Modeling Communication Networks with Hybrid Systems Extended Version

1 Modeling Communication Networks with Hybrid Systems:

Extended Version

Junsoo Lee Stephan Bohacek Jo?a o P.Hespanha Katia Obraczka jslee@sookmyung.ac.kr bohacek@https://www.sodocs.net/doc/e510056313.html, hespanha@https://www.sodocs.net/doc/e510056313.html, katia@https://www.sodocs.net/doc/e510056313.html, Dept.Electrical&Computer Engineering,Univ.of Delaware,Newark,DE19716

Dept.Electrical&Computer Engineering,Univ.of California Santa Barbara,CA93106-9560

Department of Computer Science,Sookmyung Women’s Univ.,Seoul,Korea140-742

Computer Engineering Department,University of California Santa Cruz,CA95064

Abstract—This paper introduces a general hybrid systems framework to model the?ow of traf?c in communication networks.The proposed models use averaging to continuously approximate discrete variables such as congestion window and queue size.Because averaging occurs over short time intervals, discrete events such as the occurrence of a drop and the consequent reaction by congestion control can still be captured. This modeling framework thus?lls a gap between purely packet-level and?uid-based models,faithfully capturing the dynamics of transient phenomena and yet providing signi?cant?exibility in modeling various congestion control mechanisms,different queuing policies,multicast transmission,etc.

The modeling framework is validated by comparing simula-tions of the hybrid models against packet-level simulations.It is shown that the probability density functions produced by the ns-2network simulator match closely those obtained with hybrid models.Moreover,a complexity analysis supports the observation that in networks with large per-?ow bandwidths,simulations using hybrid models require signi?cantly less computational resources than ns-2simulations.

Tools developed to automate the generation and simulation of hybrid systems models are also presented.Their use is showcased in a study,which simulates TCP?ows with different round-trip times over the Abilene backbone.

Index Terms—Data Communication Networks,Congestion Control,TCP,UDP,Simulation,Hybrid Systems

I.I NTRODUCTION

D ATA communication networks are highly complex sys-

tems,thus modeling and analyzing their behavior is quite challenging.The problem aggravates as networks be-come larger and more complex.Packet-level models are the most accurate network models and work by keeping track of individual packets as they travel across the network.Packet-level models,which are used in network simulators such as ns-2[1],have two main drawbacks:the large computational requirements(both in processing and storage)for large-scale simulations and the dif?culty in understanding how network parameters affect the overall system performance.Aggregate ?uid-like models overcome these problems by simply keeping track of the average quantities that are relevant for network design and provisioning(such as queue sizes,transmission rates,drop rates,etc).Examples of?uid models that have This work has been supported by the National Science Foundation under Grant Nos.ANI-0322476and CCR-0311084.been proposed to study computer networks include[2],[3]. The main limitation of these aggregate models is that they mostly capture steady state behavior because the averaging is typically done over large time scales.Thus,detailed transient behavior during congestion control cannot be captured.Conse-quently,these models are unsuitable for a number of scenarios, including capturing the dynamics of short-lived?ows.

Our approach to modeling computer networks and its pro-tocols is to use hybrid systems[4]which combine continuous-time dynamics with event-based logic.These models permit complexity reduction through continuous approximation of variables like queue and congestion window size,without compromising the expressiveness of logic-based models.The “hybridness”of the model comes from the fact that,by using averaging,many variables that are essentially discrete(such as queue and window sizes)are allowed to take continuous values.However,because averaging occurs over short time intervals,one still models discrete events such as the occur-rence of a drop and the consequent reaction by congestion control.

In this paper,we propose a general framework for building hybrid models that describe network behavior.Our hybrid systems framework?lls the gap between packet-level and aggregate models by averaging discrete variables over a short time scale on the order of a round-trip time(RTT).This means that the model is able to capture the dynamics of transient phenomena fairly accurately,as long as their time constants are larger than a couple of RTTs.This time scale is appropriate for the analysis and design of network protocols including congestion control mechanisms.

We use TCP as a case-study to showcase the accuracy and ef?ciency of the models that can be built using the proposed framework.We are able to model fairly accurately TCP’s distinct congestion control modes(e.g.,slow-start,congestion avoidance,fast recovery,etc.)as these last for periods no shorter than one RTT.One should keep in mind that the timing at which events occur in the model(e.g.,drops or transitions between TCP modes)is only accurate up to roughly one RTT. However,since the variations on the RTT typically occur at a slower time scale,the hybrid models can still capture quite accurately the dynamics of RTT evolution.In fact,that is one

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of the strengths of the models proposed here,i.e.,the fact that they do not assume constant RTT.

We validate our modeling methodology by comparing sim-ulation results obtained from hybrid models and packet-level simulations.We ran extensive simulations using different net-work topologies subject to different traf?c conditions(includ-ing background traf?c).Our results show that hybrid models are able to reproduce packet-level simulations quite accurately. We also compare the run-time of the two approaches and show that hybrid models incur considerably less computational load. We anticipate that speedups yielded by hybrid models will be instrumental in studying large-scale,more complex networks. Finally,we describe the Network Description Scripting Language(NDSL)and the NDSL Translator,which were developed to automate the generation and simulation of hybrid systems models.NDSL is a scripting language that allows the user to specify network topologies and traf?c.The NDSL translator automatically generates the corresponding hybrid models in the modelica modeling language[5].We show-case these tools in a simulation study on the effect of the RTT on the throughput of TCP?ows over the Abilene backbone[6]. An early version of this work appeared in[7].The current paper includes additional models and improvements to the models proposed in[7]and a far more extensive validation study using complex topologies.The hybrid language imple-mentations described in this paper are available at[8].We also introduce the NDSL and the NDSL Translator as well as an illustration of their use in a real,larger-scale,high-speed network.

II.R ELATED W ORK

Several approaches to the modeling and simulation of networks have been widely used by the networking community to design and evaluate network protocols.On one side of the spectrum,there are packet-level simulation models:ns-2[1],QualNet[9],SSFNET[10],Opnet[11]are event simulators where an event is the arrival or departure of a packet.Whenever a packet arrives at the link or node,events are generated and stored in the event list and handled in the appropriate order.These models are highly accurate,but are not scalable to large networks.On the other extreme,static models provide approximations using?rst principles:[3],[12] provide simple formulas that model how TCP behaves in steady-state.These models ignore much of the dynamics of the network.For example,the RTT and loss probability are assumed constant and the interaction between?ows is not considered.

Dynamic model fall between static models and detailed packet-level simulators.By allowing some parameters to vary, these models attempt to obtain more accuracy than static approaches,and yet alleviate some of the computational over-head of packet-level simulations.This modeling approach was followed by[13],where TCP’s sending rate is taken as an ensemble average.When averaging across multiple?ows,the sending rates do not exhibit the linear increase and divide in half.However,the ensemble average still varies dynamically with queue size and drop probability.[2]proposes a stochastic differential equation(SDE)model of TCP,in which the sending rate increases linearly until a drop event occurs and then it is divided in half.Along the same lines,[14]developed an alternative SDE model that allows the RTT to vary and includes more accurate packet drop models.While these SDE approaches make sense from an end-to-end perspective,they are dif?cult to justify in models of the overall network.The main dif?culty is that,from the network perspective,drops in different?ows are highly correlated.This interdependence is dif?cult to ef?ciently incorporate into the SDE approach. While the dynamic models above proved very useful for developing a theoretical understanding of networks,their pur-pose was not to simulate networks.In an effort to simulate networks ef?ciently,[15],[16]proposed a?uid-like approach in which bit rates are assumed to be piecewise constant.This type of network simulator only needs to keep track of rate changes that occur due to queuing,multiplexing,and services. As a results,the computational effort may be reduced with respect to a packet-level simulators.However,the piecewise constant assumption can lead to an explosion of events known as the ripple effect[17],which can signi?cantly increase the computational load.A somewhat similar approach was followed by[18],in which packets are aggregated into sets and during a single time-step,it is assumed that all packets in a set behave the same.

Systems that exhibit continuously varying variables whose values are affected by events generated by discrete-logic are known as hybrid systems and have been widely used in many ?elds to model physical systems.The reader is referred to[4] for a general overview of hybrid systems.An early hybrid modeling approach to computer systems appeared in[19], where the author proposes to combine discrete-event models with continuous analytic models.The former are used to capture“rare-events,”whereas the latter avoid the need to carry out the detailed simulation of very frequent events. This general framework was used in[19]to simulate a central server systems consisting of a CPU and several IO devices serving multiple jobs.The hybrid model was shown to accurately predict the behavior of a detailed purely event-based simulation with reduced computation.Our work can be viewed as an instantiation of the general framework proposed in[19]to the problem of traf?c modeling.[20]applied hybrid simulation techniques to perform large-scale multicast simulations.To decrease the computational cost,the message exchanges needed to update routes are not explicitly simulated (centralized multicast abstraction).To further improve scala-bility the authors also propose to avoid the explicit modeling of hop-by-hop transmissions between intermediate nodes and only consider end-to-end transmissions,assuming very simple models for end-to-end queuing delay.The resulting models are very scalable but,according to the authors of[20],not adequate to study queuing behavior and congestion control. More recently,[21]proposed a simulation method that com-bines?uid models of background TCP traf?c with packet-level models of foreground traf?c.The approach used in[21] requires active queue management(AQM)for the background TCP traf?c using the stochastic?uid models in[2].

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Traf?c sampling [22]consists of taking a sample of network traf?c,feeding it into a suitably scaled version of the network,and then using the results so obtained to extrapolate the behavior of the original network.This has been proposed as a methodology to ef?ciently simulate large-scale networks by combining simulation and analytical techniques.However,it loses scalability when packet drops are bursty and correlated,or when packet drops are not accurately modeled by a Poisson process.

The remainder of the paper is organized as follows.Sec-tion III presents our hybrid systems modeling framework.In Section IV,we validate our hybrid models by comparing them to packet-level simulations.Section V shows results comparing the computational complexity of hybrid-and packet-level models,and section VII shows development tools and case study using these tools.Finally,we present our concluding remarks and directions for future work in Section VIII.

III.H YBRID M ODELING F RAMEWORK

Consider a communication network consisting of a set of nodes connected by a set of links .We assume that all links are unidirectional and denote by the link from node to node (cf.Figure 1).Every link is characterized by a ?nite bandwidth and a propagation delay

.

where denotes the set of links involved in one round-trip for ?ow .

A.Flow conservation laws

Consider a link in the path of ?ow .We denote by the rate at which -?ow packets arrive (or originate)at the node where starts.We call the -link/-?ow arrival

rate .The link/?ow arrival rates

are related to the ?ow sending rates and the link/?ow transmission rates by the following simple ?ow-conservation law :for every and ,

starts at the node where

starts

otherwise

(3)

where denotes the previous link in the path of the -?ow.For simplicity,we are assuming single-path routing and unicast transmission.It would be straightforward to derive conserva-tion laws for multi-path routing and multi-cast transmission.

The ?ow-conservation law (3)implicitly assumes that pack-ets are not dropped “on-the-?y.”For consistency,we will re-gard packet drops that occur in the transmission medium (e.g.,needed to model wireless links)as taking place upon arrival at the destination node.From a traf?c modeling perspective this makes no difference but somewhat simpli?es the notation.B.Queue dynamics

In this section,we make two basic assumptions regarding ?ow uniformity that are used to derive our models for the queue dynamics:

Assumption 1(Arrival uniformity):The packets of the all ?ows arrive at each node in their paths roughly uniformly distributed over time.Consequently,the packets of each ?ow are roughly uniformly distributed along each queue.Because of packet quantization,bursting,synchronization,etc.,this assumption are never quite true over a very small interval of time.However,they are generally accurate over time intervals of a few RTTs.In fact,we shall see shortly that they are suf?ciently accurate to lead to models that match closely packet-level simulations.

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1)Queue-evolution and drop rates:Consider a link

that is in the path of the?ow.The queue dynamics associated with this pair link/?ow are given by

where denotes the-?ow drop rate.In this equation should be regarded as an input whose value is determined by upstream nodes.To determine the values of and we consider three cases separately:

1)Empty queue(i.e.,).In this situation there are no

drops and the outgoing rates are equal to the arrival rates,as long as the bandwidth constrain(1)is not violated.However,when,we cannot have,and the available link bandwidth

must be somehow distributed amount the?ows so that

.To determine how to distribute,we note that a total of bytes arrive at the queue in a single unit of time.Assuming arrival uniformity (Assumption1)all incoming packets are equally likely to be transmitted so the probability that a packet of?ow

is indeed transmitted is given by

The above discussion can be summarized as follows:for every,

(5)

Since a total of bytes will be transmitted per unit of time,the faction of these that correspond to?ow is given by

3)Queue full and still?lling(i.e.,and

).In this situation the total drop rate must equal the difference between the total arrival rate and the link bandwidth,i.e.,.

Once again,we must determine how this total drop rate should be distributed among all?ows.Assuming arrival uniformity(Assumption1)all incoming packets are equally likely to be dropped so the probability that

a packet of?ow is indeed dropped is given by

The rate at which packets are transmitted is the same as when the queue is neither empty not full,which was considered above.This leads to the following model:for every,

(7)

To complete the queue dynamics model,it remains to determine when and which?ows suffer drops.To this ef-fect,suppose that at time,reached with

.Clearly,a drop will occur at time but, multiple drops may occur.In general,if a drop occurred at time a new drop is expected at a time for which the total drop rate integrates from to to exactly the packet-size,i.e.,for which

(8)

This equation determines,for all drops after. We call(8)the drop-count model.

The question as to which?ows suffer drops must be consistent with the drop probability speci?ed by(6),which was a consequence of the arrival uniformity Assumption1.In particular,the selection of the?ow where a drop occurs is made by drawing the?ow randomly from the set,according to the distribution

(9) We assume that the?ows,that suffer drops at two distinct time instants,are(conditionally) independent random variables(given that the drops did occur at times and).We call(9)the drop-selection model. The uniformity Assumption1was used in the construc-tion of our queue model to justify the formulas(4),(5) for the packet transmission probabilities and the formula(6) for the packet drop probability.To validate this assumption,

5 we matched these formulas with the results of several ns-

2[1]simulations.Figure2shows the result of one such

validation procedure for the formula(6).Figure2(a)refers

to a simulation in which2TCP?ows(RED and BLUE)

compete for bandwidth on a bottleneck queue(with10%ON-

OFF UDP traf?c).The-axis shows the fraction of arrival rate

for each?ow given by the formula(6)and the-axis shows the

corresponding drop probability.A near perfect45-degree line

shows that(6)does provide a very good approximation to the

packet drop probability.Figure2(b)shows a network with very

strong drop synchronization for which Assumption1breaks

down.We postpone the discussion of this plot to Section III-

B.3.Similar plots can be made to validate the formulas(4),

(5)for the packet transmission probabilities,but we do not

include them here for lack of space.However,in Section IV

we present a systematic validation of our overall hybrid model,

which includes the queue mode above as a sub-component.

(a)10%background traf?c

(b)packet synchronization

Fig.2.Drop probability vs.fraction of arrival rate.

2)Hybrid model for queue dynamics:The queue model developed above can be compactly expressed by the hybrid

automaton represented in Figure3.Each ellipse in this?gure

corresponds to a discrete state(or mode)and the continuous state of the hybrid system consists of the?ow byte rate, and the variable used to track the number of drops in the queue-full mode.The differential equations for these variables

in each mode are shown inside the corresponding ellipse.The arrows between ellipses represent transitions between modes. These transitions are labeled with their enabling conditions (which can include events generated by other transitions); any necessary reset of the continuous state that must take place when the transition occurs;and events generated by the transition.Events are denoted by.We assume here that a jump always occurs when the transition condition is enabled.This model is consistent with most of the hybrid system frameworks proposed in the literature(cf.,e.g.,[4]). The transition triggered by the Poisson counter should only be considered under active queue management(cf.,Section III-B.3below).The inputs to this model are the rates,

of the upstream queues,which determine the arrival rates,;and the outputs are the transmission rates ,.For the purpose of congestion control,we should also regard the drop events and the queue size as outputs of the hybrid model.Note that the queue sizes will eventually determine packet RTTs.The division by used in the queue-not-full mode to compute should never result in a division by zero because,if becomes zero,there is immediately a transition to the queue-empty mode where no division by

is needed.However,errors in the detection of the transition may cause a division by zero(or almost zero).To minimize numerical errors,it is then convenient to transition from queue-not-full to queue-empty when becomes smaller than some small positive constant.

3)Other drop models:For completeness one should add that the drop-selection model described by(9)is not universal. For example,in dumbbell topologies without background traf?c,one can observe synchronization phenomena that some-times lead to?ows with smaller sending rates suffering more drops than?ows with larger sending rates.The right plot in Figure2shows an extreme example of this(2TCP?ows in a5Mbps dumbbell topology with no background traf?c and drop-tail queuing).In this example,the BLUE?ow suffers most of the drops,in spite of using a smaller fraction of the bandwidth.In[23],it was suggested that10%of random delay would remove synchronization between TCP connections. However,this does not appear to be the case when the number of connections is small.To avoid synchronization we mostly used background traf?c.In fact,the left plot in Figure2 shows results obtained with10%background traf?c,whereas the right plot shows results obtained without any background traf?c.

The remainder of this section brie?y discusses other drop models that lead to different distributions for,which may be useful in speci?c situations.

Drop rotation:The drop model in(9)is not very accurate when strong synchronization occurs.Constructing drop models that remain accurate under packet-drops synchronized is gener-ally very challenging,except under special network conditions. The drop rotation model is valid in topologies with drop-tail queuing,when several TCP?ows have the roughly the same RTT and there is a bottleneck link with bandwidth signi?cantly smaller than that of the remaining links and there is no(or little)background traf?c[7],[24],[25].Under this model, when the queue gets full each?ow gets a drop in a round-robin fashion.The rationale for this is that,once the queue gets full,it will remain full until TCP reacts(approximately one RTT after the drop).In the meanwhile,all TCP?ows are in the congestion avoidance mode and each will increase its window size by one.When this occurs each will attempt to send two packets back-to-back and,under a drop-tail queuing policy,the second packet will almost certainly be dropped. Although the drop rotation model is only valid for special networks,these networks are very useful to validate congestion control because they lead to essentially deterministic drops. This allows one to compare exactly traces obtained from packet-level models with traces obtained from hybrid models. We will use this feature of drop rotation to validate our hybrid models for TCP in Section IV.

Drop-head:In the above discussion,we assumed a drop-tail queuing policy,i.e.,when the queue is full and a new packet arrives,the incoming packet is dropped.An alternative

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drop in?ow

Fig.3.Hybrid model for the queue at link.In this?gure,is given by(2),the,are given by(3),and,.

that typically leads to faster reaction to congestion is a drop-

head policy,i.e.,when the queue is full and a new packet

arrives,the head of the queue is dropped to make room for the

incoming packet.In this case,the total drop rate should be

distributed among all?ows proportionally to their percentage

of bytes already in the queue.Therefore,(7)should be replaced

by

and(9)by

Active queuing:So far we only considered drops due to

queue over?ow.When the queue at the-link operates under

an active queuing policy—such as Random Early Detection

(RED)[26]—drops or markings may occur even when

.In RED,the packets arriving at the queue associated

with the-link are dropped with a probability,which is

generally a function of the queue size(or a smoothened

version of it).The number of packet drops for the?ow in

the-link queue per unit of time is called the drop rate and

is denoted by.This rate is equal to the packet arrival rate

(in packets per second)multiplied by the probability that

each packet is dropped,i.e.,

,where denotes

the number of drops on an a small internal of length.A

more detailed discussion of this type of drop model can be

found in[27].Drops based on incoming rate and queue size

are studied in[28].

C.TCP model

So far our discussion focused on the modeling of the

transmission rates and the queue sizes across the

network,taking as inputs the sending rates of the end-to-end

?ows.We now construct a hybrid model for a single TCP?ow

that should be composed with the?ow-conservation

laws and queue dynamics presented in Sections III-A and III-

B to describe the overall system.We start by describing the

behavior of TCP in each of its main modes and later combine

them into a uni?ed hybrid model of TCP.

1)Slow-start mode:During slow-start,the congestion win-

dow(cwnd)increases exponentially,being multiplied by

2every RTT.This can be modeled by

Since packets are sent each RTT,the instantaneous sending

rate should be given by

(13)

because slow-start packets are sent in bursts.To see why the

factor is needed in slow-start,note that one packet is sent

as soon as slow-start is initiated,two more packets are sent

at the end of the?rst RTT,four additional packets are sent at

7 the end of the second RTT,and so on.This means that in the

?rst RTTs the number of packets sent is essentially equal to

(14)

On the other hand,if one integrates the sending rate(13)

over the same?rst RTTs,with given by(11),one obtains:

(15)

The two formulas(14)and(15)match when

.It turns out that a slightly better matching between the

hybrid model and ns-2traces is possible by choosing

.This is explained by the fact that in deriving(15)we

assumed that remains approximately constant,which

is not quite correct.

The slow-start mode lasts until a drop or a timeout are

detected.Detection of a drop leads the system to the fast-

recovery mode,whereas the detection of a timeout leads the

system to the timeout mode.

The formulas(11)and(13)hold as long as the congestion

window is below the receiver’s advertised window size

.When exceeds this value,the sending rate is limited

by and(13)should be replaced by

with the instantaneous sending rate given by(12).When the receiver’s advertised window size is?nite,(12)should be replaced by

on

In case a single packet was dropped,fast recovery will?nish at,but otherwise it will continue until all the retransmissions take place and are successful.However,from on,each acknowledgment received will also de-crease the number of outstanding packets so one will observe an exponential increase in the window size.In particular,from to the number of acknowledgments received is(which was the number of packets sent in the previous interval)and each will both increase the congestion window size and decrease the number of outstanding packets.This will lead to a total number of packets sent equal to and therefore

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and the sender will exit fast recovery when this number reaches ,i.e.,when

(17) RTTs.The previous reasoning is only valid when the number of drops does not exceed.As shown in[29],when

the sender does not receive enough acknowledgments in the?rst RTT to retransmit any other packets and there is a timeout.When

only one packet will be sent on each of the?rst two RTTs, followed by exponential increase in the remaining RTTs.In this case,the fast recovery mode will last approximately

(18) RTTs.

In ns-2,the value of the congestion window variable (cwnd)is actually not changed inside the fast-recovery mode. Instead,a variable(pipe)is used to emulate the congestion window of standard TCP-Sack algorithm described above.For compatibility with ns-2,in our model we actually keep the congestion window constant throughout the whole duration of fast recovery but adjust the sending rates according to the previous formulas.

TCP-NewReno:TCP-NewReno differs from TCP-Sack in that the sender will only learn about the existence of each additional drop when the retransmission for the previous drop was successful.This means that it must remain in the fast-recovery mode for as many RTTs as the number of drops and therefore the duration of fast recovery increases linearly with the number of packets dropped.Therefore,the hybrid model for TCP-NewReno is similar to that of Sack except that the period of fast recovery linearly depends on the number of packet loss.However,NewReno shows better performance since NewReno does not reduce cwnd as often as Reno[30].

TCP-Reno:In TCP-Reno,the sender leaves the fast-recovery mode as soon as the acknowledgment of the?rst retransmitted packet is received,regardless of the occurrence of more drops.When several drops occur,these will be detected right after the system leaves fast-recovery,causing it to re-enter this mode again.The net result of each time the fast-recovery mode is entered is a division by two of the congestion window size.With TCP-Reno,three dropped packets in a window often lead to a timeout[30].Hybrid model and analysis of Reno can be found in[8].

TCP-Tahoe:TCP-Tahoe senders do not implement fast recovery.The sender simply retransmits a packet after receiv-ing a number of duplicate acknowledgments and the sender’s congestion window is always decreased to one.Hence,the hybrid model for TCP-Tahoe does not include the fast recovery mode.

4)Timeouts:Timeouts occur when the timeout timer ex-ceeds a threshold that provides a measure of the current RTT.This timer is reset to zero whenever the number of outstanding packets decreases(i.e.,when it has received an acknowledgment for a new packet).Even when there are drops,this should occur at least once every,except in the following cases:

1)The number of drops is larger or equal to

and therefore the number of duplicate acknowledgments received is smaller or equal to2.These are not enough to trigger a transition to the fast-recovery mode.

2)The number of drops is suf?ciently large so that

the sender will not be able to exit fast recovery because it does not receive enough acknowledgments to retransmit all the packets that were dropped.As seen above,this corresponds to.

These two cases can be combined into the following condition under which a timeout will occur:

When a timeout occurs at time the variable is set equal to half the congestion window size,which is reset to1, i.e.,

At this point,and until reaches,we have multi-plicative increase similar to what happens in slow start and therefore(16)holds.This lasts until reaches

or a drop/timeout is detected.The former leads to a transition into the congestion avoidance mode,whereas the latter to a transition into the fast-recovery/timeout mode.

5)Hybrid model for TCP-Sack:The model in Figure4 combines the modes described in Sections III-C.1,III-C.2,III-C.3,and III-C.4for TCP-Sack.This model also takes into account that there is a delay between the occurrence of a drop and its detection.This drop-detection delay is determined by the“round-trip time”from the queue where the drop occurred,all the way to the receiver,and back to the sender. It can be computed using

The inputs to the TCP-Sack?ow model are the RTTs, the drop events,and the corresponding drop-detection delays (which can be obtained from the?ow-conservation law and queue dynamics in Sections III-A,III-B)and its outputs are the sending rates of the end-to-end?ows.

The model in Figure4assumes that the?ow is always active.It is straightforward to turn the?ow on and off by adding appropriate modes(similar to what is done in Section III-D for UDP?ows).In fact,in the simulation results described in Section IV-B we used random starting times for the persistent TCP?ows.

For lack of space we do not include here the graphical representation of hybrid models for the other versions of TCP mentioned in Section III-C.3.However,these can be automatically generated using the software tool described in Section VII.

D.UDP model

UDP sources differ from TCP sources in that the former do not exercise congestion control.The diagram in Figure5 represents a simple hybrid model for an ON-OFF UDP source with peak rate equal to and exponential distributions for the on and the off times with means and,respectively. The average sending rate for this source is given by

on:

off:?

?

Fig.5.Hybrid model for a UDP?ow with exponential on/off-times.

E.Full network model

In Sections III-A,III-B,III-C,and III-D we developed hybrid models for network traf?c?ows,queues,and TCP/UDP packet sources.By composing them,one can construct hybrid models for arbitrarily complex networks with end-to-end TCP and UDP packet sources.This is shown schematically in Figure6.

protocol symbol meaning

,

TCP-NewReno

,

,

,

Fig.4.Hybrid model for the ?ow under TCP.The meaning of the symbols and

depend on the version of TCP under consideration and is shown in

the table above,where is de?ned by

(17)–(18).

500Mbps 500Mbps

Src

Src

Src

Src

Dest

Dest

Dest

Dest

Fig.7.Dumbbell (upper-left),Y-shape multi-queue with 4different propagation delays (upper-right)and parking-lot with 4different propagation delays (bottom)topologies.

accuracy of the hybrid system simulations does not degrade as more short-live traf?c is considered.

As previously mentioned,the drop model is topology de-pendent.As observed in [7],for the single bottleneck topology with uniform propagation delays,drops are deterministic with each ?ow experiencing drops in a round-robin fashion.How-ever,when background on/off traf?c is considered,losses are best modeled stochastically.

The variables used for comparing the hybrid and the packet-level models include the RTTs,the packet drop rates,the throughput and congestion window size for the TCP ?ows,and the queue size at the bottleneck links.C.Results

We start by considering a dumbbell topology with no background traf?c for which the drop rotation model in

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Section III-B.3is valid.As discussed above,in such networks drops are essentially deterministic phenomena and one can directly compare ns-2traces with our hybrid model,without resorting to statistical analysis.Figure 8compares simulation results for a single TCP ?ow (no background traf?c).These plots show traces of TCP’s congestion window size and the bottleneck queue size over time.The plots show a nearly perfect match and one can easily identify the slow-start,congestion-avoidance,and fast-recovery modes discussed in Section III-C.While most previous models of TCP are able

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Q u e u e S i z e (P a c k e t s )

Time (seconds)CWND size in Hybrid Model Queue size in Hybrid Model

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https://www.sodocs.net/doc/e510056313.html,parison of the congestion window and queue sizes over time for the dumbbell topology with one TCP ?ow and no background traf?c.

to capture TCP’s steady-state behavior,TCP slow-start is typically harder to model because it often results in a large number of drops within the same window.We can observe in Figure 8that after the initial drops,the congestion window is divided by two and maintains this value for about half a second before it begins to increase linearly.This is consistent with the basic slow-start behavior of TCP Sack1when the number of losses is around cwnd/2.In this case,TCP Sack1eventually leaves fast-recovery but only after several multiples of the RTT (cf.Section III-C.3and [29]).

In the next set of experiments,we simulate 4TCP ?ows on the dumbbell topology with and without background traf?c.Figure 9shows the simulation results without background traf?c.As observed in previous studies,TCP connections with the same RTT get synchronized and this synchronization persists even for a large number of connections [23],[33].This synchronization is modeled using drop rotation.Similarly to the single ?ow case,the two simulations coincide almost exactly.Speci?cally,in steady state,all ?ows synchronize to a saw-tooth pattern with period close to 1sec.

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02468

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e u e S i z e (P a c k e t s )

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e o

f Q1

(b)hybrid model

Fig.9.Congestion window and queue size over time for the dumbbell topology with 4TCP ?ows and no background traf?c.

Simulation results for 4TCP ?ows with background traf?c are shown in Figure 10.Even a small amount of background

traf?c breaks packet-drop synchronization and the stochastic drop-selection model (9)becomes valid.We can see that the traces obtained with ns-2are qualitatively very similar to those obtained with the hybrid model.A quantitative com-parison between ns-2and a hybrid model is summarized in Table I,which presents average throughput and RTT for each ?ow for both hybrid system and ns-2simulations.These

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(b)hybrid model

Fig.10.Congestion window and queue size over time for the dumbbell topology with 4TCP ?ows and 10%background traf?c.

statistics con?rm that the hybrid model reproduces accurately the results obtained with the packet-level simulation.To validate our hybrid models,we also use the Y-shape,multi-queue topology with different RTTs shown on the right-hand side of Figure 7.We consider the drop-count and drop-selection models described by Equations (8)and (9),respectively,which generate stochastic drops.Since losses are random,no two simulations will be exactly equal so one cannot expect the hybrid model to exactly reproduce the results from ns-2.Figure 11shows simulation results for ns-2and the hybrid system for 4TCP ?ows with 10%background traf?c on the Y-shape topology under the drop tail discipline.While these time-series provide insight as to weather the simulations are close enough,stochastic processes should be compared by examining various statistics.Table II presents

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Queue size of Q1Queue size of Q3

(b)hybrid model

Fig.11.Congestion window and queue size over time for the Y-shape topology with 4TCP ?ows and 10%background traf?c.

the mean throughput and mean RTT for each competing TCP ?ow.The relative error is always less than 10%and in most cases well under this value.Similar results hold for variations of the Y-shape topology with different RTTs and different numbers of competing ?ows.However,for the stochastic drop model to hold,there must be background traf?c and/or enough

A VERAGE THROUGHPUT AND RTT FOR THE

DUMBBELL TOPOLOGY WITH

4TCP FLOWS AND 10%

BACKGROUND TRAFFIC .

Thru Thru RTT RTT ns-2

1.14

1.14

0.097

0.097

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0.096

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0%

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complexity in the topology and ?ows such that synchronization does not occur.When synchronization does occur,then a deterministic model for drops needs to be used.As described in Section III-B.3,in single bottleneck topologies

provides an accurate model.In more complex settings,construction of drop models for synchronized ?ows to be quite challenging.This is one direction of future we plan to pursue.

To accurately compare stochastic processes one examine their probability density functions.Figure 12plots probability density functions corresponding to the used to generate the results in Table II.We observe that hybrid model reproduces fairly well the probability obtained with ns-2.For the congestion window,three of the ?ows closely agree,while one shows a slight bias towards larger values.The density function of the queue is similar for both models.One noticeable difference is that the peak near the queue-full state is sharper for the hybrid model.This is due to the fact that the queue in ns-2can only take integer values,

(a)ns-2(b)hybrid model

Fig.12.Probability density functions for the congestion window and queue size for the Y-shape topology with 4TCP ?ows and 10%background traf?c.

We also validate the hybrid models in high bandwidth net-works with drop-tail queuing.These networks are especially challenging because,due to the larger window sizes,they are more prone to synchronized losses even when the drop rates are small [34].Also,TCP’s unfairness towards connections with higher propagation delays is more pronounced in high bandwidth-delay networks where synchronization occurs [35].We simulate dumbbell,Y-shape,and parking-lot topologies with a bottleneck of 500Mbps and 10%background traf?c.

The bottleneck queues are set to be large enough to hold the bandwidth-delay product.

(a)ns-2(b)hybrid model

Fig.13.Probability density functions for the congestion window and queue size for the Y-shape topology with 4TCP ?ows and 10%background traf?c (500Mbps bottleneck).

Table III presents the mean throughput and mean RTT for each competing TCP ?ow for the dumbbell,Y-shape,and parking-lot topologies with 500Mbs bottleneck(s).The relative errors between the results obtained with ns-2and the hybrid models are always smaller than 10%.The corresponding probability density functions for the congestion window and queue size for the Y-shape and parking-lot topologies are given in Figures 13and 14,respectively.In both cases,the probability density functions match fairly well.

It is interesting to compare the distributions of the bot-tleneck queue and congestion window sizes for the low-bandwidth Y-shape topology in Figure 12with those obtained for the high bandwidth Y-shape topologies in Figure 13.The explanation for the signi?cant differences observed lie

A VERAGE THROUGHPUT AND RTT FOR THE Y-SHAPE TOPOLOGY(5M BPS)WITH4TCP FLOWS AND10%BACKGROUND TRAFFIC.

Thru Thru RTT RTT

ns-2 1.1340.6680.1360.225

1.8160.8760.0930.183

relative error 2.4% 1.0% 1.5% 1.3%

TABLE III

A VERAGE THROUGHPUT AND AVERAGE RTT FOR Y-SHAPE TOPOLOGY FOR500M BPS BOTTLENECK

Thru Thru RTT RTT

ns-2113.37110.310.0850.085

hybrid model114.08110.080.08190.0819

relative error0.6%0.2% 3.6% 3.6%

ns-297.8739.310.1220.212

hybrid model102.0837.680.1210.211

relative error 4.1% 4.1% 1.6%0.09%

ns-2113.2046.790.1670.257

hybrid model114.1648.600.1670.258

relative error0.8% 1.8%0%0.4%

ns-2116.9054.380.2040.295

hybrid model113.7658.960.2030.293

relative error 2.7%8.4%0.5%0.6%

Parking-lot(qsize=4000)

260.152.70.0780.168

259.650.80.0770.167

0.2% 3.6% 1.3%0.6%

ns-2110.749.50.1710.261 hybrid model112.245.90.1680.258 relative error 1.3%7.3% 1.8% 1.1%

Parking-lot(qsize=11250)197.8780.1580.248 19474.920.1620.252 1.95% 4.1% 2.5% 1.6%

-DISTANCE BETWEEN HISTOGRAMS COMPUTED FROM SIMULATIONS USING N S-2AND HYBRID MODEL.

cwnd2cwnd4bottleneck queue2 dumbbell(5Mbps)0.17640.1771-

0.10400.22130.3333

parking-lot(5Mbps)0.10540.154602061

0.21380.23540.1836

Y-shape(500Mbps)0.19500.1852-

0.12060.05110.1313

15

VI.A PPLICABILITY OF H YBRID MODELS

The two previous sections highlight both the strengths and the weaknesses of the hybrid modeling framework.We have saw in Section IV that the hybrid models match very closely packet-level ns-2simulations.In fact,we saw that it is not easy to distinguish between the predictions made by the hybrid model and ns-2traces for queue lengths or for the window sizes of individual?ows.The computational analysis in Section V shows that simulation time scales roughly linearly with the number of?ows but is inversely proportional to the bottleneck bandwidths,which should be contrasted with packet level simulators for which simulation time scales with the produce of the number of?ows times the bottleneck bandwidths.

The conclusion to be drawn is that simulations using hybrid models should be preferred over packet-level simulators in the study of networks with large per-?ow bandwidths,when one wants to accurately capture traces of individual?ows and the evolution of buffer sizes.For networks with small bandwidth, the computational saving introduced by hybrid model are small and one might as well rely on packet-level simulators,which are generally fast for such networks.

The simulation time of both packet-level and hybrid model simulators scales roughly linearly with the number of?ows, thus both simulation techniques will encounter dif?culties when simulating a very large number of?ows.The only way to avoid the linear scaling with the number of?ows is to model?ow aggregates.For example by keeping track of the average(or total)packet-transmission rate of a large number of?ows,instead of the individual packet-transmission rates of each individual?ows.Several?uid models take precisely this approach[2],[38].The price to pay is that it is no longer possible to study traces of the individual?ows that have been aggregated.The authors of[21]propose to only aggregate background traf?c,while maintaining packet-level models of foreground traf?c for which one could obtain detailed traces. For high-bandwidth networks one could use a similar approach to combine aggregate models of background traf?c with hybrid models of foreground traf?c.However,it should be noted that most aggregate models for traf?c are not valid under drop-tail queuing,which dominates today’s Internet.

In the next section we illustrate the use of hybrid models in a situation in which they yield the most bene?t:a high-bandwidth network,for which we want to study the effect of buffer sizes on fairness between different?ows.

VII.T OOLS AND C ASE S TUDY

Hybrid systems modeling languages such as modelica[5] are special-purpose languages designed to model complex physical systems.To simplify the use of hybrid modeling by networking researchers,we developed the Network Descrip-tion Scripting Language(NDSL)to specify succinctly large, complex networks using a syntax similar to Object Oriented TCL(OTCL)in ns-2.

The following list enumerates some of the primitives avail-able in NDSL:

define symbol value is used to de?ne a named con-stant.

nodes symbol1symbol2...creates named network nodes.Ranges of nodes can be de?ned using“–”as in node node1-node5.

links n1n2b t q-type q-size[q-opt]creates

a link from node n1to node n2with bandwidth

b and

propagation delay t.A queue of type q-type and size q-size is associated with the link.Valid types include “roundrobin”,“fastroundrobin”,“droptail”,“RED”,and “wireless”among others.The optional argument q-opt is used for queue types that require additional parameters

(e.g.,pre-speci?ed drop probabilities).

Tcp-Sack n ti tf[t-opt]src path dst

[pckt]creates n TCP Sack traf?c sources between nodes src and dst.The path following is speci?ed by the sequence of nodes in path.The sources are active between times ti and tf.Two optional parameters are available:t-opt is used to randomize the start and?nish times by adding to these a random variable uniformly distributed between0and t-opt;pckt speci?es the packet size.

udp n ti tf[t-opt]dist-on[dist-on-opt]

dist-off[dist-off-opt]src path dst creates n UDP traf?c sources.The parameters ti,tf,t-opt, src,path,and dst are as in the TCP-Sack primitive.

The parameters dist-on and dist-off specify the distributions of the ON and OFF times with optional parameters dist-on-opt,dist-on-off.Valid distributions include exp for exponential,uni for uniform,and par for Pareto.

An NDSL translator automatically converts a network NDSL speci?cation into a hybrid model expressed in modelica. The code generated can be fed directly to simulation engines such as DYMOLA[39].In the remainder of this section,we illustrate the use of these tools in the simulation of TCP?ows over a realistic high-bandwidth network for which packet-level simulations would be prohibitively long.

A.NDSL Translator

The NDSL translator is a PERL script which translates Net-work Description Scripting Language scripts into modelica. It?rst parses the primitives and corresponding parameters from the NDSL script.Then,converts the NDSL primitives into the corresponding modelica code which will be simulated in DYMOLA environment.

In order to convert from NDSL to modelica,the trans-lator uses the network library,which consists of modules corresponding to the modelica implementation of NDSL’s basic primitives.The network library is updated every time an existing primitive is modi?ed or a new one is added. The current version of the network library is divided into several packages,including traf?c source,traf?c sink,node, link,connector,functions).

The traf?c source package contains modelica implementa-tion for traf?c sources such as TCP variants and UDP.Because traf?c sources typically require a sink,the traf?c sink package

16

includes TCP sink models which respond (e.g.,by sending acknowledgements)to the corresponding source.Functions and characteristics associated with links are implemented by the link package.These include bandwidth,propagation delay,and queing policy.For example,we implement droptail,round robin,RED,and wireless drop policies.The Connector pack-age includes input and output “connectors”that are used to connect the basic componentscomponents (e.g.,sources,sinks,links).This is analagous to global variables shared by different functions in general-purpose programming languages.Finally,utility components are de?ned in the function and can be invoked by other model.Example of utility components is function that compute sum or minium value out of array.The NDSL Translator works in two passes.In the ?rst pass,the translator scans the NDSL input ?le;it then processes the define commands,storing (variable,value)pairs in a hash table.Next,the translator parses the input ?le into nodes ,links ,traf?c sources ,connectors ,and traf?c sinks .

In the second pass,the translator creates an output ?le in modelica containing the appropriate models from the network library ?le.As a result,an overall system model is created consisting of declarations of traf?c sources ,connectors ,pro-tocol sinks ,etc.

B.Case Study:Abilene Backbone Network

The Abilene Network (shown in Figure 18)is an Internet-2high-performance backbone network connecting research institutions to enable the development of advanced Internet applications and protocols [6].Recently,its has been upgraded to 10Gbps backbone links using OC-192circuits.The links propagation delays considered are shown in Table V.All links have a bandwidth of 10Gbps and we assume droptail queues with size equal to 25,000packets with 1K packet size.In this experiment,we simulate the three sets of ten ?ows described in Table VI.Each ?ow starts randomly between 0and 1sec and terminates at time 40,000sec.The NDSL description of this network is shown in Table

VII.

Fig.18.Abilene Backbone Network

C.Results

We use our hybrid model of the Abilene network to study how queue size impacts throughput fairness.To this effect we vary the queue sizes from 25,000to 150,000packets in increments of 25,000and measure the throughput obtained.We ran 11hours of simulation time.In this network,one needs simulations this large if one wants to obtain steady-state throughput.Note that for a 10Gbps backbone with 70ms

TABLE V

T WO -WAY PROPAGATION DELAY BETWEEN NODES IN THE A BILENE

B ACKBONE

source prop.delay Seattle (STTL)

25.608ms

Denver (DNVR)

Denver (DNVR)

10.674ms Indianapolis (IPLS)

Indianapolis (IPLS)

3.990ms New York (NYCM)

Sunnyvale (SNV A)

7.772ms Houston (HSTN)

Houston (HSTN)

19.756ms Washington (W ASH)

Washington (W ASH)

4.412ms Seattle (STTL)

Houston (HSTN)

15.504ms Indianapolis (IPLS)

number of ?ows

source/destination

set one 15ms set two 28.8ms set three

69.5ms

17

TABLE VII

I NPUT FILE FOR THE NDSL TRANSLATOR

de?ne qsize25000

de?ne qtype Droptail

de?ne band10000M

#nodes

node STTL DNVR KSCY IPLS CHIN NYCM W ASH

node ATLA HSTN LOSA SNV A

#links and queue

link STTL DNVR band0.0257qtype qsize

link SNV A DNVR band0.0250qtype qsize

link DNVR KSCY band0.0107qtype qsize

link KSCY IPLS band0.0093qtype qsize

link IPLS CHIN band0.0040qtype qsize

link CHIN NYCM band0.0205qtype qsize

link SNV A LOSA band0.0077qtype qsize

link LOSA HSTN band0.0316qtype qsize

link HSTN ATLA band0.0198qtype qsize

link ATLA W ASH band0.0159qtype qsize

link W ASH NYCM band0.0044qtype qsize

link SNV A STTL band0.0168qtype qsize

link HSTN KSCY band0.0155qtype qsize

link ATLA IPLS band0.0110qtype qsize

#de?ne?ows

TcpSack1004000000ATLA IPLS CHIN

TcpSack1004000000HSTN KSCY IPLS CHIN

TcpSack1004000000SNV A DNVR KSCY IPLS CHIN NYCM

3.1times the average throughput of set three,but when the queue size increases to150,000,the throughput ratio becomes only1.5.This is consistent with the expectation that,when the queuing delay increases considerably,it will dominate the RTT thus decreasing the RTT ratio between the two?ows with different propagation delays.However,in topologies like this one,the precise dependence of the fairness ratio with the buffer size is dif?cult to predict without resorting to simulations. Figure19also shows the ratio between the average RTTs of the?ows in sets and(in the reciprocal order). Since all the?ows go through the same bottleneck(Chicago-Indianapolis),based on the TCP-friendly formula one could expect the fairness ratio to match the reciprocal of the RTT ratio.The simulations reveal that this generally underestimates the fairness ratio,especially when the ratio is far from one. This phenomena has been con?rmed by ns-2simulations in smaller networks and is further studied in[40].

Fig.20.Average RTT of TCP?ows on the Abilene Network

VIII.C ONCLUSION AND F UTURE W ORK

This paper proposes a general framework for building hybrid models to describe network behavior.This framework ?lls the gap between packet-level and aggregate models by averaging discrete variables over very short time scales.This means that the models are able to capture the dynamics of transient phenomena fairly accurately,as long as their time constants are larger than a couple of RTTs.This is quite appropriate for the analysis and design of network protocols including congestion control mechanisms.

To validate our hybrid systems modeling framework,we compare hybrid model against packet-level simulations and show that the probability density functions match very closely. We also brie?y describe the software tools that we developed to automate the generation of hybrid models for complex networks.We showcased their use with a case study involving the Abilene backbone network.

Our results indicate that simulations using hybrid models should be preferred over packet-level simulators in the study of networks with large per-?ow bandwidths,when one wants to accurately capture traces of individual?ows and the evo-lution of buffer sizes.For networks with small bandwidth,the computational saving introduced by hybrid model are small and one might as well rely on packet-level simulators.

We plan to pursue the use of hybrid models to character-ize the performance of large-scale,high-speed networks.For example,recent proposals of high-speed protocols such as FAST-TCP,STCP and HSTCP show severe unfairness where heterogeneous RTTs exist[34].Hybrid models will allow us to evaluate these protocols more ef?ciently than packet-level simulators.Another direction of future work is to improve the hybrid systems simulator’s scalability.We believe techniques such as prediction and combination of drop events,and traf?c aggregation can reduce execution time further.

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C．便于靠离码头D．建造方便 18．集装箱船通常用______表示其载重能力 A．总载重量B．满载排水量 C．总吨位 19. 油船的______ A. 杂物舱C．压载舱D．淡水舱 20 A. 集装箱船B，油船C滚装船 21．常用的两种集装箱型号和标准箱分别是 B．40ft集装箱、30ft集装箱 C．40ft集装箱、10ft集装箱 D．30ft集装箱、20ft集装箱 22．集装箱船设置双层船壳的主要原因是 A．提高抗沉性 C．作为压载舱 D. 作为货舱 23．结构简单，成本低，装卸轻杂货物作业效率高，调运过程中货物摇晃小的起货设备是 B．双联回转式 C．单个回转式D．双吊杆式 24. 具有操作与维修保养方便、劳动强度小、作业的准备和收尾工作少，并且可以遥控操 作的起货设备是 B．双联回转式 D.双吊杆式 25．加强船舶首尾端的结构，是为了提高船舶的 A．总纵强B．扭转强度 C．横向强度 26. 肋板属于 A. 纵向骨材 C．连接件D．A十B 27. 在船体结构的构件中，属于主要构件的是：Ⅰ．强横梁；Ⅱ．肋骨；Ⅲ．主肋板；Ⅳ. 甲板纵桁；Ⅴ．纵骨；Ⅵ．舷侧纵桁 A．Ⅰ，Ⅱ，Ⅲ，ⅣB．I，Ⅱ，Ⅲ，Ⅴ D．I，Ⅲ，Ⅳ, Ⅴ 28．船体受到最大总纵弯矩的部位是 A．主甲板B．船底板 D．离首或尾为1／4的船长处 29. ______则其扭转强度越差 A．船越长B．船越宽 C．船越大 30 A．便于检修机器B．增加燃料舱 D．B+C 31

考试大纲-重庆交通大学知识交流

硕士生入学复试考试《船舶原理与结构》 考试大纲 1考试性质 《船舶原理》和《船舶结构设计》均是船舶与海洋工程专业学生重要的专业基础课。它的评价标准是优秀本科毕业生能达到的水平，以保证被录取者具有较好的船舶原理和结构设计理论基础。 2考试形式与试卷结构 (1)答卷方式：闭卷，笔试 (2)答题时间：180分钟 (3)题型：计算题50%；简答题35%；名词解释15% (4)参考数目： 《船舶原理》，盛振邦、刘应中，上海交通大学出版社，2003 《船舶结构设计》，谢永和、吴剑国、李俊来，上海交通大学出版社，2011年 3考试要点 3.1 《船舶原理》 （1）浮性 浮性的一般概念；浮态种类；浮性曲线的计算与应用；邦戎曲线的计算与应用；储备浮力与载重线标志。 （2）船舶初稳性 稳性的一般概念与分类；初稳性公式的建立与应用；重物移动、

增减对稳性的影响；自由液面对稳性的影响；浮态及初稳性的计算；倾斜试验方法。 （3）船舶大倾角稳性 大倾角稳性、静稳性与动稳性的概念；静、动稳性曲线的计算及其特性；稳性的衡准；极限重心高度曲线；IMO建议的稳性衡准原则；提高稳性的措施。 （4）抗沉性 抗沉性的概念；安全限界线、渗透率、可浸长度、分舱因数的概念；可浸长度计算方法；船舶分舱制；提高抗沉性的方法。 （5）船舶阻力的基本概念与特点 船舶阻力的分类；阻力相似定律；阻力（摩擦阻力、粘压阻力、兴波阻力）产生的机理和特性。 （6）船舶阻力的确定方法 船模阻力试验方法；阻力换算方法；阻力近似计算的概念及方法；艾尔法、海军系数法等。 （7）船型对阻力的影响 船型变化及船型参数，主尺度及船型系数的影响，横剖面面积曲线形状的影响，满载水线形状的影响，首尾端形状的影响。 （8）浅水阻力特性 浅水对阻力影响的特点；浅窄航道对船舶阻力的影响。 （9）船舶推进器一般概念 推进器的种类、传送效率及推进效率；螺旋桨的几何特性。

奋进强军新时代 演讲稿

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