女，山东泰安人，泰山学院外语系教师，现为天津外国语学院研究生部2003级研究生，研究方向为翻译理论与实践。 - 34 -

base on的例句

意见应以事实为根据. 3 来自辞典例句 192. The bombers swooped ( down ) onthe air base. 轰炸机突袭空军基地. 来自辞典例句 193. He mounted their engines on a rubber base. 他把他们的发动机装在一个橡胶垫座上. 14 来自辞典例句 194. The column stands on a narrow base. 柱子竖立在狭窄的地基上. 14 来自辞典例句 195. When one stretched it, it looked like grey flakes on the carvas base. 你要是把它摊直, 看上去就象好一些灰色的粉片落在帆布底子上. 18 来自辞典例句 196. Economic growth and human well - being depend on the natural resource base that supports all living systems. 经济增长和人类的福利依赖于支持所有生命系统的自然资源. 12 1 来自辞典例句 197. The base was just a smudge onthe untouched hundred - mile coast of Manila Bay. 那基地只是马尼拉湾一百英里长安然无恙的海岸线上一个硝烟滚滚的污点. 6 来自辞典例句 198. You can't base an operation on the presumption that miracles are going to happen. 你不能把行动计划建筑在可能出现奇迹的假想基础上.

奈达翻译理论简介

奈达翻译理论简介（一）奈达其人尤金?奈达（EugeneA.Nida）1914年出生于美国俄克勒荷马州，当代著名语言学家、翻译家和翻译理论家。也是西方语言学派翻译理论的主要代表，被誉为西方“现代翻译理论之父”。尤金是当代翻译理论的主要奠基人，其理论核心是功能对等。尤金先后访问过90个国家和地区，并著书立说，单独或合作出版了40多部书，比较著名的有《翻译科学探索》、《语言与文化———翻译中的语境》等，他还发表论文250余篇，是世界译坛的一位长青学者。他还参与过《圣经》的翻译工作。他与塔伯合著的《翻译理论与实践》对翻译界影响颇深。此书说明了中国与西方译界人士思维方式的巨大差别：前者是静的，崇尚“信、达、雅”，讲究“神似”，追求“化境”；后者是动的，将语言学、符号学、交际理论运用到翻译研究当中，提倡“动态对等”，注重读者反应。中国译论多概括，可操作性不强；西方译论较具体，往往从点出发。他在该书中提到了动态对等，详细地描述了翻译过程的三个阶段：分析、转换和重组，对于翻译实践的作用是不言而喻的。（二）奈达对翻译的定义按照奈达的定义：“所谓翻译，是指从语义到文体（风格）在译语中用最切近而又最自然的对等语再现源语的信息。”其中，“对等”是核心，“最切近”和“最自然”都是为寻找对等语服务的。奈达从社会语言学和语言交际功能的观点出发，认为必须以读者的反应作为衡量译作是否正确的重要标准。翻译要想达到预期的交际目的，必须使译文从信息内容、说话方式、文章风格、语言文化到社会因素等方面尽可能多地反映出原文的面貌。他试图运用乔姆斯基的语言学理论建立起一套新的研究方法。他根据转换生成语法，特别是其中有关核心句的原理，提出在语言的深层结构里进行传译的设想。奈达提出了词的4种语义单位的概念，即词具有表述事物、事件、抽象概念和关系等功能。这4种语义单位是“核心”，语言的表层结构就是以“核心”为基础构建的，如果能将语法结构归纳到核心层次，翻译过程就可最大限度地避免对源语的曲解。按照4种语义单位的关系，奈达将英语句子归结为7个核心句：（1）Johnranquickly.（2）JohnhitBill.（3）JohngaveBillaball.（4）Johnisinthehouse.（5）Johnissick.（6）Johnisaboy.（7）Johnismyfather. （三）奈达翻译理论的经历阶段奈达翻译理论的发展经历过三个阶段，分别是描写语言阶段、交际理论阶段和和社会符号学阶段。第一个阶段始于1943年发表《英语句法概要》，止于1959年发表《从圣经翻译看翻译原则》。这一阶段是奈达翻译思想及学术活动的初期。第二阶段始于1959年发表的《从圣经翻译看翻译原则》，止于1969年出版的《翻译理论与实践》。主要著作有《翻译科学探索》、《信息与使命》。在这10年中，奈达确立了自己在整个西方翻译理论界的权威地位。1964年出版的《翻译科学探索》标志着其翻译思想发展过程中一个最重要的里程碑。第三阶段始于70年代，奈达通过不断修正和发展自己翻译理论创建了新的理论模式———社会符号学模式。奈达在继承原有理论有用成分的基础上，将语言看成一种符号现象，并结合所在社会环境进行解释。在《从一种语言到另一种语言》一书中，奈达强调了形式的重要性，认为形式也具有意义，指出语言的修辞特征在语言交际及翻译中的重要作用，并且用“功能对等”取代了“动态对等”的提法，是含义更加明确。三、对奈达翻译理论的评价（一）贡献奈达是一位硕果累累的翻译理论家。可以说，在两千年的西方翻译思想发展史上，奈达的研究成果之丰是名列前茅的。他的研究范围从翻译史、翻译原则、翻译过程和翻译方法到翻译教学和翻译的组织工作，从口译到笔译，从人工翻译到机器翻译，从语义学到人类文化学，几乎无所不包，从而丰富并拓展了西方的翻译研究领地。奈达的理论贡献，主要在于他帮助创造了一种用新姿态对待不同语言和文化的气氛，以增进人类相互之间的语言交流和了解。他坚持认为：任何能用一种语言表达的东西都能够用另一种语言来表达；在语言之间、文化之间能通过寻找翻译对等语，以适当方式重组原文形式和语义结构来进行交际。因此也说明，某

英语造句大全

英语造句大全English sentence 在句子中，更好的记忆单词！ 1、(1)、able adj. 能句子：We are able to live under the sea in the future. (2)、ability n. 能力句子：Most school care for children of different abilities. (3)、enable v. 使。。。能句子：This pass enables me to travel half-price on trains. 2、(1)、accurate adj. 精确的句子：We must have the accurate calculation. (2)、accurately adv. 精确地句子：His calculation is accurately. 3、(1)、act v. 扮演句子：He act the interesting character. （2）、actor n. 演员句子：He was a famous actor. (3)、actress n. 女演员句子：She was a famous actress. (4)、active adj. 积极的句子：He is an active boy. 4、add v. 加句子：He adds a little sugar in the milk. 5、advantage n. 优势句子：His advantage is fight. 6、age 年龄n. 句子：His age is 15. 7、amusing 娱人的adj. 句子：This story is amusing. 8、angry 生气的adj. 句子：He is angry. 9、America 美国n.

(完整版)主谓造句

主语+谓语 1. 理解主谓结构 1) The students arrived. The students arrived at the park. 2) They are listening. They are listening to the music. 3) The disaster happened. 2．体会状语的位置 1) Tom always works hard. 2) Sometimes I go to the park at weekends.. 3) The girl cries very often. 4) We seldom come here. The disaster happened to the poor family. 3. 多个状语的排列次序 1) He works. 2) He works hard. 3) He always works hard. 4) He always works hard in the company. 5) He always works hard in the company recently. 6) He always works hard in the company recently because he wants to get promoted. 4. 写作常用不及物动词 1. ache My head aches. I’m aching all over. 2. agree agree with sb. about sth. agree to do sth. 3. apologize to sb. for sth. 4. appear (at the meeting, on the screen) 5. arrive at / in 6. belong to 7. chat with sb. about sth. 8. come (to …) 9. cry 10. dance 11. depend on /upon 12. die 13. fall 14. go to … 15. graduate from 16. … happen 17. laugh 18. listen to... 19. live 20. rise 21. sit 22. smile 23. swim 24. stay (at home / in a hotel) 25. work 26. wait for 汉译英： 1.昨天我去了电影院。 2.我能用英语跟外国人自由交谈。 3.晚上7点我们到达了机场。 4.暑假就要到了。 5.现在很多老人独自居住。 6.老师同意了。 7.刚才发生了一场车祸。 8.课上我们应该认真听讲。9. 我们的态度很重要。 10. 能否成功取决于你的态度。 11. 能取得多大进步取决于你付出多少努力。 12. 这个木桶能盛多少水取决于最短的一块板子的长度。

奈达翻译理论动态功能对等的新认识

To Equivalence and Beyond: Reflections on the Significance of Eugene A. Nida for Bible Translating1 Kenneth A. Cherney, Jr. It’s been said, and it may be true, that there are two kinds of people—those who divide people into two kinds and those who don’t. Similarly, there are two approaches to Bible translation—approaches that divide translations into two kinds and those that refuse. The parade example of the former is Jerome’s claim that a translator’s options are finally only two: “word-for-word” or “sense-for-sense.”2 Regardless of whether he intended to, Jerome set the entire conversation about Bible translating on a course from which it would not deviate for more than fifteen hundred years; and some observers in the field of translation studies have come to view Jerome’s “either/or” as an unhelpful rut from which the field has begun to extricate itself only recently and with difficulty. Another familiar dichotomy is the distinction between “formal correspondence” translating on one hand and “dynamic equivalence” (more properly “functional equivalence,” on which see below) on the other. The distinction arose via the work of the most influential figure in the modern history of Bible translating: Eugene Albert Nida (1914-2011). It is impossible to imagine the current state of the field of translation studies, and especially Bible translating, without Nida. Not only is he the unquestioned pioneer of modern, so-called “meaning-based” translating;3 he may be more responsible than any other individual for putting Bibles in the hands of people around the world that they can read and understand. 1 This article includes material from the author’s doctoral thesis (still in progress), “Allusion as Translation Problem: Portuguese Versions of Second Isaiah as Test Case” (Stellenbosch University, Drs. Christo Van der Merwe and Hendrik Bosman, promoters). 2 Jerome, “Letter to Pammachius,” in Lawrence Venuti, ed., The Translation Studies Reader, 2nd ed. (NY and London: Routledge, 2004), p. 23. 3 Nigel Statham, "Nida and 'Functional Equivalence': The Evolution of a Concept, Some Problems, and Some Possible Ways Forward," Bible Translator 56, no. 1 (2005), p. 39.