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Analysis of Binary Adjustment Algorithms in Fair Heterogeneous Networks

Analysis of Binary Adjustment Algorithms in Fair Heterogeneous Networks
Analysis of Binary Adjustment Algorithms in Fair Heterogeneous Networks

Analysis of Binary Adjustment Algorithms in Fair Heterogeneous Networks

Sergey Gorinsky Harrick Vin

Technical Report TR2000-32

Department of Computer Sciences,University of Texas at Austin

Taylor Hall2.124,Austin,Texas78712-1188,USA

gorinsky,vin@https://www.wendangku.net/doc/c310980846.html,

November29,2000

Abstract

Many congestion control schemes rely on binary noti?cations of congestion from the network:on detecting network con-gestion,they reduce transmission rates;and on receiving a signal indicating no congestion,they increase transmission rates.

For conventional networks with First-In First-Out(FIFO)scheduling of packets,the effectiveness of such algorithms has been evaluated with respect to their responsiveness,smoothness,and fairness properties.Recently,it has been argued that it is pos-sible to design high-speed network routers that can guarantee fair allocation of link capacities and buffers.In networks that employ such routers,fairness is ensured by the routers,thereby making responsiveness and smoothness the two main criteria for evaluating and selecting a binary adjustment algorithm.

In this paper,we consider binary adjustment algorithms with four increase policies proposed in the literature:multiplicative increase(MI),additive increase(AI),inverse-square-root increase(ISI),and inverse increase(II).We analyze these algorithms in fair heterogeneous networks.We?nd that the multiplicative increase policy,which is considered inappropriate for conventional networks due to its fairness property,provides superior performance over the other policies in fair networks.

1Introduction

This paper studies congestion control schemes based on binary adjustment algorithms that adjust load on the network in response to a binary feedback about the congestion status of the network.Numerous congestion control schemes use binary adjustment algorithms.For instance,DECbit relies on the additive-increase multiplicative-decrease(AIMD)algorithm to adjust the load in response to an explicit binary feedback:if the feedback indicates congestion,the load is reduced to its fraction; otherwise,the load is raised by a constant[22].Binary adjustment algorithms also enjoy wide deployment in the Internet where most of the traf?c is subject to congestion control by Transmission Control Protocol(TCP)[3]:in the slow start mode,the congestion window of a TCP session is approximately doubled during each round-trip time when congestion is not detected; in the congestion avoidance mode of TCP,the adjustments of the congestion window are similar on the round-trip timescale to the behavior of AIMD[1,10].

The design of binary adjustment algorithms for conventional networks–with First-In First-Out(FIFO)link scheduling–has been motivated by three requirements:responsiveness to congestion noti?cations;smoothness of rate adjustments;and fairness of resource allocation across?ows[11,12,16,29].For instance,the large load oscillations characteristic of TCP has led to the development of several adjustment algorithms that provide smoother congestion control for streaming media appli-cations[27].To achieve the goal of smoothness,some solutions offer new settings for the parameters of the TCP adjustment algorithms[6,30],while other proposals suggest replacing the TCP adjustment algorithm for the congestion avoidance mode by new algorithms such as the IIAD(inverse-increase additive-decrease)and SQRT algorithms[2].

The aim of this paper is to analyze the performance of binary adjustment algorithms in fair networks–networks in which routers instantiate fair resource allocation mechanisms such as fair link scheduling[5]and fair buffer management[26].Fair networks have a number of advantages over traditional networks.For example,while the performance of a traditional net-work can be disrupted by the?ows that do not exercise congestion control[18],fair networks offer protection against these nonadaptive?ows.Furthermore,as long as?ows employ some form of congestion control in a fair network(i.e.,each?ow decreases or increases its load depending on the congestion status),the network converges towards the fair allocation of its

capacity[9].The argument against fair networks has traditionally been the complexity,and hence the perceived lack of scala-

bility,of the mechanisms for ensuring fairness in routers.However,recent studies suggest that fair resource allocation can be implemented in high-speed networks[26];in fact,a number of manufacturers are currently designing routers with support for fair link scheduling[20].Besides,there exist promising approaches to build simpler fair networks where core routers do not

perform per-?ow management[25].We would like to point out that this paper does not argue for ubiquitous deployment of fair link scheduling or fair buffer management.It aims to establish which adjustment algorithms would be preferable in fair networks if such networks were to be deployed.

It is important to note that fair networks are characterized by inherent fairness;hence the design of adjustment algorithms in a fair network is driven solely by considerations of ef?ciency of resource utilization(i.e.,the responsiveness and smoothness requirements).In conventional routers with FIFO link scheduling and Drop-Tail buffer management,on the other hand,the goal

of achieving fairness restricts the choice of adjustment algorithms.For instance,the objective of TCP-friendliness in traditional networks[15,19]couples the increase and decrease policies of an adjustment algorithm(and thus imposes an undesirable coupling between the speed of capacity acquisition and responsiveness to congestion):in GAIMD,the parameter setting of the

decrease policy is determined by the parameter setting selected for its increase policy[30];similarly,the choice of the increase policy for a binomial algorithm,such as IIAD and SQRT,dictates the decrease policy of the algorithm[2].Congestion control

schemes in fair networks do not need to coordinate their load adjustments policies in order to support fairness;rate adjustment algorithms can select the increase and decrease policies independently.

In this paper,we evaluate rate adjustment algorithms with respect to their ef?ciency in a fair network.Our analysis method-

ology has two unique features.

1.Due to the intrinsic fairness of resource allocation in fair networks,we conduct the evaluation of the algorithms in a new

way.We examine the impact of a binary adjustment algorithm on the performance of a particular?ow without making

many unrealistic assumptions common for the analysis of traditional networks.Our methodology allows cross traf?c to:

(1)have different round-trip times,(2)be bottlenecked at different links,(3)use different adjustment algorithms,and(4)

transmit less data than suggested by congestion control mechanisms.

2.We analyze binary adjustment algorithms in heterogeneous environments,where the capacity available to a?ow changes

over time.It is known that the ef?ciency of a binary adjustment algorithm is subject to a fundamental tradeoff between the smoothness and responsiveness of the algorithm:an algorithm with smoother oscillations of load at a steady state is less

responsive to changing network conditions[4].Earlier studies of the tradeoff between smoothness and responsiveness were conducted for relatively static network conditions[4].Such an approach seems inappropriate since tuning the parameters of an algorithm for a particular network setting does not ensure good performance of the selected algorithm

in diverse scenarios.For instance,consider the following additive algorithm and multiplicative algorithm:algorithm adjusts the current load by units;algorithm adjusts the current load by.When the fair share of load is units,algorithm is smoother at the fair state than algorithm.If the fair share of load equals units,algorithm

is smoother at the fair state than algorithm.What is required in reality is an assurance that the examined algorithm provides acceptable performance for all possible(or important in practice)con?gurations resulting from the mix of network technologies as well as from the dynamic nature of network traf?c.Our methodology establishes whether the evaluated algorithm provides an appropriate tradeoff between smoothness and responsiveness in fair heterogeneous networks.

Using this methodology,we analyze binary adjustment algorithms with four increase policies proposed in the literature: multiplicative increase(MI),additive increase(AI),inverse-square-root increase(ISI),and inverse increase(II).We?nd that the multiplicative increase policy,which is considered inappropriate for conventional networks due to its fairness property,provides superior performance than the other policies in fair networks.

Before proceeding to the main part of the paper,we would like to point out that adjustments of load in response to a bi-nary congestion signal are not the only means of congestion control.Even though binary adjustment algorithms are routinely adopted by congestion control schemes for unicast[23,30]and multicast[17,24],adjustment algorithms can be more effec-tive in congestion control designs with more sophisticated feedback.Examples of such schemes include the equation-based congestion control for traditional networks[7]or packet-pair protocols for fair networks[13,14].Our paper considers only binary adjustment algorithms.Assessment of non-binary adjustment algorithms and their comparison with binary algorithms lie beyond the scope of this paper.

The paper is organized as follows.First,we specify our model of fair networks in Section2.The examined binary adjustment

algorithms are presented in Section3.Section4describes the theoretical foundations of our evaluation.Section5contains de?nitions and justi?cations for the chosen metrics of performance.Section6outlines our evaluation methodology.Analysis

of the compared policies is provided in Section7.Section8summarizes our conclusions.

2Network Model

In this paper,we analyze the performance of a particular?ow(called the examined?ow)that employs a binary algorithm to adjust its load in a fair network.We model the network as the bottleneck link of this?ow(see Figure1).The network capacity equals the capacity of this link and is a positive real number.The network is shared by?ows.At time,?ow imposes load on the network,where is a positive real number.The total load on the network at time equals:

(1)

Other Flows

Examined Flow

Figure1:The network model.

The network splits its capacity between?ows according to the principle of maxmin fairness[8,11].A recursive procedure for computing this fair allocation is given in[21].The procedure assigns a throughput to?ow based on the notion of fair share at time.If the?ow demands less than the fair share,its demand is fully satis?ed.Otherwise,the?ow receives the fair share:

min(2) When,all the demands can be satis?ed,and the fair share is assumed to be the maximum among the imposed loads. When,only the demands from a proper subset of all the?ows can be fully satis?ed.The other?ows split the remaining capacity equally:

max if

(4) To facilitate ef?cient congestion control,the network provides?ow with binary feedback:

if

if(5)

We examine the performance of a particular?ow which adjusts its load in response to the network feedback.For succinctness of the notation,we omit the subscript when we refer to the characteristics of this?ow:,,and denote the load, feedback,and throughput of this?ow respectively.

We model time as the number of adjustments performed by the examined?ow.Thus,time is integer:represents the moment when the examined?ow imposes its initial load on the network;for,corresponds to the-th adjustment of the load for this?ow.

The?ow uses the following binary algorithm to adjust its load:

if

if(6) where and are an increase policy and decrease policy,respectively.We consider increase policies that always increase the load:

(7) and are guaranteed to produce unbounded values if applied repetitively:

(8) where is the result of consecutive applications of to.

Similar constraints are imposed on decrease policies:a decrease policy always decreases the load to a positive value:

(9) and is guaranteed to produce a value below any positive number if applied repetitively:

(10) where is the result of consecutive applications of to.

Constraints(7)and(9)implement the principle of negative feedback:when the load of the examined?ow is below the fair share,the adjustment algorithm increases the load;when the load exceeds the fair share,the adjustment algorithm decreases the load of the examined?ow[4].Constraints(8)and(10)ensure that regardless of the initial load and fair share,the adjustment algorithm eventually brings the load of the examined?ow to the fair share.

Our model does not make any assumptions about how and when the other?ows adjust their loads on the network.

The next section presents the binary adjustment algorithms examined in this paper.

3Binary Adjustment Algorithms

A binary adjustment algorithm consists of two components:an increase policy and a decrease policy.The following increase and decrease policies have been proposed in the literature.

Increase policies:

1.Multiplicative Increase(MI)policy:where is a constant.This policy models the behavior of

TCP during its slow start mode[1,10].

2.Additive Increase(AI)policy:where is a constant.This policy models the increase behaviors

of AIMD[22],GAIMD[30],and TCP congestion avoidance mode[1,10].

3.Inverse-Square-root Increase(ISI)policy:where is a constant.This policy represents the

increase behavior of SQRT algorithm[2].

4.Inverse Increase(II)policy:

1.Multiplicative Decrease(MD)policy:where is a constant.This policy models the decrease

behaviors of AIMD,GAIMD,and TCP.

2.Square-root Decrease(SD)policy:

,and for

.This nice property holds regardless of the initial load for the examined?ow or the behaviors of the other?ows.We prove this property in Lemma2below and refer to

5Performance Metrics

We evaluate the increase policies with respect to their responsiveness–measured in terms of convergence time–and smooth-ness–measured in terms of overload.

Convergence time of a policy refers to the amount of time it takes for the policy to increase the load of the examined ?ow from to the guaranteed throughput:

min(14) This metric for convergence time can be expressed differently based on the following observation:as long as the through-put of the examined?ow is below the guaranteed throughput,the load of the?ow does not exceed the fair share,and the ?ow keeps increasing its load.Thus,we can transform(14)into a form which is more suitable for computation:

min(15)

Overload of a policy refers to the maximum relative increase produced by applying the policy to the fair share when the fair share reaches the guaranteed throughput:

max

(17)

Unfortunately,as the following example illustrates,this measure depends on the behaviors of the other?ows and is not suitable for representing the contribution of the evaluated increase policy to overload.

Example1Consider a fair network with capacity and two?ows.Let the examined?ow employ the additive increase policy with parameter.Assume that the load of the examined?ow after adjustments is while the other?ow imposes load of at time.Because,the examined ?ow increases its load at time to.If the other?ow raises its load at time to,then the fair share at time

becomes.Since the examined?ow exceeds the fair share at time,its throughput equals the fair share:.Then,we have.According to(17),metric is at least.Note that such a high value of is caused not by the increase policy of the examined?ow(the examined?ow increases its load from to,i.e.,by)but by the drastic load increase of the other?ow.

6Evaluation Methodology

Since the capacities of links,the number of?ows,and the locations of bottlenecks can vary dramatically in heterogeneous networks,we assume that the guaranteed load is not known a priori but lies between some positive values and:

(18) We refer to

To characterize the ability of a policy to provide a satisfactory behavior over the whole range of possible guaranteed through-puts,we introduce a notion of feasibility of an increase policy with respect to responsiveness and smoothness requirements: De?nition6.1An increase policy is feasible with respect to responsiveness and smoothness iff there exists such a single setting for the parameters of the policy that:

(21) To compare two policies qualitatively,we de?ne a relation“more feasible than”and denote it as“”:

De?nition6.2Policy is more feasible than policy iff whenever policy is feasible with respect to some responsiveness and smoothness,policy is feasible with respect to the same and:

(is feasible with respect to and)(is feasible with respect to and)(22) To assess an increase policy quantitatively,we measure the responsiveness of the policy when this policy provides acceptable performance in terms of its smoothness.First,we consider such parameter settings of the policy that the overload does not exceed the smoothness requirement.We refer to them as-smooth settings:

De?nition6.3A parameter setting of a policy is-smooth iff:

(23)

policy MI ISI

(15)

(21)

guaranteed convergence time(24)

Table1:The performances of increase policies.

Then,in the set of-smooth settings of the policy,we distinguish such a setting that provides the policy with the smallest maximum convergence time.We refer to this time as the guaranteed convergence time of this policy and use it as a quantitative measure of the policy performance:

De?nition6.4The guaranteed convergence time of an increase policy with respect to smoothness is the smallest among the maximum convergence times of the policy when the parameter setting belongs to the set of-smooth settings of the policy:

min max(24) We bound the overload to compare the convergence times(rather than limiting the convergence time to compare the over-loads)because a speci?c bound on overload–e.g.,the buffer size when overload is measured in terms of the buffer occupancy–can correspond to a boundary between two qualitatively different modes of network operation–e.g.,lossless transmission ver-sus packet drops.On the other hand,it is dif?cult to provide speci?c bounds on convergence times such that exceeding them results in qualitatively different performances.

Using the described methodology,we compare increase policies in the next section.

7Analysis

We analyze the four increase policies introduced in Section3:multiplicative increase(MI),additive increase(AI),inverse-square-root increase(ISI),and inverse increase(II).We present our?ndings as a series of lemmata below.While the proofs for the lemmata are given in Appendix B,Table1summarizes the results of our analysis.For some properties of ISI and II policies, closed-form expressions could not be obtained,and the table refers to the general de?nitions(15),(21),and(24)in these cases.

First,we derive the values of overload and convergence time for the considered policies:

Lemma3The values of overload for MI,AI,ISI,and II policies are,respectively.

Lemma4The values of convergence time for MI and AI policies are respectively.

Having obtained the closed-form expressions for both overload and convergence time of MI and AI policies,we can derive feasibility conditions as well as closed-form expressions for guaranteed convergence times of these policies:

Lemma5MI is feasible with respect to responsiveness and smoothness iff:

(25) Lemma6AI is feasible with respect to responsiveness and smoothness iff:

(26)

Lemma7The values of guaranteed convergence time for MI and AI policies are and

Theorem3AI ISI.

Proof:Let us denote the convergence time and overload of ISI policy with parameter as and respectively.Then, consider AI policy with parameter and denote its convergence time and overload as and respectively.

Let us compare the results of applying these ISI and AI policies to some and such that.

De?nition of ISI policy

De?nition of AI policy

Thus,.By induction,.Using(15),we derive:

(27)

Relying on(27),we obtain:

ISI is feasible with respect to responsiveness and smoothness

De?nition6.1

Lemma3

(27)

Lemma3

De?nition6.1

AI is feasible with respect to responsiveness and smoothness. According to De?nition6.2,AI ISI.

:

.

Now,let us compare the results of applying these and policies to some and such that

De?nition of II policy

De?nition of ISI policy

Thus,, we derive by induction that.Then,according to(15),we have:

(28) Relying on(28),we obtain:

II is feasible with respect to responsiveness and smoothness

De?nition6.1

Lemma3

(28)

Theorems2,3,and4establish an interesting chain of superiorities in terms of the abilities of the considered policies to satisfy the smoothness and responsiveness requirements:

MI AI ISI II(29) i.e.,MI is superior to AI which is superior to ISI which is superior to II.Thus,MI provides the best performance in fair heterogeneous networks in comparison to the other examined increase policies.

We assess quantitative advantages of MI over AI,ISI,and II in terms of the guaranteed convergence times of the compared policies.According to Lemma7,the guaranteed convergence times of MI and AI policies depend only on the smoothness requirement and the heterogeneity index of the network.In particular,the guaranteed convergence times of these policies do not depend on the minimum guaranteed throughput.Lemmata8and9show that ISI and II policies share the same property.Thus,we evaluate the guaranteed convergence times of the four compared policies as functions of the heterogeneity index(see Figure2)and smoothness requirement(see Figure3).Figure2shows that the larger heterogeneity index for the network,the larger advantage MI provides in comparison to the other considered policies.Figure3shows that MI consistently provides better performance than AI,ISI,and II policies for all considered smoothness requirements.

8Summary and Discussion

In this paper,we analyze binary adjustment algorithms in fair heterogeneous networks.We introduce a network model where routers allocate link capacities among?ows according to the principle of maxmin fairness.We evaluate four different increase

5

10

152******** 1.52 2.5

3 3.54g u a r a n t e e d c o n v e r g e n c e t i m e

heterogeneity index II ISI AI MI 05000

100001500020000120406080100

g u a r a n t e e d c o n v e r g e n c e t i m e heterogeneity index II ISI AI MI

Figure 2:The guaranteed convergence times as functions of the heterogeneity index for smoothness requirement

.

20406080100120

14016000.050.10.150.20.25

0.30.350.40.450.5g u a r a n t e e d c o n v e r g e n c e t i m e smoothness II ISI AI MI 0500

1000

1500

2000250030003500400000.050.10.150.20.250.30.350.40.450.5

g u a r a n t e e d c o n v e r g e n c e t i m e smoothness II ISI AI MI

(a)(b)

Figure 3:The guaranteed convergence times as functions of the smoothness requirement.

policies proposed in the literature:multiplicative increase (MI ),additive increase (AI ),inverse-square-root increase (ISI ),and inverse increase (II ).Our analysis shows that MI is superior to the other increase policies in fair networks.

There are several salient features of our analysis methodology and the results.

Since fair networks provide ?ow isolation,the guaranteed throughput of a ?ow is independent of the behaviors of other ?ows.Hence,our analysis methodology considers only the performance of the examined ?ow.This is fundamentally

different from conventional networks with FIFO link scheduling;in such networks,the guaranteed performance of a ?ow

is affected by the behaviors of other ?ows.

We consider a heterogeneous network environment in which the examined ?ow shares its bottleneck link with other ?ows that can have diverse round-trip times,be bottlenecked at different links,employ various forms of congestion control

(including,no congestion control at all),and transmit less data than suggested by their congestion control mechanisms.

Further,the number of ?ows that share the bottleneck link with the examined ?ow as well as the bottleneck link capacity

may change over time.This is a realistic model of traf?c for large heterogeneous networks.For such networks,it is

essential to evaluate binary adjustment algorithms with respect to their ability to provide acceptable performance at all

of the possible operating points.Our analysis methodology is founded on this requirement.It is important to note that

this is an important methodological departure from previous work on analyzing adjustment algorithms in FIFO networks;

most of the prior work evaluate the relative performance of these algorithms for a ?xed network setting.

Our analysis shows that MI is superior to the other increase policies in fair networks.This is an interesting ?nding because it suggests that the multiplicative-increase multiplicative-decrease (MIMD )algorithm is preferable to the additive-

increase multiplicative-decrease(AIMD)algorithm in fair networks.In traditional networks,AIMD is considered to be more suitable than MIMD since MIMD does not ensure convergence to fairness in such networks under the assumption of synchronous feedback[4].Thus,the choice of the network architecture proves to be an important parameter in evaluating adjustment algorithms.

Our study can also be used for selecting an adjustment algorithm for a streaming application in a fair network.If the application needs its overload to be bounded by some smoothness requirement,then the adjustment algorithm should employ the multiplicative increase policy with increase coef?cient.The decrease coef?cient for the multiplicative decrease policy could be selected in a similar fashion based on the smoothness requirement of the application in terms of its underload.

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A Proofs for Section4

Lemma1In the overloaded network,the fair share is at least the guaranteed throughput:

Proof:According to(3),implies that and consequently

Lemma2The examined?ow is assured to reach the guaranteed throughput:

Proof:Let us assume that the lemma statement is false;i.e.,.Then,we can derive:

min

min min

according to(3),if

min

according to Lemma1,if

induction on(6)

(8)where,,and

according to(1),

Lemma1

according to(11),

min

A contradiction.Thus,.The?ow is assured to reach the guaranteed throughput.

Theorem1is the maximum throughput that the examined?ow is guaranteed to reach.

Proof:In the case of,the examined?ow shares the network with a nonempty set of other?ows.Consider a scenario when each of all these?ows always imposes load on the network.Then,the network is permanently overloaded:

(30) Since(3)implies that the fair share does not exceed,each?ow in demands more than the fair share.Then,according to(4):

(31) Taking into account(3),(30),(31),and(4),we derive that:

(32)

if

According to(32),if,then

if(33) Then,

min

if

if

(32)for

(11)

Thus,.The throughput of the examined?ow never exceeds.

In the case when,we have according to(11).Since the throughput can not exceed the network capacity,the throughput of the examined?ow does not exceed.

In both cases,the throughput of the?ow does not exceed.According to Lemma2,the?ow is guaranteed to reach. Therefore,is the maximum throughput that the?ow is guaranteed to reach.

,,and

max

max The overload for AI policy equals:

(16)

max

max The overload for ISI policy equals:

(16)

max

max

The overload for II policy equals:

(16)

max

max

Thus,the values of overload for MI,AI,ISI,and II policies are,respectively.

and

.Using(15),we derive the convergence time for MI policy:

.Using(15),we derive the convergence time for AI policy:

Lemma5MI is feasible with respect to responsiveness and smoothness iff:

Proof:

MI is feasible with respect to responsiveness and smoothness

De?nition6.1

Lemma3and Lemma4

Lemma6AI is feasible with respect to responsiveness and smoothness iff:

Proof:

AI is feasible with respect to responsiveness and smoothness

De?nition6.1

Lemma3and Lemma4

Lemma7The values of guaranteed convergence time for MI and AI policies are and

min

(19)

According to Lemma3,the overload of AI policy is

.Thus,https://www.wendangku.net/doc/c310980846.html,ing this,we derive the guaranteed convergence time for AI policy:

(24)

min max

Lemma4

min max

iff

(19)

respectively.

.Using this,we can rewrite(24)to express the guaranteed convergence time for ISI policy:

max

. Similarly,the guaranteed convergence time of ISI policy in the second network is provided by policy with parameter setting

By induction,we have for any.Thus,policy reaches the guaranteed throughput between and in the?rst network after exactly the same number of adjustments as the number of adjustments it takes for policy to reach the guaranteed throughput between and in the second network.Thus,the guaranteed convergence time of ISI policy does not depend on the minimum guaranteed throughput.

.Then,according to De?nition6.3,the set of-smooth settings for II policy consists of such that

the guaranteed convergence time of II policy in the?rst network is provided by policy with parameter setting. Similarly,the guaranteed convergence time of II policy in the second network is provided by policy with parameter setting .

Note that.Let us assume that.Then,

policy is the II policy with parameter setting

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公司目前的主要产品有“平安宝典”和“长寿秘笈”两大系列,涉及高档精美挂历、撕历、台历、记事周历、家庭消防安全红宝书、安全系列扑克、享“瘦”日志等,融实用性与知识性为一体;既有古典韵味,又具时尚气质;既可自用, 更是送礼佳品!更多精彩产品,即将陆续上市,敬请期待!

标题(含副标题):全面,新颖 针对每款产品作详细介绍,如:特色、定位、规格、辐射范围(国内外)、合作单位等 《享瘦日志》 《家庭消防安全红宝书》 《消防安全知识扑克》 《家居安全知识扑克》 《地震安全知识扑克》 《交通安全知识扑克》 《长寿秘笈-四季养生篇》周历 《长寿秘笈-长寿名人篇》周历 《平安宝典-避险求生篇》周历 《长寿秘笈》撕历双日历形式 《平安宝典》撕历双日历形式 《长寿秘笈-四季养生篇》方形撕历双日历形式《办公室养生》台历 《享瘦日志》 享瘦日志——快乐的减肥旅程 Easy diet and exercise jour nal

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创建连接点:如下图,在下面2个圆柱孔的中心,注意是圆柱体的中心,不是某个面得中心,创建2个keypoints。具体方法,看个人而定。 1.3 划分单元 对体用3D单元划分,我选用meshtool方法

接下来设置real constants,这个参数设置,一定要到等到3D网格划分完后再设置 对MASS21 进行设置。

Real constant Set No. 要大于2,下面的值要非常小。 然后对连接点,即keypoints进行单元划分:先设置keypoints 属性,如下 然后划分单元,用meshtool, 对keypoints划分单元,结果如下如下图

1.4建立刚性区域 刚性区域都是节点=连接节点+刚柔接触的面上所有节点 在ANSYS里面,这一步,连接点为主节点,刚柔接触面上的所有节点为从节点首先得按如下2个图片进行主节点和从节点节点组合。(或者用循环语句也行)

1.4.1建立主节点component 选择1个主节点,即连接节点。 接下来

怎样介绍自己的产品

怎样介绍自己的产品怎样介绍自己的产品 叶志常

许多销售员朋友,总在抱怨产品销售不出去总是说价格太高,产品包装不漂亮,产品没有特色, 可就是不去思考自己的销售思路对不对, 自己为销售付出了多少? 掌握销售知识有多少? 自己付出了多少热情和智慧? 如何向客户介绍产品呢?

在向客户介绍产品之前一定要搞清楚一个概念:产品的弱点.产品的弱点是指没有质量问题,却在竞争中 相对于同类产品处于劣势的产品特点,比如:耗电大,价格贵,包装不美观,样式太老,使用不太方便等等...... 这些产品弱点有的是为了 产品的其他优点而产生的,有的是可以改变的,有的 是不能马上改变的.在回答 客户时,一定要做以区分.

常言到:有一利必有一弊.反之有一弊也必有一利.当我们遇到客户问到产品的弱点时, 首先,不要回避问题,也不要去和客户争执.正面承认自己产品存在的弱点.比如:你可以说:您说的很对,在长期的销售中,我们也发现了自己产品的这个弱点,你能指出来我 非常感谢,我们会尽力去改进的. 第二,要委婉的把自己产品产生的弱点原因讲清楚.

比如:你可以说:我们的产品之所以耗电量大,是因为我们为了保障产品的大功率,保障在紧急的情况下,我们的产品一样能正常的工作.再比如:我们的产品之所以价格贵过同类产品,是由于我们为了保证产品的功效,选择了质量最好的原材料,所以它的效果一定要比同类产品好.这一点是得到市场验证了的.

第三,向客户讲明为了弥补产品的弱点,所做的售后增值服务. 比如:我公司生产的电子产品虽然比不上做了很长时间的厂家有名气,可我们电子产品也在极力打造自己的品牌,在售后服务上,我们承诺做到免费保修五年,终生维修的原则.

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ADAMS与ANSYS的双向数据交换

ADAMS与ANSYS的双向数据交换ADAMS软件是著名的机械系统动力学仿真分析软件,分析对象主要是多刚体。但与ANSYS软件结合使用可以考虑零部件的弹性特性。反之,ADAMS的分析结果可为ANSYS分析提供人工难以确定的边界条件。 ANSYS进行模态分析的同时,可生成ADAMS使用的柔性体模态中性文件(即.mnf文件)。然后利用ADAMS中的ADAMS/Flex模块将此文件调入ADAMS 以生成模型中的柔性体,利用模态叠加法计算其在动力学仿真过程中的变形及连接节点上的受力情况。这样在机械系统的动力学模型中就可以考虑零部件的弹性特性,提高系统仿真的精度。 反之,ADAMS进行动力学分析时可生成ANSYS软件使用的载荷文件(即.lod 文件),利用此文件可向ANSYS软件输出动力学仿真后的载荷谱和位移谱信息。ANSYS可直接调用此文件生成有限元分析中力的边界条件,以进行应力、应变以及疲劳寿命的评估分析和研究,这样可得到基于精确动力学仿真结果的应力应变分析结果,提高计算精度。 在ANSYS中生成mmf文件的方法: ANSYS软件是当今最著名的有限元分析程序,其强大的分析功能已为全球工业界所广泛接受,成为拥有最大用户群的CAE软件供应商。其特点如:多场及多场耦合分析、多物理场优化、统一数据库及并行计算等等都代表着CAE软件的发展潮流。 ADAMS软件是目前最具权威的机械系统动力学仿真软件,通过在计算机上创建虚拟样机来模拟复杂机械系统的整个运动过程,从而达到改进设计质量、节约成本、节省时间的目的。 通过ANSYS软件与ADAMS软件之间的双向接口,可以很方便的考虑柔性体部件对机械系统运动的影响,并得到基于精确动力学仿真结果的应力应变分析结果,提高分析精度。 接口背景 ADAMS/Flex软件允许在ADAMS模型中根据模态频率数据创建柔性体部件,柔

三生中国产品特色产品介绍

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Modeling/Create/Volumes/Cylinder/By Dimensions Modeling/Operate/Booleans/Subtract/Volumes 先拾取长方体,再拾取圆柱体。 Modeling/Create/Volumes/Cylinder/By Dimensions 、 划分掠扫网格 Meshing/Size Cntrls/ManualSize/Lines/Picked Lines 拾取插销前端的水平和垂直直线,输入NDIV=3再拾取插座前端的曲线,输入NDIV=4

PlotCtrls/Style/Size and Shape,在Facets/element edge列表中选择2 facets/edge 建立接触单元 : Modeling/Create/Contact pair,弹出Contact Manager对话框,如图所示。 单击最左边的按钮,启动Contact Wizard(接触向导),如图所示。

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7.建立刚性区域(在ADAMS作为和外界连接的不变形区域,必不可少的), preprocessor->coupling/ceqn->rigid region,选择interface nodes附近的区域的nodes与其相连,由于连接点的数目必须大于或等于2,所以刚性区域至少两个;先选择interface node,单击Apply,再选周围的nodes。

8.执行solution->ADAMS connection->Export to ADAMS命令,要选择的 节点为7中建立刚性区域的节点(仅仅是interface nodes),输出单位就选SI就行;即可生成*.mnf文件。

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4.创建截面类型。主要是设定面积,转动惯量等,为梁单元的截面。 5. 用SOLID185给连杆划分网格。 6. 在两个圆孔中心创建两个节点。这两个节点在后面用于与ADAMS中的刚体相连接。 7. 在第一个节点与周围的圆上节点之间创建BAEM188蛛网单元。

8. 在第二个节点与周围的圆上节点之间创建BAEM188蛛网单元。 这是创建完毕后的整体效果 9.进入到ANSYS中的ADAMS接口设置。 首先选择两个圆心接口节点。

OK后弹出下面的设置对话框 确定选择后,点击“solve and create export file to ADAMS”1分钟不到就生成了ADAMS所需要的模态中性文件,如下图。

下面进入到ADAMS。 1. 打开ADAMS201 2. 2. 在工具栏中选择ADAMS/FLEX按钮以创建柔性体 3. 在下面对话框确定柔性体的名称,并指定前面的模态中性文件的位置,然后OK 4. 片刻之后,该模型生成,如下图。

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