On the predictability of data network traffic
On the Predictability of Data Network Tra?c Khushboo Shah,Stephan Bohacek and Edmond Jonckheere
Abstract
The predictably of data network tra?c is assessed.Dif-ferent topologies,types of tra?c,and queueing disci-plines are studied.Linear and nonlinear AR(MA)mod-els as well as state space,and models based on canoni-cal correlation are employed.These predictors are com-pared against two simple predictors:1.the prediction is the mean value of the time series,2.the predic-tion is the last observation.The signi?cant conclusion is that the dynamic predictors fail to perform signif-icantly better than the simple predictors over higher frequencies.The implication of this result with regard to active queue management is discussed.
1Introduction
There has been a large body of work focused on de-veloping dynamic controllers for computer data net-works[1],[2],[3].However,before a controller can be developed,the open-loop system must be under-stood through some model.In this sense,before a con-troller can be considered,some predictor must be avail-able.This paper carefully examines the predictabil-ity of data network tra?c.The main result is that network tra?c is not predictable at high frequencies. Thus,there seems to be little hope of developing a controller to damp out the high frequency variations in network tra?c.Speci?cally,control of TCP’s dynam-ics does not seem possible.This result does not contra-dict other work that produced controllers and demon-strated their e?ectiveness over lower frequency band. The present work only examines the high frequency aspects of the https://www.wendangku.net/doc/967903678.html,work tra?c is dynamic on many time scales.At small time scales,the tra?c dy-namics is dominated by TCP.However,at longer time scales,tra?c is dominated by end-user action and the steady state behavior of TCP.The present work says nothing about the ability to achieve performance ob-jectives through active queue management when the time scale of focus is centered around end-user action and steady state TCP.Indeed,it is the belief of the authors that such control is possible and that previ-ous work has demonstrated this.The present paper only shows that one should not expect to control the dynamic aspects of TCP.
Network tra?c analysis has been the focus of count-less papers following three avenues of approach.First, much work has focused on measuring tra?c?ow across real networks[4],[5],[6],[7].These measurements have attempted to quantify the variation or growth in tra?c at very long time scale.The second and very active area of investigation in network tra?c has been the study of steady state sending rate produced by a single TCP ?ow.This work has led to the TCP-friendly equations [8],[9],which establish a steady state relationship be-tween the round-trip time,the packet loss probability, and the TCP sending rate.The third area of focus has been the dynamic behavior of TCP.Much work has fo-cused on a?rst principles approach to modeling the dy-namics of TCP[10],[11],[12],[13],[14].The approach followed in the present paper is distinct for these other works in that no modeling assumptions are made,that is,the models are developed via the“black box”ap-proach by collecting a large data record and applying time series modeling techniques.In[15],the variability of TCP dynamics was demonstrated.In[16],it was shown that TCP can display chaotic dynamics.These results led to the suspicion that TCP tra?c is di?cult to predict.This paper seeks to con?rm this suspicion. The result that the dynamic aspects of TCP are not predictable is based on experimentation on two topolo-gies(dumbbell and parking lot)and two types of traf-?c(FTP and HTTP).Many classes of predictors have been employed;these include linear AR models,lin-ear ARMA models,a large selection of nonlinear AR models,state space,as well as predictors based on lin-ear and nonlinear canonical correlation analysis.It is demonstrated in Section3that these di?erent models perform similarly and hence the remainder of the paper focuses on the linear and nonlinear AR models.
Two types of systems are investigated based on the queuing discipline.In Section4.1,a queuing discipline is considered where the drop probability of packets is set and the packet arrivals over a sample period are ob-served.The behavior of this system is modeled over a small operating range with the type of tra?c and num-ber of?ows stable and the input only slightly varying. The second type of system is studied in Section4.2and is the basic drop tailed queue.Here the drop probabil-ity is not being set but is observed.The output of this system is packet arrivals over a sample period.The objective is to predict the number of packet arrivals in both disciplines.Before the investigation begins,the types of models considered and the simulation setup
are discussed.
2Models and Simulation Set-up
2.1Prediction Models
Many classes of models are considered.These classes include linear AR models[17]without input
y(k+1)=L?1
X i=0a i y(k?i)+w(k),
where w is a noise.A linear AR model with input is de?ned as
y(k+1)=L?1
X i=0a i y(k?i)+L?1X i=0b i u(k?i)+w(k),
Also,nonlinear AR models were considered,
y(k+1)=L?1
X i=0a i y(k?i)+X d∈D L?1X i=0a d,i y(k?i)d+... +
L?1
X i=0b i u(k?i)+X d∈D L?1X i=0b d,i u(k?i)d.... +w(k),
where the D is one of the following sets:
D={1,2,3...,10},for“All”nonlinearities(1) D={1,2,4,6,8,10},for“Even”nonlinearities D={1,3,5,7,9},for“Odd”nonlinearities
In the case where the input is not used,the coe?cients b i are set to zero.Standard least-squares techniques were used to estimate the coe?cients of these AR mod-els.
Linear state space models are of the form
x(k+1)=Ax(k)+B1u(k)+B2w(k)
y(k)=Cx(k)+Dw(k)
Here,estimates of the parameters were identi?ed using techniques described in[17].
Lastly,prediction models based on the canonical corre-lation analysis(CCA)were considered.The two mod-els that have been investigated here are nonlinear AR and state space models.Both models are implemented as described in[18].
Two simple predictors were employed to compare the performance of the dynamic models described above. The?rst predictor is written as
mean (2)
Hence,this predictor simply uses the mean as a predic-
tion.The second simple predictor is
b y simple(k+1)=y(k).(3)
In this case the prediction is simply the last observa-
tion.
2.2Measures of Model Fit:
The most common measure of predictability is the
mean square error(MSE)de?ned as,
MSE=E((b y est?y)2).
MSE is a measure of the absolute error.This measure
su?ers from the problem that the amplitude of the sig-
nal to be predicted plays a strong role in the size of the
measurement error.To avoid this problem,a relative
error measurement is considered.A typical approach
is to normalize the MSE relative to the variance of the
time series to be predicted.The result is called the
normalized mean square error(NMSE),
NMSE=
E((b y est?y)2)
E((b y mean?y)2)
One can view this normalization as a comparison
between two predictors.One predictor yields the
prediction b y est while the other predictor trivially pre-
dicts the mean.The NMSE is then the ratio of error
variance between these two prediction approaches pro-
vided that b y est is unbiased.
Following this interpretation of NMSE as a comparison
between two predictors,we consider the relative perfor-
mance of the simple predictor(3).The prediction error
when this predictor is considered is denoted NMSE-SP
and is de?ned as,
NMSE?SP=
E((b y est?y)2)
E((b y simple?y)2),
where y simple is given by(3).
Note that if NMSE is near1,then the dynamic pre-
dictor performs about the same task as just using the
mean as the prediction.Thus,only when both the
NMSE and NMSE-SP are small can we conclude that
the dynamic predictor is a good predictor.
2.3Model Order Selection:
Because the best choice of the?lter order,θ,is generally
not known a priori,it is usually necessary in practice
to postulate several model orders.Many criteria have
been proposed as allegedly objective functions for se-
lecting the AR model order.The two best known ones
are Akaike’s Information Theoretic Criterion,AIC[19],
which has the form(for gaussian disturbances),
AIC[θ]=N ln(MSEθ)+2θ
and Rissanen’s Minimum Description Length Crite-rion,MDL[20],which has the form
MDL[θ]=N ln(MSEθ)+θln(θ),
where N is the length of the data record.The orderθis selected to minimize the information theoretic crite-rion.
2.4Simulation Setup
We used the Network Simulator(ns)[21]developed by LBNL to perform our simulations.Ns is a dis-crete event simulator widely accepted for networking research.We studied many environment set-ups:two types of tra?c,two topologies,and two types of sys-tems.
The types of systems investigated were distinguished by their queueing discipline.In the?rst system,the queue imposes a drop probability on every arriving packet.This drop probability is uniformly distributed over[0.0295,0.0305]over many sample periods.Hence, at time step k,the probability p k is set for the time pe-riod[kT,(k+1)T),where T is the sample period.We consider sample periods from10ms to nearly an hour and a half.In order to keep the scale of the packet arrivals the same for all sample periods,we de?ne y k+1 to be the normalized packet arrivals over the period [kT,(k+1)T).The normalization is done by dividing the observed packet arrivals by the link speed which is the maximum number of packets per time period [kT,(k+1)T).The second queuing discipline is a sim-ple drop tail.In this case,the drop probability cannot be set but can be observed.Speci?cally,at time kT, we observe d k,the empirical probability over the time interval[(k?1)T,kT).We observe the drop probabil-ity d k+1over the time period[kT,(k+1)T).Hence, there is a delay in the drop probability as compared to the?rst setup where p k was the drop probability over [kT,(k+1)T).In the second queuing discipline,the queue is set to be drop tail;hence,drops occur when the queue is?lled.In the?rst queue discipline,drops could occur if the queue?lls.However,the queue size is taken su?ciently large and the drop probability is taken large enough,so that the queue does not?ll up. Both the dumbbell and parking lot topologies were in-vestigated.The dumbbell topology is shown in Figure 1.The nodes S i(i=2,...,6)are set as the sources and the nodes D i(i=7,...,11)are set as the destinations. The monitored link,the bottleneck link,is0to1.The parking lot topology is a more complicated topology and is shown in Figure2.The nodes0,8,10,12are set as the sources and the nodes7,9,11,13are set as the
Destinations Figure1:Dumbbell topology.The tra?c is sent from sources to destinations.Link0-1,bottleneck
link,is monitored.
destinations.For this topology,the monitored link is the one from4to5.
FTP tra?c was modeled as long lived TCP tra?c, that is,for each source-destination pair a single TCP connection sent data for the entire simulation.The starting time of the?ows was varied slightly randomly so that each simulation was di?erent.HTTP tra?c was modeled by a collection of?ows with an ON/OFF behavior.Speci?cally,a single HTTP connection was made up of a single TCP?ow.This?ow transmits a single?le.The size of the?le is a random variable with Pareto distribution.Thus,the cumulative distribution of the?les size is given by
P(?le size whereα=1.06and C=10000.These parameters are common estimates of the?les size distribution found on the web[22],[23].Upon completion of the transmission of the?le,the connection lies dormant for a period of time that is exponentially distributed.This tra?c obeys the assumptions in[24]and should lead to bursty tra?c. Each simulation was run for extremely long runs to ensure that all parameters were accurately estimated. For example,most simulations used over30000sample points.Hence,when the sample period was100sec-onds,the simulation ran for3,000,000secs or nearly35 days. The rationale behind these long simulation times and very small variations in the drop probability discussed above is that we hope to study the predictability of network tra?c in the best possible light.Hence,in the?rst queuing discipline,since the queue never?lls, the nonlinearity due to queue over?ow does not occur. Furthermore,since the drop probability only slightly varies,a linear model should be accurate.Indeed,it is easily argued that the simulation environment is overly generous and that any predictor that would be de-ployed would have to perform well in far more di?cult situations.As will be shown,even in this simulation environment,linear and some nonlinear predictors are unable to accurately predict packet arrivals. Figure2:Parking lot topology.The tra?c is sent from sources to their downsteam destinations.Link 4-5is monitored. 3Models Type Selection We begin by investigating which model,linear AR,non-linear AR,statespace,nonlinear AR(CCA),or states-pace(CCA),yields the best predictor.To this end, several environments were simulated.Here,the results from one environment are presented. The topology being considered is dumbbell(Figure1) and the tra?c is FTP.The analysis is2-fold:?rst,an “input-output”system(where p k is the input and y k is the output);second,a“free”system(where there is no input to the system and y k is the freely gener-ated signal).The comparison between the NMSE for both types of systems for six models(linear AR,lin-ear ARMA,nonlinear AR,statespace,nonlinear AR (CCA),statespace(CCA))is performed.Furthermore, the nonlinear AR models are investigated in detail by considering various nonlinearities for both systems. Figure3shows a comparison between NMSE for vari-ous models for both types of systems.For both systems (Figures on the left and on the right in Figure3),at sampling period0.01,linear AR works slightly better (5?10%)than the rest of the models.As the sampling period increases,the NMSE becomes nearly the same for all the predictors.Hence,we can conclude that the type of predictor does not matter for the predic-tion of y k.Furthermore,considering the nonlinearities in the network(eg.queue over?ow,dividing congestion window by2,etc.),one would expect that nonlinear models might perform better.However,our simulation cases,the nonlinearities do not appear to improve the prediction quality.The reason behind that is that the residual error from the linear predictor is gaussian as shown in Figure5.Hence,we can conclude that the nonlinear predictors would not achieve better results than the linear predictors for the prediction of y k. Comparing the Figures on the left and on the right (Figure3),we see that for small sampling periods(0.01, 0.05),the NMSE are similar.Thus we can deduce that, at smaller sampling periods,the p k does not have much Figure3:Comparison of various models for the input-output system and the free system.Topology is dumbbell and tra?c is FTP. Figure4:Comparison of various nonlinear models for the input-output system and free system.Topol- ogy is dumbbell and tra?c is FTP. e?ect on the prediction of y k,only the past y k is im-portant.In contrast,at large sampling periods,NMSE decreases for the input-output system while NMSE in-creases for the free system.This means that the p k begins to have a great e?ect while the past y k does not a?ect the prediction as much. Next,we compare nonlinear models(nonlinear AR and nonlinear AR(CCA))to see which nonlinear model is better and which nonlinearities in particular play an important role in prediction.“All”means all the non-linearities are considered;“even”means all the even and“odd”means all the odd nonlinearities are consid-ered(1). Figure3shows the comparison between all the non-linear models.Observe that there is a slight gap be-tween nonlinear AR and nonlinear AR(CCA)for small sample period.As the sample period gets larger,the gap gets smaller.Identi?cation of nonlinear AR mod-els is computationally much faster than nonlinear AR (CCA),as the later involves large matrix computation, SVD,etc.Since the gain in prediction error by us-ing nonlinear AR(CCA)is only slight(less than5%), we use linear AR and nonlinear AR models for further prediction analysis. Figure5:Probability versus residual error(from linear AR)plot for di?erent sampling periods.The blue curve?ts the red line,which means that the residual error is gaussian. Figure4also shows that there is not much di?erence in NMSE when di?erent nonlinearities are used.Speci?-cally,models nonlinear AR“Even”and nonlinear AR “Odd”give the same prediction error as model non-linear AR“All”.Since,nonlinear AR“All”is signi?-cantly simpler than the other nonlinear AR models,we restrict our attention to nonlinear AR“All”. Similar tests were carried out for other types of nonlin-earities,including cross terms between the past and the present samples.These tests yield similar conclusion as above.In addition,other simulations for other topolo-gies and other types of tra?c also yield similar results. Thus,we only consider linear AR and nonlinear AR “All”models. 4Predictability of FTP and HTTP Tra?c In this section,we investigate the predictability of FTP and HTTP tra?c.In the following subsection,we dis-cuss the?ndings for the?rst queuing discipline where the drop probability is set and packet arrivals are ob- served.In subsection4.2,we discuss predictability with the second queuing discipline,where we observe the packet arrivals and packet drops are a result of queue over?ow.Moreover,the study of each discipline is divided into a4-fold study,two di?erent topologies (dumbbell and parking lot)and two types of tra?c (FTP and HTTP). 4.1Predictability of FTP and HTTP Tra?c with Variable Drop Probability Here we focus on the?rst queuing discipline.First,we discuss the results for FTP tra?c and then for HTTP tra?c.And last,we study the worst case prediction Figure6:MSE versus sampling period for dumbbell and parking lot topologies for FTP tra?c. Figure7:NMSE versus sampling period for dumbbell and parking lot topologies for FTP tra?c. scenario for this queue discipline. 4.1.1Predictability of FTP Tra?c with Variable Drop Probability:Figures6,7,8,and 9show the MSE,NMSE,NMSE-SP,and the order,re-spectively,for both topologies.In these simulations, the tra?c is FTP.The models under investigation are linear AR and nonlinear AR.Each model makes a one step ahead prediction of packet arrivals given the packet arrivals and drop probability(labeled as“with input”)or given only the past packet arrivals(labeled as“without input”). First consider the performance at small sample periods. Observe that the MSE,NMSE,and NMSE-SP are the Figure8:NMSE-SP versus sampling period for dumbbell and parking lot topologies for FTP tra?c. Figure9:Order of the system versus sampling period for dumbbell and parking lot topologies for FTP tra?c. same regardless of whether input is used or not(Fig- ures6,7,and8).Hence,y mainly depends on its past and the drop probability does not play a signi?cant role.This conclusion seems to hold for both parking lot and dumbbell topologies.By examining Figure7, it appears that the dynamic model outperforms a pre-dictor that just uses the mean as the prediction.This conclusion seems to hold for both the dumbbell topol-ogy and the parking lot topology.However,for the very small sample period of10ms,NMSE is large for the parking lot topology.This large error may be due to the fact that the system order for these small sample periods are very large and we limited the system order to less than50.Note that Figure9shows that for small sample periods,the system order is large.This seems to indicate that the tra?c is described by a complicated dynamical system.However,for these small sample pe-riods,it is possible to use the simple predictor(3).Such a simple predictor performs quite well for small sample periods(Figure8).Hence,we conclude that,while the tra?c may incorporate some complicated dynamics,a signi?cant part of the dynamics is simple. One might expect that for very small sample periods such as10ms,the predictor(3)should perform well. However,the packet arrivals make a discrete event sys-tem.Hence,for very small sample periods,there is either one arrival or none.Such a signal might not be well modeled by(3). For large sampling periods,an increase in the sampling period leads to decrease in the MSE for the models with input whereas it leads to an increase in the MSE for the models without input(Figure6).Similarly,Figures7 and8indicate that a signi?cantly better predictor can be obtained if drop probability is utilized.Further-more,Figure9shows that for large sample periods the system order is small.By examining the coe?cients,it can be seen that,for these sample periods,the arrivals solely depends on the drop probability.Essentially,for large sample periods,the predictor b y(k+1)is an ap-proximation of the function E(b y(k+1)|p k).Figure10:MSE versus sampling period for dumbbell and parking lot topologies for HTTP tra?c. Figure11:NMSE versus sampling period for dumbbell and parking lot topologies for HTTP tra?c. Comparing the left and right plots in Figures7and8it can be observed that,as the sample period is increased, the prediction error decreases faster for the dumbbell topology than for the parking lot topology.This is due to the more complicated dynamics of the parking lot topology.Speci?cally,it seems that the transients take longer to die out in the case of the parking lot topology. This implies that in order to determine the average behavior of the link,it is necessary to average over time windows at least500seconds long.It is plausible that the time windows would have to be even larger for more complicated topologies found in the Internet. Finally,note that the nonlinear AR has nearly the same or slightly less prediction error than the linear AR. 4.1.2Predictability of HTTP Tra?c with Variable Drop Probability:Figures10,11,and 12show the MSE,NMSE,and NMSE-SP,respectively, for both topologies.In these simulations,the tra?c is HTTP. HTTP tra?c is more stochastic as there are many fac-tors in?uencing the tra?c.As a consequence,even for the dumbbell topology,the degree of predictability for all the models is the same(Figure10).As in the case of FTP tra?c,the prediction error is fairly large for small sample period.However,when normalized by the variance of the signal,we see that the NMSE Figure12:NMSE-SP versus sampling period for dumb-bell and parking lot topologies for HTTP traf- ?c. is small for these sample periods.For example,in all cases,the NMSE is less than0.50when sample period is100ms.Furthermore,as above,nonlinear AR per-forms slightly better at smaller sampling period than linear AR(Figures7,12). As the sampling period gets larger,we see a strong dis-crepancy between FTP and HTTP tra?c.One might expect the NMSE to be small for larger sampling pe-riods for the input-output system.But that does not hold true in the case of HTTP tra?c.For example, consider the large NMSE at sample period of5000sec-onds for the input-output system.In the case of FTP tra?c,NMSE was very small due to averaging over large sampling periods.The dynamic model found for these large sample periods is an approximation of the function E(y|p).However,this function strongly de-pends on the number of FTP?ows,which is?xed.On the other hand,at any particular moment,HTTP traf-?c is made up of a varying number of TCP?ows.The number of TCP?ows is a random variable whose dis-tribution depends on parameters such as the average time between the completion of a transmission and the start of the next connection,the distribution of the?le sizes,and the topology.Thus,while it may be possible to determine E(y|p,number of TCP?ows),in order to predict the HTTP tra?c,the number of?ows must also be predicted.These results show that linear prediction of the number of?ows does not seem to work very well. 4.1.3Predictability in the Worst Case En-vironment:While the above showed that in some cases the dynamic predictor works well,it seems that its performance is dependent on the topology and type of tra?c.In general,the exact mix of tra?c is not known in advance and the topology is not?xed.Thus, we demand that a predictor works well in all envi-ronments.Figure13shows the worst case normal-ized prediction error.Speci?cally,the normalized error for a particular sample period is normalized over both topologies and both types of tra?c.The left plot in Figure13:Maximum NMSE and NMSE-SP versus Sam-pling Period.NMSE and NMSE-SP are maxi- mized over both the topologies and both types of tra?cs. Figure13shows the error when normalized with the result from the error when predictor(2)is used,while the right shows the result when normalized by the error when predictor(3)is used.It is clear that the linear and nonlinear dynamic predictors fail to perform signif-icantly better than trivial predictors.Speci?cally,while it is true that at a sample period of100ms,the dynamic predictors perform better than a constant predictor of the mean,at this sample period,the predictor(3)per-forms nearly as well as the dynamic predictor.On the other hand,for large sample periods,the predictor(3) does not perform very well.However,for large sample periods,the mean predictor(2)performs as well as the dynamic predictor.Note that in no case can we expect the error variance from the dynamic predictors to be less than half the size of the error variance due to the simple predictors.π 4.2Predictability of FTP and HTTP with Drop Tail Queue Next,we discuss the?ndings for the second environ-ment where we observe the packet drops caused by queue over?ow.In this setting we do not know the packet drops ahead of time.However,in an attempt to improve performance,the drop probability over the previous sample period is found and this observation is utilized to predict the packet arrivals.Note that in the case of variable drop probability,the drop proba-bility was known for the sample over which the packet arrivals are to be predicted.In the case investigated in this section,the drop probability is observed over the sample interval prior to the one over which the packet arrivals is to be predicted.As will be made clear,this delay results in the drop probability observation having little e?ect on the quality of prediction. Again,we study?rst FTP and then HTTP tra?c.And last we discuss the worst case prediction scenario for this queueing discipline. Figure 14:MSE versus sampling period for dumbbell and parking lot topologies for FTP tra ?c. Figure 15:NMSE versus sampling period for dumbbell and parking lot topologies for FTP tra ?c. Figures 14,15,and 16show the MSE,NMSE and NMSE-SP plots respectively,for dumbbell and park-ing lot topologies.Observe that the MSE decreases as the sampling period increases for both the topol-ogy (Figure 14).However,Figure 15shows that the NMSE increases with the sampling period.Speci ?cally,for sample periods of 500ms for the dumbbell topology and 10seconds for the parking lot topology,the mean is as good of a predictor as the dynamic predictors.For small sample periods,we see that dynamic predic-tors greatly out-perform the simple predictors in the case of the dumbbell topology.Indeed,the prediction error variance for the dynamic predictors can be as much as 100times smaller than the error variance for the simple predictors.However,the left hand plots of Figures 15and 16show that,if a more complex topol-ogy is considered,the predictability evaporates.The results for HTTP tra ?c are similar.For small sample periods,it appears that the tra ?c is slightly predictable,and as the sample period increases,the normalized prediction error becomes large. Figure 20shows the normalize prediction error maxi-mized over all topologies and all types of tra ?c.This Figure shows that the dynamic predictor’s error vari-ance is between the same size as the simple predictors’error variance and half the size of the simple predictors’error variance. Figure 16:NMSE versus sampling period for dumbbell and parking lot topology for FTP tra ?c. Figure 17:MSE versus sampling period for dumbbell and parking lot topology for HTTP tra ?c. Figure 18:NMSE versus sampling period for dumbbell and parking lot topologies for HTTP tra ?c. Figure 19:NMSE-SP versus sampling period for dumb-bell and parking lot topologies for HTTP traf-?c. Figure20:Maximum NMSE and NMSE-SP versus Sam-pling Period.NMSE and NMSE-SP are maxi- mized over both the topologies and both types of tra?cs. 5Conclusion Improving congestion control and queue management algorithms have been active areas of research over the past few years.The inherent problem with these AQM algorithms is that they use average queue length as in-dicator of the severity of the congestion.Perhaps the most signi?cant approach is Random Early Drop(RED [1]).The basic idea behind the RED scheme is to de-tect incipient congestion early and to convey congestion noti?cation to the end-hosts,allowing them to reduce their transmission rates before queues in the network over?ow and packets are dropped.RED uses average queue length to re?ect future congestion to which it reacts by setting a packet drop/mark probability.This paper shows that such an approach could not be feasi-ble as prediction of the future packet arrivals based on a smoothed version of queue occupancy appears to not be possible over arbitrary time scales.However,there are other interpretations of RED.For example,when more?ows are active,the queue is typically larger than when there are fewer?ows.From this point of view, RED does not attempt to control the dynamic behav-ior of TCP,but instead accounts for variations in the number of?ows by exploiting the steady state relation-ship between TCP’s sending rate.Our work says that there is a possibility of controlling at larger time scale when the focus is centered around end-user action.On the other hand,our work says that at smaller time scale where the TCP’s dynamics dominates the tra?c characteristics,control does not seem to be possible. Finally,in TCP’s steady state,the dynamical predic-tors do not show improvement over simple predictor E(y/p)(2).Hence,the mean of the packet arrivals is a good estimate of end-user behavior. Furthermore,from the deeper control theoretic view-point of limiting packet arrival?uctuation,the issue is whether a loop wrapped around the model could reject the modeling error noise,which has a?at power spec-tral density.The Bode limitation[25]indicates that this can be done only over low frequency,and away from the nonminimum phase zeros,and at the expense of amplifying the small time scale modeling error.This is left for further research. References [1]S.Floyd and V.Jacobson,“Random early detec-tion gateways for congestion avoidance,”vol.V1N.4, pp.397—413,August1993. [2]S.Athuraliya,V.H.Li,S.H.Low,and Q.Yin,“REM:Active queue management,”in IEEE Network, May/June2001. [3]S.Kunniyur and R.Srikant,“Analysis and de-sign of an adaptive virtual queue(AVQ)algorigthm for active queue management,”in SIGCOMM,2001. [4] C. A.for Internet Data Analysis(CAIDA),“https://www.wendangku.net/doc/967903678.html,.” [5]N.L.for Applied Network Research(NLANR),“https://www.wendangku.net/doc/967903678.html,.” [6] C.You and K.Chandra,“TIME SERIES MOD-ELS FOR INTERNET DATA TRAFFIC,”in Proc. 24th Conf.On Local Computer Networks,1999. [7]K.Thompson,https://www.wendangku.net/doc/967903678.html,ler,and R.Wilder,“Wide-area internet tra?c patterns and characteris-tics,”IEEE Network,vol.11,1997. [8]S.Floyd,“Connections with muliple congested gateways in packet-switched networks part1:One-way tra?c,”Computer Communication Review,vol.21, pp.30—47,1991. [9]M.Mathis,J.Semke,J.Mahdavi,and T.Ott,“The macroscopic behavior of TCP congestion avoid-ance algorithm,”Computer Communication Review, vol.27,1997. [10]S.Low, F.Paganini,and J.Doyle,“Internet congestion control,”IEEE Control Systems Magazine, vol.22,pp.28—43,2002. [11]S.Kunniyur and R.Srikant,“End-to-end conges-tion control:Utility functions,random loss and ECN marks,”in Proceedings of INFOCOM2000,March, 2000. [12]S.Bohacek,J.Hespanha,K.Obraczka,and J.Lee,“Analysis of a TCP hybird model,”in In Pro-ceedings of the39th Annual Allerton Conference on Communication,Control and Computing,,2001. [13] F.Baccelli and D.Hong,“TCP is max-plus lin-ear,”Proc.of ACMSIGCOMM,vol.30,No.4,pp.219—230,2000. [14]Y.Chait, C.Hollot,V.Misra,H.Han,and Y.Halevi,“Dynamic analysis of congested TCP net-works,”in ACC,2002. [15]Y.Joo,V.Ribeiro,A.Feldmann,A.C.Gilbert, and W.Willinger,“TCP/IP tra?c dynamics and net-work performance:A lesson in workload modeling,?ow control,and trace-driven simulations,”SIGCOMM Computer Communication Review,vol.31,2001. [16] A.Veres and M.Boda,“The chaotic nature of TCP congestion control,”in INFOCOM,pp.1715—1723,2000. [17]L.Ljung,System Identi?cation;Theory for the User.Prentice Hall,1987. [18]K.S.Edmond Jonckheere and S.Bohacek,“Time series modeling of internet tra?c for intrusion detec-tion,”in American Conference on Control,June2002. [19]H.Akaike,“A new look at the statistical model identi?cation,”in IEEE Transactions on Automatic Control,AC-19,pp.716—723,1974. [20]J.Rissanen,“Modeling by shortest data descrip-tion,”Automatica,vol.14,pp.465—471,1978. [21]S.Floyd,“Simulation tests.available at ftp://https://www.wendangku.net/doc/967903678.html,/Papers/Simtests.ps.z.ns is avail-able at https://www.wendangku.net/doc/967903678.html,/Nrg.,”July1995. [22] B.A.Mah,“An empirical model of HTTP net-work tra?c,”(Kobe,Japan),Published in the Proceed-ings of INFOCOM,April7-11,1997. [23]M.E.Crovella and A.Bestavros,“Self-similarity in world wide web tra?c:Evidence and possible causes.,”in In the Proceedings of the ACM SIGMET-RICS Confernece on Measurement and Modeling of Computer Systems.,(Philadelphia,PA),pp.160—169, May1996. [24]W.Leland,M.Taqqu,W.Willinger,and D.Wil-son,“On the self-similar nature of ethernet traf-?c(extended version),”pp.1—15,IEEE/ACM Trans-actions on Networking,2,1994. [25] B.-F.Wu and E.Jonckheere,“A simpli?ed ap-proach to bode’s theorem for continuous-time and discrete-time systems,”IEEE Transactions on Auto-matic Control,vol.37,No.11,pp.1797—1802,1992. 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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. 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The weather was so comfortable that I settled myself into the 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 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. 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. 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. 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。 【it's time to和it's time for】 ——————这其实是一个句型,只不过后面要跟不同的东西. ——————It's time to跟的是不定式（to do）.也就是说,要跟一个动词,意思是“到做某事的时候了”.如： It's time to go home. It's time to tell him the truth. ——————It's time for 跟的是名词.也就是说,不能跟动词.如： It's time for lunch.(没必要说It's time to have lunch) It's time for class.(没必要说It's time to begin the class.) They can't wait to see you Please ask liming to study tonight. Please ask liming not to play computer games tonight. Don’t make/let me to smoke I can hear/see you dance at the stage You had better go to bed early. You had better not watch tv It’s better to go to bed early It’s best to run in the morning I am enjoy running with music. With 表伴随听音乐 I already finish studying You should keep working. You should keep on studying English Keep calm and carry on 保持冷静继续前行二战开始前英国皇家政府制造的海报名字 I have to go on studying I feel like I am flying I have to stop playing computer games and stop to go home now I forget/remember to finish my homework. I forget/remember cleaning the classroom We keep/percent/stop him from eating more chips I prefer orange to apple I prefer to walk rather than run I used to sing when I was young What’s wrong with you There have nothing to do with you I am so busy studying You are too young to na?ve I am so tired that I have to go to bed early 《The Kite Runner》追风筝的人--------------------------------美句摘抄 1.I can still see Hassan up on that tree, sunlight flickering through the leaves on his almost perfectly round face, a face like a Chinese doll chiseled from hardwood: his flat, broad nose and slanting, narrow eyes like bamboo leaves, eyes that looked, depending on the light, gold, green even sapphire 翻译：我依然能记得哈桑坐在树上的样子，阳光穿过叶子，照着他那浑圆的脸庞。他的脸很像木头刻成的中国娃娃，鼻子大而扁平，双眼眯斜如同竹叶，在不同光线下会显现出金色、绿色，甚至是宝石蓝。 E.g.: A shadow of disquiet flickering over his face. 2.Never told that the mirror, like shooting walnuts at the neighbor's dog, was always my idea. 翻译：从来不提镜子、用胡桃射狗其实都是我的鬼主意。E.g.:His secret died with him, for he never told anyone. 3.We would sit across from each other on a pair of high 一、翻译 1. The idea of consciously seeking out a special title was new to me., but not without appeal. 让我自己挑选自己最喜欢的书籍这个有意思的想法真的对我具有吸引力。 2.I was plunged into the aching tragedy of the Holocaust, the extraordinary clash of good, represented by the one decent man, and evil. 我陷入到大屠杀悲剧的痛苦之中，一个体面的人所代表的善与恶的猛烈冲击之中。 3.I was astonished by the the great power a novel could contain. I lacked the vocabulary to translate my feelings into words. 我被这部小说所包含的巨大能量感到震惊。我无法用语言来表达我的感情（心情）。 4，make sth. long to short长话短说 5.I learned that summer that reading was not the innocent(简单的) pastime(消遣) I have assumed it to be., not a breezy, instantly forgettable escape in the hammock(吊床)，( though I’ ve enjoyed many of those too ). I discovered that a book, if it arrives at the right moment, in the proper season, will change the course of all that follows. 那年夏天，我懂得了读书不是我认为的简单的娱乐消遣，也不只是躺在吊床上，一阵风吹过就忘记的消遣。我发现如果在适宜的时间、合适的季节读一本书的话，他将能改变一个人以后的人生道路。 二、词组造句 1. on purpose 特意，故意 This is especially true here, and it was ~. (这一点在这里尤其准确，并且他是故意的) 2.think up 虚构，编造，想出 She has thought up a good idea. 她想出了一个好的主意。 His story was thought up. 他的故事是编出来的。 3. in the meantime 与此同时 助记：in advance 事前in the meantime 与此同时in place 适当地... In the meantime, what can you do? 在这期间您能做什么呢？ In the meantime, we may not know how it works, but we know that it works. 在此期间，我们不知道它是如何工作的，但我们知道，它的确在发挥作用。 4.as though 好像，仿佛 It sounds as though you enjoyed Great wall. 这听起来好像你喜欢长城。 5. plunge into 使陷入 He plunged the room into darkness by switching off the light. 他把灯一关，房 The effective sentences:(improve the sentences!) 1.She hopes to spend this holiday either in Shanghai or in Suzhou. 2.Showing/to show sincerity and to keep/keeping promises are the basic requirements of a real friend. 3.I want to know the space of this house and when it was built. I want to know how big this house is and when it was built. I want to know the space of this house and the building time of the house. 4.In the past ten years,Mr.Smith has been a waiter,a tour guide,and taught English. In the past ten years,Mr.Smith has been a waiter,a tour guide,and an English teacher. 5.They are sweeping the floor wearing masks. They are sweeping the floor by wearing masks. wearing masks,They are sweeping the floor. 6.the drivers are told to drive carefully on the radio. the drivers are told on the radio to drive carefully 7.I almost spent two hours on this exercises. I spent almost two hours on this exercises. 8.Checking carefully,a serious mistake was found in the design. Checking carefully,I found a serious mistake in the design. M1 U1 一. 把下列短语填入每个句子的空白处（注意所填短语的形式变化）： add up (to) be concerned about go through set down a series of on purpose in order to according to get along with fall in love (with) join in have got to hide away face to face 1 We’ve chatted online for some time but we have never met ___________. 2 It is nearly 11 o’clock yet he is not back. His mother ____________ him. 3 The Lius ___________ hard times before liberation. 4 ____________ get a good mark I worked very hard before the exam. 5 I think the window was broken ___________ by someone. 6 You should ___________ the language points on the blackboard. They are useful. 7 They met at Tom’s party and later on ____________ with each other. 8 You can find ____________ English reading materials in the school library. 9 I am easy to be with and _____________my classmates pretty well. 10 They __________ in a small village so that they might not be found. 11 Which of the following statements is not right ____________ the above passage? 12 It’s getting dark. I ___________ be off now. 13 More than 1,000 workers ___________ the general strike last week. 14 All her earnings _____________ about 3,000 yuan per month. 二.用以下短语造句： 1.go through 2. no longer/ not… any longer 3. on purpose 4. calm… down 5. happen to 6. set down 7. wonder if 三. 翻译： 1.曾经有段时间，我对学习丧失了兴趣。（there was a time when…） 2. 这是我第一次和她交流。（It is/was the first time that …注意时态） 3.他昨天公园里遇到的是他的一个老朋友。（强调句） 4. 他是在知道真相之后才意识到错怪女儿了。（强调句） M 1 U 2 一. 把下列短语填入每个句子的空白处（注意所填短语的形式变化）： play a …role (in) because of come up such as even if play a …part (in) 1 Dujiangyan(都江堰) is still ___________in irrigation(灌溉) today. 2 That question ___________ at yesterday’s meeting. 3 Karl Marx could speak a few foreign languages, _________Russian and English. 4 You must ask for leave first __________ you have something very important. 5 The media _________ major ________ in influencing people’s opinion s. 6 _________ years of hard work she looked like a woman in her fifties. 二.用以下短语造句： 1.make (good/full) use of 2. play a(n) important role in 3. even if 4. believe it or not 5. such as 6. because of English sentence 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. 句子：He is in America. 10、appear 出现v. He appears in this place. 11. artist 艺术家n. He is an artist. 12. attract 吸引 He attracts the dog. 13. Australia 澳大利亚 He is in Australia. 14.base 基地 She is in the base now. 15.basket 篮子 His basket is nice. 16.beautiful 美丽的 She is very beautiful. 17.begin 开始 He begins writing. 18.black 黑色的 He is black. 19.bright 明亮的 His eyes are bright. 20.good 好的 He is good at basketball. 21.British 英国人 He is British. 22.building 建造物 The building is highest in this city 23.busy 忙的 He is busy now. 24.calculate 计算 He calculates this test well. 25.Canada 加拿大 He borns in Canada. 26.care 照顾 He cared she yesterday. 27.certain 无疑的 They are certain to succeed. 28.change 改变 He changes the system. 29.chemical 化学药品on the contrary的解析
英语造句
学生造句--Unit 1
英语句子结构和造句
六级单词解析造句记忆MNO
base on的例句
英语造句大全
(完整版)主谓造句
初中英语造句
The Kite Runner-美句摘抄及造句
翻译加造句
改写句子练习2标准答案
用以下短语造句
英语造句