A Mobility Model For UAV Ad hoc Network
For UA V Ad hoc Network Abrassart,Fabien Garcia,Nicolas Larrieu
for Civil Aviation(ENAC),Toulouse,France
https://www.sodocs.net/doc/7937748.html,rrieu}@enac.fr
alinoe.abrassart@free.fr
Abstract—With the technological advances,there is an in-creasing attention on micro-UA Vs in the military area as well as in the civilian domain.They are used as swarm(several UA Vs) forming a UAS(Unmanned Aircraft System)since they are relatively cheap and offer better performance than one aircraft.
The UA Vs,in a UAS,have to exchange information with each other and with the control station in order to create a clear vision of the swarm situation and the task performance. This exchange is made possible by the application of an ad hoc network between UA Vs which is a challenging issue
of the node mobility,the network topology change,and the operation communication requirements in term of quality of service(delay,throughput or loss rate for instance).
This paper presents a realistic mobility model designed for UA V ad hoc networks.since evaluating the performances of ad hoc protocols is an important step in order to predict possible problems that can affect the system in the real environment.This mobility model behavior is compared to the well-known mobility model behavior Random-Way Point.It is also compared to real movements traces using several metrics.
Index Terms—Mobility models,Ad hoc networks,UA V,Pa-parazzi system.
I.I NTRODUCTION
Nowadays,utilization of UA Vs has become extremely popular thanks to automation and sensor technology advances that encourages many researchers to study the use of several collaborative UA Vs in order to reduce the human intervention as much as possible([1],[2],[3],[4]and[5]).UA Vs have to exchange information with each other(inside the swarm)and with the control station(outside the swarm)in order to meet the needs of applications such as?cooperative task allocation?[4],?path planning?[5]or?communication relaying?[6].
The Mobile Ad hoc Network(MANET)[7]is a solution to deliver this information to its destination over long ranges via one or multiple relays[8](Figure1).In fact,MANET is multi-hop wireless network:each node in the network act as a mobile wireless terminal as well as a router to forward information to its neighbors.Thus,all nodes in the network are connected without requiring a pre-existing infrastructure (such as satellites or central stations with several antennas) which makes MANET a cost-effective technology.Moreover, nodes in an ad hoc network have the possibility to move freely,they move toward and away from other nodes which creates new links and breaks others.Therefore,MANET necessitates speci?c communication protocols in order to be an autonomous system that can faces dynamic,random, sometimes rapidly changing multi-hop topology due to UA Vs mobility.Routing protocols are an example of these proto-cols,they are the responsible for discovering the network topology and for establishing routes to each destination.A route is the list of intermediate nodes(relays)traversed by each message in order to achieve its destination.
Fig.1:UA V Ad hoc Network
The evaluation of an ad hoc network in order to predict possible problems that can affect the communication system, is achievable by resorting either to experimentation networks, called test-bed,or to simulation,using network simulators. Test-beds enable the experimentation of protocols and their application in a real environment.In general,several draw-backs hinder the realization of a test-bed[9],mainly,the inherent lack of?exibility(i.e.scenarios repetition)and the dif?culty of managing and deploying network monitoring mechanisms.The monitoring should have minimal impact on the normal operation of the network;it has to use minimal computing,storage,and bandwidth resources.These dif?culties can impede the network scalability[8].
On the contrary,simulations allow an easier way to mon-itor the network since it consists in a synthetic environment which models experiments.Protocols and experimentations are described as reproducible scenarios in?les that are easily modi?able.Consequently,simulation is the most widely used solution because it offers a viable alternative,although it idealizes situations since it models them.
Mobility models are one of these features of the simulation environment.They de?ne trajectories and speed variations
of the mobile nodes and represents their positions,which generate network topology changes and then communication perturbations since new links will be created and others will be broken.Therefore,the mobility model plays an important role in the evaluation of the ad hoc network performance [10].
This paper presents a realistic mobility model designed for UA V ad hoc networks based on the Paparazzi UA V movements,presented in III-A,then it compares it to another mobility model and UA V real traces as a validation mean using several metrics selected from the literature.
It is organized as follow:the?rst section presents some related work.The second section introduces Paparazzi system and the context of this study,then it presents the realistic mobility model designed for UA Vs.After that,The validation part is presented in the third section,then the conclusion and the future work end this paper.
II.R ELATED WORK
Mobility models are indispensable for ad hoc network research in order to create a realistic simulation environment. In fact,in[10],authors showed how the performance of an ad hoc protocol can vary signi?cantly with different mobility models.They compared the impact of the most common mobility models on a well-known ad hoc routing proto-col,Dynamic Source Routing Protocol(DSR)[11].Results showed that DSR performance is greatly affected by mobility model changes.Another study in[12],showed that the mobility model affect the network performance.Therefore, the mobility model has to be the most closely matched to the expected real environment.For this reason,many researchers chose to create realistic models for MANET like in[13],[14] and[15].However,fewer propositions are studied for UA V ad hoc networks like in[16],and in[17].In general,The well-known?Random-Way Point mobility model?(RWP)[10]is used in such situation.
In[16],authors presented two for recon-naissance application:?random mobility model?and?dis-tributed pheromone repel mobility model?.These mobility models are based on three actions:going straight,turn left and turn right.With the random mobility model proposed, UA Vs decide on their actions according to?xed probabilities while with pheromone model,a pheromone map is used to guide UA Vs.The aircraft exchange information about their scanned area,and according to what they decide,they turn left,right or go straight ahead.
In[17],the Semi-Random Circular Movement?SRCM?, is presented.This mobility model is designed for the curved movement scenarios of UA Vs,it is suitable for simulating UA Vs turning around a speci?c position in order to gather some information.
In[18],authors proposed two mobility models for airborne networks based on circular trajectories.They permit changing ?ight altitude.The?rst model captures the correlation of movement among all three dimensions while in the second,z-dimensional movement(altitude)is independent from the two other dimensions.
The mobility model validation issue is not addressed in the literature.There is no common methodology to validate a new mobility model or to compare it to another model.Authors in [10]compared common mobility patterns between each other using only network performance measures like data packet delivery ratio or hop count.
Other papers develop new models and compare them to other models or to real traces.Indeed,in[16],authors compared the two proposed models only to each other using a geometric criterion:the scan coverage and a network measure:the UA V connectivity.This comparison did not show the effect of the mobility-related information exchange on the behavior of the network.
Away from the UA V networks,in[19],authors evaluated their new mobility model based on the comparison with real movement traces using two properties:the contact duration (the time interval in which two are in radio range) and the inter-contacts time(the frequency and the probability of being in contact with the packet receiver).The idea of comparing the new mobility model with real traces seems to be a good way to validate the behavior of the new mobility model.
The validation process we de?ned for our study will be described in section IV-A of this paper.
III.P APARAZZI M OBILITY M ODEL(PPRZM)
A.Paparazzi System
Paparazzi[20]is an open source system of hardware and software for the UAS:for?xed-wing aircraft as well as multicopters.It is composed by an automatic pilot,a ground station mission planner and monitoring software.Paparazzi is being used by a number of universities,companies and hobbyists all over the world and it has been developed at ENAC(French University for Civil Aviation).
In the context of the European project D3CoS[21]?De-signing Dynamic Distributed Cooperative Human-Machine Systems?which focuses on the cooperation between different types of intelligent agents(such as UA Vs,cars,boats,air-planes),the communication between several Paparazzi UA Vs and the ground station over an ad hoc network is studied as an example of collaborative agents.
The communication system plays an important role in the success of such cooperative applications.Therefore,it is necessary to evaluate communication protocols which will be used.This evaluation can be realized by a simulation in realistic conditions to predict problems that can affect the network in the real environment.Thus,it is important to choose the appropriate mobility model.In this context,we present Paparazzi mobility
B.Paparazzi Mobility Model(PPRZM)
According to Paparazzi experts,Paparazzi UA Vs have?ve possible movements:
?Stay-At:the UA V hovers over a?xed position(Figure 2a);
?Way-Point:the UA V follows a straight path to a desti-nation position(Figure2b);
?Eight:the aircraft trajectory has the?8?form around two?xed position(Figure2c);
?Scan:the UA V performs a scan of an area de?ned by two points along the round-trip trajectories(Figure2d);?Oval:a shifted round-trip between two points with a turn around once pass each point(Figure2e).
(b)
(c)
(d)
(e)
Fig.2:Paparazzi UA V Movements
Paparazzi mobility model(PPRZM)is a stochastic mobil-
ity model that imitates Paparazzi UA V behavior based on the
state machine presented in?gure3.
Fig.3:PPRZM state machine
Each UA V chooses a movement type and?xes its charac-
teristics:
?Location:the center positions for?Stay-At?,?Eight?
and?Oval?movements or the starting and the ending
positions for?Scan?and?Way-Point?movements;
?Speed:a uniform random value between15m/s and25
m/s.
Thus,UA Vs are assigned a speci?c position through a
?Way-Point?movement,then it follows a well-de?ned path
according to the movement chosen.Each aircraft altitude is
?xed randomly at the beginning.Once reached,it remains
constant till the end of the simulation.
All of these movements have different probabilities to
occur.According to Paparazzi experts,?Stay-At?,?Oval?,
and?Scan?are the movements the most produced during
a mission?ight.Therefore,probabilities used were?xed as
follow:
??Stay-At?,?Oval?,and?Scan?probabilities are equal
to30%for each movement;
??Eight?and?Way-Point?probabilities are equal to5%
for each movement.
PPRZM was implemented in OMNET++[22]simulator
and it is available by contacting the authors.OMNET++is
a communication network simulator.It is component-based
C++simulation library and framework,used to evaluate
communication systems and protocols.
IV.S IMULATIONS AND RESULTS
This section presents a comparison between PPRZM,the
Random Way-Point(RWP),and real Paparazzi movement
traces in order to show that PPRZM has closer behavior to
the real traces than RWP.
RWP is characterized by straight trajectories.Each mobile
nodes selects a random destination,moves with a random
speed and pauses for a?pause time?at the destination.When
the pause time expires,the node chooses another random
position and moves with another speed value at this location.
The Paparazzi movement traces are extracted from the
Paparazzi emulator which is based on the same software used
to pilot real UA Vs.This emulator,also takes into account the
wind conditions.
A.Evaluation Means
As presented in section II,there is no common method-
ology to validate a mobility model.Therefore,we chose to
compare PPRZM behavior with the behavior of the well-
known mobility model RWP and with Paparazzi movement
traces.This comparison is based on different measures pre-
sented in the literature.The selected metrics are classi?ed
into two classes:geometric and network related.
1)Geometric measure:geometric measures are based on
the physical traces of the mobile nodes(trajectories)and
their impact on the network topology.For this study,?ve
are selected to be used:
?Empty Cells:the simulated area is divided into cells of the same size as a grid.the cell number has to be equal to the node number.So,UA Vs are uniformly distributed, if,on average,there is one aircraft per cell.This metric calculates the number of empty cells over time.It refers to the distribution uniformity of UA Vs in the simulation area;
?Frequency:it is based on the same principle of dividing the simulated area into cells.It refers to the average of the number of times that a UA V crosses each cell over the visited cell number.The?nal value is the average over the UA V number.So,the frequency has a high value if each UA V visits limited number of cell;?Number of Neighbor:it is the average of neighbor number per aircraft.Two nodes are neighbors if they are in range of communication.This metric refers to the possibility to create a multi-hop network.However, an important number of neighbor can affect the network performance since it increases the interference rate.?Meeting:it is the number of created and broken links during the simulation.This measure refers to the net-work stability.The higher the value,the less stable the network is;
?Clustering:it is the ratio of one node neighbor number and its two hop-distance neighbor number(neighbors of neighbors).The clustering value is higher if the nodes tends to clump together in clusters.
These metrics reveal the geometric characteristics of the network,that refers to its topology,it seems to give an intuition of the dif?culties that can affect the communication protocol(i.e.the possibility of creating a multi-hop network, or forming disconnected clusters,etc.)but they cannot reveal the impact of this behavior on the network.Thus,other metrics should be used to evaluate the network performance.
2)Network related measure:the network measures aims at evaluating the communication protocol performance.In this context,some metrics are selected:
?Delivery Ratio it presents the comparison between the packet received number of each UA V and the total packet sent number;
?End To End Delay:it is the delay between the?rst byte transmitted and the last byte received;
?Hop Count:it refers to the number of intermediate nodes used to deliver each packet to its destination.?Rate:it is the network rate;
?RREQ Number:it is the number of routing packet sent, it refers to the dif?culty that may encounter the selected routing protocol,which is AODV[23].
AODV is selected because it is one of the most popular reactive routing protocol.The reactive protocols establish routes only when needed.Therefore,they save bandwidth. Moreover,AODV implementation are readily available for simulations and real systems alike which will be an asset later in our research which will be implemented on Paparazzi UA Vs.
Different importance or weight could be allocated to each measure depending on the application?eld of the mobility model.For this study,all selected measures have equal weight,there is no emphasis given to speci?c metrics.This assumption is made because we do not want to make speci?c utilization of PPRZM since this evaluation has a validation purpose.
B.Simulation Scenario
In order to compare PPRZM,RWP and real traces,the scenario presented in table I,is?xed;
TABLE I:Simulation scenario
UA V number40
Simulation duration1000sec
Speed Uniform random value
between[15m/s,25m/s] Scan movement radius75m
Other circular movement radius80m
Simulated area1500m x1500m
Evaluated routing protocol AODV
Transmission range100m
MAC protocol802.11
Channel capacity54Mbps
Traf?c per UA V UDP(64Bps)
As in the real traces,the UA Vs are stationary at their initial positions for the?rst10seconds.After that,they start moving until the end of the simulation.
UA Vs exchange UDP messages of64Bytes every second over an ad hoc network using AODV routing protocol,this enables us to calculate network measures in terms of delivery ratio,end to end delay,etc.
C.Simulation Results
All measures of the same type(geometric and network related)are presented on a Kiviat diagram which allows to represent each metric relative to its maximum value and to facilitate the comparison between the three mobility models (PPRZM,RWP and real movement traces).For each metric, the presented values on the Kiviat are the ratio of the calculated value to the maximum value of the three mobility models.Hence,the maximum value for each measure is presented as the value1.
Figure4presents the geometric results of PPRZM,RWP and real Paparazzi traces presented on the Kiviat diagram.A ?rst look at the chart shows a different behavior between the three simulated models which con?rms that each mobility model has a unique effect on the network behavior.?Empty Cells?,?Frequency?and?Meeting?measures of PPRZM are the closest to real traces ones.Therefore,PPRZM has three results than RWP over?ve since there is no emphasis given to speci?c metrics.
Neighbor
Fig.4:Geometric comparison
Fig.5:Network comparison
Figure 5presents the network performance measures of PPRZM,RWP and real Paparazzi traces.The Kiviat diagram shows,also,a difference between the behavior of the mobility models.PPRZM have three closest value to real trace ones which are:?End To End Delay?,?RREQ Number?and ?Hop Count?.
For the second time,PPRZM has three better results than RWP over ?ve.
For a general study,in which there is no emphasis given
to speci?c metrics.PPRZM has the closest behavior to Paparazzi real traces.
PPRZM Use Case
PPRZM can be used to evaluate any communication pro-tocol in the context of swarm of collaborative UA Vs since it affords a realistic movement scenario.For instance,it may be used to compare several routing in order to ?nd the suitable one for UA V Ad hoc network.Moreover,PPRZM can adapt to any type of mission because it groups most UA V possible movement by changing the probability of each movement type as needed.For example,just by ?xing the probability of ?Scan?movement equal to 1and all the others equal to zero,it is possible to evaluate a communication protocol in the scenario of scan mission,in which UA Vs do only ?Scan?movement.
V.C ONCLUSION AND FUTURE WORK
Wireless communications are a challenging issue to pro-vide a better performance for a UAS using several collabo-rating UA Vs.In fact,aircraft have to exchange information about their situation and their tasks with each other as well as with the control station.In such environment,the ad hoc network is a promising solution.
In order to predict communication problems that may affect the UAS performance,ad hoc protocols have to be evaluated using a test-bed or a simulation under a realistic environment.It is important to use a realistic mobility model.In fact,the node mobility has a great effect on the network topology and the communication protocol performance.This paper presented a realistic mobility model designed for UA V ad hoc network based on Paparazzi UA Vs move-ments.It can be used by any researcher studying UA V networks.
First,section III introduced PPRZM (Paparazzi Mobility Model).After that,in section IV ,a validation methodology was presented.It compared PPRZM to a common used mobility model,the Random Way-Point,and real UA V traces generated from Paparazzi emulator.
Since there is no common methodology to validate a mobility model,we made our comparison based on geometric and network related measures selected from the literature.For this study which has a validation purpose,all measures selected have equal weight,there is no emphasis given to speci?c metrics.In fact,this assumption could be modi?ed depending on the application ?eld of PPRZM;different weight or importance could be allocated to the selected metrics.
Results of both metric types;geometric and network per-formance,show that PPRZM has a closer behavior to the Paparazzi real traces than RWP.
In future work,PPRZM will be evaluated under different environment conditions and compared with other mobility models designed for UA V ad hoc network such as the models presented in section II.After that,it will be used to evaluate our QoS ad hoc architecture designed for UA V networks [24].
A CKNOWLEDGMENT
We would like to thank the ENAC?Paparazzi Team?for their constructive feedback and information.We also would like to thank Miss Chifa Abassi for her contribution to this work.
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ISLM模型
IS-LM模型（IS-LM Model） 什么是IS-LM模型 IS—LM模型是反映和同时均衡条件下，和关系的模型。 "IS-LM"模型，是由英国现代着名的(John Richard Hicks)和美国的创始人(AlvinHansen)，在理论基础上概括出的一个模式，即"希克斯-汉森模型"，也称"希克斯-汉森综合"或"希克斯-汉森图形"。 按照的观点，(L)和货币数量(M)决定着的均衡，而人们持有的货币数量既决定于利率(i)，又决定于(y)的水平。由此，在以纵轴表示利率、横轴表示收入的坐标平面上，可以作出一条(如图1)。 (1) I(i)=S(Y) 即IS, Investment - Saving (2) M/P=L1(i)+L2(Y） 即LM，Liquidity preference - Money Supply 其中，I为，S为，M为名义货币量，P为，M/P为实际货币量，Y为总产出，i为利率。 曲线上的每一点都表示持有的愿望和货币数量相等，即和相一致，并且同既定的利率和收入水平相一致。 希克斯又认为，社会储蓄(S)和投资(I)的愿望，决定的均衡，而储蓄和投资又必须同收入水平和利率相一致。由此，在纵轴表示利率、横轴表示收入的座标平面上，又可作出一条(如图1)，曲线上的每一点都表示储蓄等于投资，并且同既定的利率和收入水平相适应。 通过以上分析，对收入的决定作出了新的解释，认为收入(Y)的均衡水平是由与LM曲线的交点决定的，即凯恩斯体系的四大根基--、、和货币数量同时决定收入的均衡水平。在收入均衡点上，同时存在着以LM表示的货币市场的均衡和以IS表示的资本市场的均衡。如图1-5中， IS-LM模型在一个平面坐标中表示，横轴表示经济需求面决定的收入或产出（Y），纵轴表示利率（R）。IS曲线表示产品市场均衡条件，LM曲线表示货币市场均衡条件。 (1) 在横轴表示收入，纵轴表示利率的平面系统中，是一条向右下方倾斜的曲线。IS线代表满足产品市场均衡条件的利率和产出水平组合的集合。 简单收入决定模型中，investment（I）等于saving（S）是产品市场均衡条件，因而把描述商品市场均衡条件的产出与利率关系组合曲线称为IS曲线。表明： ?①I(i)=S(Y) 即IS, Investment - Saving ?②M/P=L1(i)+L2(Y）即LM，Liquidity preference - Money Supply 其中，I为投资，S为储蓄，M为名义货币量，P为物价水平，M/P为实际货币量，Y为总产出，i 为利率。
IS-LM模型
IS-LM模型 IS-LM模型（IS-LM Model） 什么是IS-LM模型 IS—LM模型是反映产品市场和货币市场同时均衡条件下，国民收入和利率关系的模型。 "IS-LM"模型，是由英国现代著名的经济学家约翰·希克斯(John Richard Hicks)和美国凯恩斯学派的创始人汉森(AlvinHansen)，在凯恩斯宏观经济理论基础上概括出的一个经济分析模式，即"希克斯-汉森模型"，也称"希克斯-汉森综合"或"希克斯-汉森图形"。 按照希克斯的观点，灵活偏好(L)和货币数量(M)决定着货币市场的均衡，而人们持有的货币数量既决定于利率(i)，又决定于收入(y)的水平。由此，在以纵轴表示利率、横轴表示收入的坐标平面上，可以作出一条LM曲线(如图1)。 (1) I(i)=S(Y) 即IS, Investment - Saving (2) M/P=L1(i)+L2(Y） 即LM，Liquidity preference - Money Supply 其中，I为投资，S为储蓄，M为名义货币量，P为物价水平，M/P为实际货币量，Y为总产出，i为利率。 曲线上的每一点都表示持有现金的愿望和货币数量相等，即货币需求和货币供给相一致，并且同既定的利率和收入水平相一致。 希克斯又认为，社会储蓄(S)和投资(I)的愿望，决定资本市场的均衡，而储蓄和投资又必须同收入水平和利率相一致。由此，在纵轴表示利率、横轴表示收入的座标平面上，又可作出一条IS曲线(如图1)，曲线上的每一点都表示储蓄等于投资，并且同既定的利率和收入水平相适应。 通过以上分析，希克斯对收入的决定作出了新的解释，认为收入(Y)的均衡水平是由IS曲线与LM曲线的交点决定的，即凯恩斯体系的四大根基--消费函
国民收入决定理论-IS-LM模型习题及答案全的
一、名词解释 1．资本边际效率2．自主投资 3．加速原理4．投资边际效率 5．IS曲线6．LM曲线 7．流动性偏好8．凯恩斯陷阱(流动偏好陷阱) 9．货币供给10．IS—LM模型 11．谨慎动机12．产品市场和货币市场的一般均衡 二、单选题 1．在凯恩斯的理论体系中，货币需求和货币供给函数决定( )。 A．名义利率B．实际利率C．价格水平D．消费水平 2．若资本边际效率低于市场利率，则企业投资( )。 A．过多B．过少C．正好D．都不对 *3．根据托宾的“q”说，当企业的股票市场价值大于新建企业的成本，则( )。 A．新建企业更合算B．购买旧企业更合算 C．两者都一样D．无法确定 4．( )，LM曲线向右移动。 A．名义利率下降B．总产量增加 C．货币需求增加D．货币供给增加 5．IS曲线右上方、LM曲线右下方的组合表示( )。 A．产品供大于求、货币供大于求B．产品供大于求、货币求大于供C．产品求大于供、货币供大于求D．产品求大于供、货币求大于供6．假定IS曲线和LM曲线的交点所表示的均衡国民收入低于充分就业的国民收入。根据IS—LM模型，如果不让利息率上升，政府应该( )。 A．增加投资B．在增加投资的同时增加货币供给 C．减少货币供给量D．减少投资的同时减少货币供给量 7．自发投资支出增加10亿美元，会使IS( )。 A．右移10亿美元B．左移10亿美元 C．右移支出乘数乘以10亿美元D．左移支出乘数乘以10亿美元 *8．假定货币需求为L=ky—hr，货币供给增加10亿美元而其他条件不变，则会使LM( )。 A．右移10亿美元B．右移k乘以10亿美元 C．右移10亿美元除以k(即10÷k) D．右移k除以10亿美元(即k÷10) 三、多选题 1．IS曲线表示( )。 A．产品市场均衡时收入与利率的组合 B．产品市场总需求等于总供给时，收人与利率的组合 C．产品市场投资等于储蓄时收入与利率的组合 D．货币市场均衡时收入与利率的组合 2．以下关于IS曲线斜率的判断，不正确的是( )。 A．投资需求对利率变化的反应程度敏感，IS曲线较为平缓 B．投资需求对利率变化的反应程度敏感，IS曲线较为陡峭 C．边际消费倾向越大，IS曲线越平缓 D．边际消费倾向越大，IS曲线越陡峭 3．下列引起IS曲线左移动的因素是( )。
IS-LM模型及AD-AS模型分析
第八章 IS-LM 模型(产品-货币市场同时均衡)及 AD-AS 模型（凯恩斯的AD-AS 总供求模型）分析 第一节 产品市场均衡：IS 曲线 一、与产品市场均衡相关的几个函数 1.消费函数：表示消费和收入之间的关系。 C=C 0+cY 其中（0〈c 〈1） C 0为自主消费，是全部消费与支出中不随收入变化而变化的部分消费支出。 C 为边际消费倾向，MPC= Y c ?? 2.储蓄函数：表示储蓄和收入之间的关系。 因为C+S=Y 所以 S=Y-C=-C 0+（1-c ）Y 1-c 为边际储蓄倾向，MPS= Y s ?? 3.投资函数：表示投资和利息率之间的关系。 （1）.投资 1）定义 投资是指资本形成，是指在一定时期内社会实际资本的增加，这里所说的实际资本包括厂房、设备、存货和住宅，不包括有价证券。 2).投资的种类： 根据投资包括范围的不同，可以划分为重置投资、净投资和总投资。 重置投资又称折旧的补偿，是指用于维护原有资本存量完整的投资支出，也就是用来补偿资本存量中已耗费部分的投资。 净投资则是指为增加资本存量而进行的投资支出，即实际资本的净增加，包括建筑、设备与存货的净增加。净投资的多少取决于国民收入水平及利率等变化情况。 重置投资与净投资的总和即总投资，即为维护和增加资本存量的全部投资支出，如下式： I T =D+△I 根据投资内容的不同，可以划分为非住宅固定投资、住宅投资和存货投资。 非住宅固定投资是指企业购买厂房和设备的投资支出。 住宅投资是指建造住宅和公寓的投资支出。 存货投资是指厂商持有存货价值的变动。 根据投资形成原因的不同，可以划分为自发投资和引致投资。
(完整word版)IS-LM模型习题
IS-LM模型 一、名词解释题 1．投资是指资本形成，是指在一定时期内社会实际资本的增加，这里所说的 实际资本包括厂房、设备、存货和住宅，不包括有价证券。 2．重置投资又称折旧的补偿，是指用于维护原有资本存量完整的投资支出，也就是用来补偿资本存量中已耗费部分的投资。 3．自发投资是指由于人口、技术、资源等外生因素的变动所引起的投资。4．引致投资是指由于国民收入的变动所引起的投资。 5．资本边际效率是一种贴现率，这种贴现率正好使一项资本品在使用期限内预期收益的现值等于这项资本品的重置成本或供给价格，一般用MEC来表示。6．投资边际效率也是一种贴现率，是在考虑资本品价格变化条件下，一项资本品在使用期内预期收益的现值等于这项资本品重置成本或供给价格。 7．IS曲线表示产品市场均衡时，国民收入y和利率r成反方向变化的曲 线。 8．货币需求是指由于各种动机而引起的对货币的需要量。 9．凯恩斯陷阱是指当利率低到一定程度时，投机性货币需求对利率的弹性为无限大，人们不再投资或购买债券，而大量持有货币。 10．LM曲线表示货币市场均衡时，国民收入Y和利率R成同方向变化的曲线。 11．IS—LM模型是指产品市场和货币市场一般均衡的模型，反映在产品市场和货币市场同时均衡条件下，国民收入和利率关系的模型。 二、判断题： 1．个人由于未来利率的不确定而要持有用于投机目的的货币余额。√ 2．凯恩斯认为，人们对货币的需求量出于以下三个动机：交易动机、预防动 机和谨慎动机。× 3．如果物价水平上升了，名义货币需求就会增加。√ 4．当利率变得很低时，人们购买债券的风险将会变得很大。√ 5．货币需求也可称为流动性偏好. √ 6．当收入增加时，人们用于满足交易需求的货币需求不变. × 7. 凯恩斯认为交易需求是收入和利率的函数. × 8. 货币供给大量增加将使利率水平趋于零. × 9．利率越高，用于投机的货币则越少. √ 10．实际货币供给增加可以通过价格水平的提高或者名义货币供给的增加来实现. × 11．所谓投机需求是人们为了低价买进高价卖出证券而保持一部分货币的需求. √ 12．当人们预期利率要上升的时候，他们将出售债券. √ 13．在利率很低的情况下，人们倾向于持有不产生利息收入的货币，而放弃持有证券. √ 14．位于LM轴线右下方的所有点表明货币需求小于货币的供给. × 15．LM曲线的斜率恒为正，说明随着收入的上升货币的投机需求也上升. ×16．在价格水平下降情况下，若名义货币供给量不变，也会引起LM曲线向外 移动. √