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A Multi-channel MAC Protocol for Ad Hoc Wireless Networks

A Multi-channel MAC Protocol for Ad Hoc

Wireless Networks

Jungmin So Nitin H.Vaidya Dept.of Computer Science,and Dept.of Electrical and Computer Eng.,and

Coordinated Science Laboratory Coordinated Science Laboratory University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign Email:jso1@https://www.wendangku.net/doc/9714771866.html, Email:nhv@https://www.wendangku.net/doc/9714771866.html,

Technical Report

January2003

Abstract—This paper proposes a medium access control (MAC)protocol for ad hoc wireless networks that can utilize multiple channels dynamically to improve perfor-mance.IEEE802.11standard provides multiple channels for use,but its MAC protocol is designed only for a single channel.We can achieve improved throughput with multiple channels because multiple transmissions can take place simultaneously without interfering each other.

We modify IEEE802.11DCF protocol to enable hosts to utilize multiple channels by switching channels dynam-ically.Our scheme requires only one transceiver for each host.The main idea is to use ATIM windows as in power saving mechanism(PSM)of IEEE802.11DCF,so that hosts can negotiate and select channels during the window using ATIM messages.Our scheme improves throughput of the network signi?cantly,especially when the network is highly congested.We have simulated our protocol to verify its performance compared to IEEE802.11and another multi-channel MAC protocol.The results show that our protocol performs better than both.The improvement over the existing multi-channel MAC protocol is obtained even though our protocol uses simpler hardware.

I.I NTRODUCTION

IEEE802.11standard for wireless LAN[1]has a medium access control(MAC)protocol designed for sharing a single channel between hosts.Due to the broadcast nature of wireless transmission,when two hosts are communicating,all other hosts within the range of the two hosts must defer their communication in order to avoid collision.This results in a signi?cant throughput degradation as the number of active hosts increases.

A lot of work has been done to improve the throughput of wireless networks,and various approaches have been proposed.One approach is to control the transmission power[2].The basic idea of power control is to have the sender transmit with power just enough to reach the target node,so that the space blocked by that particular transmission is minimized.Another approach is to use directional antennas instead of omnidirectional antennas [3],[4],[5].Directional antennas are able to transmit signal in one direction,so that the hosts located in other directions can communicate concurrently without interfering each other.

These two approaches improve the throughput by increasing spatial reuse,but still they use only a sin-gle channel.The approach in this paper,is to achieve improved performance using multiple channels[6],[7], [8],[9],[10].Data transmitted in different channels do not interfere with each other,thus can take place in the same region simultaneously.So the throughput can increase signi?cantly,proportional to number of channels in ideal case.Although not studied in this paper,having multiple channels can provide furthur bene?ts in addition to increased throughput,such as a more simple way to support QoS.

802.11a

Physical Layer OFDM2

11Mbps

Frequency Band5GHz

IEEE802.11standard already has multiple channels available for use.Table I summarizes the features of IEEE802.11standards.IEEE802.11b physical layer (PHY)has14channels,5MHz apart in frequency[1]. But to be totally non-overlapping and thus feasible for use in the same region,the frequency spacing must be at least30MHz.So channels1,6and11are typically used for communication in current implementations,and thus we have3channels available for use.IEEE802.11a provides12channels,8in the low part of the band for indoor use and4in the upper part for outdoor use[11]. There is enough motivation for concurrent use of mul-tiple channels,but the current MAC protocol is designed for sharing a single channel.The main reason for this is that each IEEE802.11host is equipped with one half-duplex transceiver,so it can only transmit or listen on one channel at a time.So when a host is listening on a particular channel,it cannot hear communication taking place on a different channel.Due to this,as observed in[9],if a single-channel MAC protocol(such as IEEE802.11DCF)is applied in a multi-channel environment wherein each node may dynamically switch channels,performance degradation may occur(unless additional precautions are taken to manage dynamic channel selection).

In this paper,we propose a MAC protocol which enables hosts to dynamically negotiate channels so that multiple communication can take place in the same region simultaneously,each in different channel.The main idea is to divide time into?xed-time intervals using beacons,and have a small window at the start of each interval to indicate traf?cs and negotiate channels for use in that interval.A similar approach is used in IEEE 802.11power saving mechanism(PSM)[1],which is explained in section III.

The rest of the paper is organized as follows.Section II reviews the related work in this topic.Section III pro-vides some background information.Section IV presents our proposed protocol in detail.Section V describes the simulation model we use,and also discusses the results of our simulation.Section VI discusses some issues in our protocol and ways to improve it.Finally,section VII concludes and presents our plans for future work.

II.R ELATED W ORK

There are many related papers that study the bene?t of using multiple channels.Dual Busy Tone Multiple Access[12]divides a common channel into two sub-channels,one data channel and one control channel. Busy tones are transmitted on a separate control channel to avoid hidden terminals,while data is transmitted on the data channel.This scheme uses only one data channel and is not intended for increasing throughput using multiple channels.

Hop Reservation Multiple Access[13]is a multi-channel protocol for networks using slow frequency hopping spread spectrum(FHSS).The hosts hop from one channel to another according to a prede?ned hopping pattern.When two hosts agree to exchange data by RTS/CTS handshake,they stay in a frequency hop for communication.Other hosts continue on hopping,and more than one communication can take place on different frequency hops.This scheme can be done using only one transceiver for each host,but it only applies to slow frequency hopping networks,and cannot be used in systems using other mechanisms such as direct sequence spread spectrum(DSSS).

Nasipuri et al.[7]proposes a multi-channel CSMA protocol with“soft”channel reservation.If there are channels,the protocol assumes that each host can listen to all channels concurrently.A host wanting to transmit a packet searches for an idle channel and transmits on that idle channel.Among the idle channels, one that was used for last successful transmission is preferred.In[6]the protocol is extended to select the best channel based on signal power observed at the sender side.

Wu et al.[9]propose a protocol that assigns channels dynamically,in an on-demand style.In this protocol, called Dynamic Channel Assignment(DCA),they main-tain one dedicated channel for control messages,and other channels for data.Each host has two transceivers, so that it can listen on the control channel and the data channel simultaneously.RTS/CTS packets are exchanged on the control channel,and data packets are transmit-ted on the data channel.In RTS packet,the sender includes suggested data channel information according to the channel condition around itself.The receiver,on receiving RTS,decides which channel to communicate and includes the selected channel information in CTS packet.Then DATA and ACK packets are exchanged on the agreed data channel.This protocol does not need synchronization and can utilize multiple channels with little control message overhead.But it does not perform well in an environment where all channels have the same bandwidth.When the number of channels is small,one channel dedicated for control messages can be costly.In case of IEEE802.11b,only3channels are available,so having one control channel can be interpreted as using 33%the total bandwidth as the control overhead.On

the other hand,if the number of channels is large,the control channel can become a bottleneck and prevent data channels from being fully utilized.[9]mentions that if every control packet has a length of and data packet length is,maximum number of channels should be no more than.

Jain et al.[8]propose a protocol that uses similar scheme as[9]in having one control channel and data channels,but selects the best channel according to the channel condition at the receiver side.By intelligently selecting the data channel,it achieves throughput im-provements,but still has the same disadvantages as DCA. Compared to the above works,our protocol operates with one transceiver per host,and thus does not require any hardware change to current IEEE802.11device. Also,it does not require a separate control channel but considers all channels as identical.Instead,our scheme requires synchronization among all the hosts.IEEE 802.11MAC protocol has a synchronization scheme that works for wireless LANs.Also,[14]discusses synchronization mechanisms for multi-hop networks.At the start of each interval we require all hosts to listen to a common channel in order to exchange traf?c indication messages.During this interval hosts do not exchange data packets.So this duration of time will be an overhead in our scheme.But as we will see in later sections,it achieves better throughput and?exibility than maintain-ing a separate control channel,in an environment where the number of available channels ranges from3to10, and all channels have the same?xed bandwidth.

III.P RELIMINARIES

In this section,we present some background informa-tion on IEEE802.11DCF and power saving mechanism.

A.IEEE802.11Distributed Coordination Function

In IEEE802.11DCF,a node reserves the channel for data transmission by exchanging RTS/CTS messages with the target node.When a node wants to send packets to another node,it?rst sends an RTS(Ready to Send) packet to the destination.The receiver,on receiving RTS,replies by sending CTS(Clear to Send)packet to the sender.RTS and CTS packets include the expected duration of time for which the channel will be in use. Other hosts that overhear these packets must defer their transmission for the duration speci?ed in the packets. For this reason,each host maintains a variable called Network Allocation Vector(NA V)that records the dura-tion of time it must defer its transmission.This whole process is called Virtual Carrier Sensing,which allows the area around the sender and receiver to be reserved for communication,thus avoiding the hidden terminal problem.Fig.1illustrates the operation of IEEE802.11 DCF.

Fig.1.Operation of IEEE802.11DCF.When B is transmitting a packet to C,A overhears the RTS packet and sets its NA V until the end of ACK,and D overhears the CTS packet and sets its NA V until the end of ACK.After the transmission completes,the stations waits for DIFS and then contends for the channel.

If a node has a packet to send but observes the channel busy,it performs a random backoff by choosing a backoff counter no greater than an interval called contention window.Each host maintains a variable,the con-tention window size,which is reset to a value

when the node is initiated.Also,after each successful transmission,is reset to.After choosing a counter value,the node will wait until the channel becomes idle,and start decrementing the counter.The counter is decremented by1after each“slot”time,as long as the channel is idle.If the channel is busy,the node will freeze the counter until the channel is free again.When the backoff counter reaches0,the node will try to reserve the channel by sending RTS to the target node.Since two nodes can pick the same backoff counter,the RTS packet may be lost because of collision. Since the probability of collision is higher as the number of nodes increase,a node will interpret the absence of CTS as a sign of congestion.In this case,the node will double its contention window to lower the probability of congestion.

Before transmitting a packet,a node has to wait for a small duration of time even if the channel is idle.This is called interframe spacing.Four different intervals enable each packet to have different priority when contending for the channel.SIFS,PIFS,DIFS,and EIFS are four interframe spacings,in an increasing order.A node waits for DIFS before transmitting RTS,but waits for SIFS before sending CTS or ACK,which is shorter.So an ACK packet will win the channel when contending with

RTS or DATA packets.

B.IEEE 802.11Power Saving Mechanism

A node can save energy by going into doze mode.In doze mode,a node consumes much less energy compared to normal mode,but cannot send or receive packets.So it is desirable for a node to enter the doze mode only when there is no need for exchanging data.In IEEE 802.11power saving mechanism (PSM),this power management is done based on Ad hoc Traf?c Indication Messages (ATIM).Time is divided into beacon intervals,and every node in the network is synchronized by periodic beacon transmissions.So every node will start and ?nish each beacon interval almost at the same time.At the start of each beacon interval,there exists an interval called ATIM window,where every node should be in awake state and be able to exchange messages.If a node A has buffered packets destined for B,it sends an ATIM packet to

B during this interval.If B receives this message,it will reply back by sending ATIM-ACK to A,and both A and B will stay awake for that entire beacon interval.If a node has not sent or received any ATIM packets during the ATIM window,it enters doze mode and stays until the next beacon time.This process is illustrated in Fig.2.

Fig.2.Operation of IEEE 802.11PSM.Nodes are synchronized by beacons.During the ATIM window,A sends an ATIM packet to B,notifying that it has packets for B.So A and B stays awake for the whole beacon interval.Since C does not send or receive any ATIM packets,it enters doze mode after the ATIM window until the end of beacon interval.

IV.P ROPOSED M ULTI -C HANNEL MAC (MMAC)

P ROTOCOL In this section,we present our proposed scheme.Be-fore describing the protocol in detail,we ?rst summarize our assumptions.

channels are available for use,and all channels have the same bandwidth.None of the channels

overlap,so the packets transmitted on different channels do not interfere with each other.Hosts have prior knowledge on how many channels are available.

Each host is equipped with a single half-duplex transceiver.So a host can either transmit or listen at a time,but cannot do both simultaneously.Also,a host can listen to or transmit on only one channel at a time.So when listening to one channel,it cannot sense carrier on other channels.Unlike our scheme,many other multi-channel MAC protocols require each host to have multiple transceivers [3],[8],[9].The transceiver is capable of switching its channel dynamically.The time elapsed for switching the

channel is less than 1

[15],[16],which is a negligible overhead.

Each host periodically sends out beacons to syn-chronize time in a distributed manner as in IEEE 802.11power saving mechanism.When transmit-ting a beacon,the host includes a timestamp of its local timer.If a node receives a beacon from another node,it cancels its beacon and adjust its timer according to the timestamp included in the beacon.[14]argues that this scheme may not be enough for multi-hop networks,and suggests several solutions to synchronize time in multi-hop networks.Solu-tions to synchronize time are outside the scope of this paper,and this paper assumes synchronization that is achieved through beacons.

Now we describe our proposed scheme in detail.From now on,our protocol will be referred as Multi-channel MAC (MMAC).

A.Preferable Channel List (PCL)

Each node maintains a data structure called Preferable Channel List (PCL),that indicates which channel is preferable to use for the node.PCL records the usage of channels inside the transmission range of the node.Based on this information,the channels are categorized into three states.

High preference (HIGH):This channel has been already selected by the node itself for use in the current beacon interval.If a channel is in this state,this channel must be selected.At most one channel can be in this state at each node.

Medium preference (MID):This channel has not been taken yet for use in the transmission range of the host.If there is no HIGH state channels,a channel in this state will be preferred.

Low Preference(LOW):This channel is already taken at least once for use in the node’s transmission range.To balance the channel load as much as possible,there is a counter for each channel in the PCL to record how many source-destination pairs have planned to use the channel for that interval.If all channels are in LOW state,a node selects the channel with the least count.

The channel states are changed in the following way.

All the channels in PCL are reset to MID state when the node is powered up,and at the start of each beacon interval.

If the source and destination nodes agree upon a channel,they both record the channel to be in HIGH state.

If a node overhears ATIM-ACK or ATIM-RES packet(explained in the next section),it changes state of the channel speci?ed in the packet to be LOW,if it was previously in MID state.When the state of a channel changes from MID to LOW,the associated counter is set to1.If the channel was previously in HIGH state,it stays in HIGH state.If the channel was already in LOW state,the counter for the channel is incremented by1.

B.Channel Negotiation during ATIM Window

In MMAC,periodically transmitted beacons divide time into beacon intervals and ATIM windows are used as in IEEE802.11PSM.The nodes that have packets to transmit negotiate channels with the destination nodes during this window.In the ATIM window,every node must not only stay in awake state,but also must listen to the default channel.The default channel is one of multi-ple channels available,which is selected for exchanging ATIM packets.Note that this channel is used for sending data outside the ATIM window,similar to other channels. If a node S has buffered packets destined for D,it will notify D by sending an ATIM packet.S includes its preferable channel list(PCL)in the ATIM packet.D, upon receiving ATIM packet,selects one channel based on the sender’s PCL and its own PCL.As explained in the next section,the receiver’s PCL has higher priority in selecting the channel.After D selects a channel,it includes the channel information in ATIM-ACK packet and sends it to S.When S receives ATIM-ACK packet, it sees if it can also select the channel speci?ed in ATIM-ACK.S can select the speci?ed channel only except when S has already selected another channel (according to rules for selecting the channel,explained in the subsequent section).If S selects the channel speci?ed in ATIM-ACK,S sends ATIM-RES packet to the D,with S’s selected channel speci?ed in the packet.The ATIM-RES(ATIM-Reservation)is a new type of packet used in our scheme,which is not in IEEE802.11PSM.The ATIM-RES packet noti?es the nodes in the vicinity of S which channel S is going to use,so that the neighboring nodes can use this information to update their PCL. Similarly,ATIM-ACK packet noti?es the nodes in the vicinity of D.After the ATIM window,S and D will switch to the selected channel and start communicating by exchanging RTS/CTS.

If S cannot select the same channel as D,because it has already selected another channel,it cannot send packets to D during the beacon interval,and has to wait for the subsequent beacon interval to negotiate channels again.Even though S?nishes transmitting all the scheduled packets on the selected channel during the beacon interval,it has to buffer all the packets destined for D until the next beacon interval.Since this can be a waste of bandwidth,we may want to let S send packets to D by switching its channel to the same channel as D, in the beacon interval.This issue is discussed in more detail in section VI.

When multiple nodes start sending ATIM packets at the beginning of a beacon interval,ATIM packets will collide with each other.To avoid such collisions, Each node waits for a random backoff interval before transmitting ATIM packet.The backoff interval is chosen in the range of0and.

Note that the receiver can always select a channel for use.Even if all the channels are selected for use in the receiver’s transmission range,the receiver can select one of the channels.This is possible because the sender and receiver still exchange RTS/CTS before sending DATA packet,after the ATIM window.If two source-destination pairs that are closely placed choose the same channel, they will have to contend with each other just as in original IEEE802.11.

Power saving is not the main goal of our protocol,but a node may save power by going into doze mode,if it has not transmitted or received ATIM packets during the ATIM window.The possibility of integration with IEEE 802.11PSM is one of the advantage of our protocol. However,in our simulations,nodes do not go into doze mode.

C.Rules for Selecting the Channel

When a node receives an ATIM packet,it selects a channel and noti?es the sender by including the channel information in the ATIM-ACK packet.The receiver

tries to select the“best”channel based on information included in the sender’s PCL(preferable channel list) and its own PCL.By the best channel we mean the channel with the least scheduled traf?c,as elaborated below.This selection algorithm will balance the channel load as much as possible,so that bandwidth waste caused by contention and backoff is minimized.For this reason,we count the number of source-destination pairs that have selected the channel by overhearing ATIM-ACK or ATIM-RES packets,and select the one with the lowest count.This scheme assumes that every source-destination pair will deliver the same amount of traf?c in a beacon interval,which may not be true.A better approach may be to count the number of packets scheduled to be transmitted on the channel in the beacon interval.To do this,the source may need to include the number of pending packets in the ATIM packet.We take the former approach in this paper,and discuss the latter approach in section VI.

Here we describe the channel selection algorithm in detail.Suppose that node A has packets for B and thus sends an ATIM packet to B during the ATIM window, with A’s PCL included in the packet.On receiving the ATIM request from A,B decides which channel to use during the beacon interval,based on its PCL and A’s PCL.The selection procedure used by B is described as follows.

1)If there is a HIGH state channel in B’s PCL,this

channel is selected.

2)Else if there is a HIGH state channel in A’s PCL,

this channel is selected.

3)Else if there is a channel which is in MID state at

both A and B,it is selected.If there are multiple

of them,one is selected arbitrarily.

4)Else if there is a channel which is in MID state at

only one side,A or B,it is selected.If there are

multiple of them,one is selected arbitrarily.

5)If all of the channels are in LOW state,add the

counters of sender’s PCL and receiver’s PCL,and

the channel with the least count is selected.Tie is

broken arbitrarily.

After selecting the channel,B sends an ATIM-ACK packet to A,specifying the channel it has chosen.When A receives the ATIM-ACK packet,A will see if it can also select the channel speci?ed in the ATIM-ACK packet.If it can,it will send an ATIM-RES packet to B, with A’s selected channel speci?ed in the packet.If A cannot select the channel which B has chosen,it does not send an ATIM-RES packet to B.

The process of channel negotiation and data exchange in MMAC is illustrated in Fig.3.During the ATIM window,A sends ATIM to B and B replies with ATIM-ACK indicating to use channel1.This ATIM-ACK is overheard by C,so channel1will be in LOW state in C’s preferable channel list.When D sends ATIM to C, C selects channel2.After the ATIM window,the two communications(between A and B,and C and D)can take place simultaneously.

Fig.3.Process of channel negotiation and data exchange in MMAC.

V.P ERFORMANCE E VALUATION In this section we evaluate the performance of our protocol by simulation.We have compared our scheme with IEEE802.11,as well as the Dynamic Channel Assignment protocol(DCA),proposed in[9](DCA was explained in section II).Recall that the DCA protocol[9] uses a separate channel for exchanging control messages and uses other channels for data.This approach is also taken by[8],[10].We have used two metrics to evaluate the performance of our protocol.

1)Aggregate throughput over all?ows in the net-

work:

The main goal of our protocol is to increase

total throughput in the network using multiple

channels.Thus,this metric will directly show how

our protocol achieves the goal.Ideally,a multi-

channel MAC will improve the total throughput

by a factor of over single-channel MAC given

that channels are available.But this is not

true in practice because of the overhead required

for negotiating channels and avoiding the hidden

terminal problem.

2)Average packet delay over all?ows in the network:

Average packet delay is the duration between the

time when the MAC layer of the sender receives

a packet to send,and the time the packet reaches

the destination.So the delay is a sum of queueing

delay,backoff delay,and transmission delay.The

queue size at each node is50packets.We ignore

the lost packets,and only measure delay of the

packets that are correctly received by the receiver.

Since MMAC uses ATIM windows,and data can-

not be transmitted in these windows,packets will

have to wait,which can result in increased packet

delay.

A.Simulation Model

For simulations,we have used ns-2[17]with CMU wireless extension[18].Simulations are performed in two network scenarios,wireless LAN and multi-hop networks.The bit rate for each channel is2Mbps.The transmission range of each node is approximately250, and beacon interval is set to100.Each source node generates and transmits constant-bit rate(CBR)traf?c. Each simulation was performed for a duration of40 seconds,and each data point in the result graphs is an average of30runs.

Unless otherwise speci?ed,we assume3channels. Also we assume packet size is512bytes,and ATIM windows are20long.To study the impact of these factors on the throughput and packet delay,we also performed simulations varying these parameters.The parameters we vary are number of nodes in the network, packet arrival rate of CBR traf?c,packet size,ATIM window size,and number of channels.

1)Wireless LAN:In the simulated wireless LAN,all nodes are within each other’s transmission range.So every source node can reach its destination in a single hop.The number of nodes we used are6,30,and64. For each scenario,half of the nodes are sources,and other half are destinations.So a source has at most one destination.The impact of a source having multiple destinations or a destination having multiple sources is not studied in this scenario,but it is studied in the multi-hop network scenario.

First,we examine the throughput and packet delay varying the network load.We use the packet arrival rate of CBR?ows to vary the network load.After that,we study the impact of different factors on the throughput. Packet size,ATIM window size,and number of channels are the factors we consider.

2)Multi-hop network:For a multi-hop network,100 nodes are randomly placed in a500x500area. 40nodes are randomly chosen to be sources,and40nodes are chosen to be destinations,such that all source-destination pairs are within a single hop.But a node may be the source for multiple destinations,and a node may be the destination for multiple sources.In a multi-hop network,we capture the situation where different traf?c loads are present in different regions,which is not captured in wireless LAN scenario.

B.Simulation Results

Simulation results are presented in this section.Note that in the graphs,the curves labelled as“802.11”refer to original IEEE802.11single channel MAC,the curves labelled as“DCA”indicate the DCA protocol from [9],and the curves labelled as“MMAC”indicate our proposed scheme.

First we present results from simulations performed for a wireless LAN.Fig.4shows the aggregate through-put of different protocols as the network load increases. The network sizes are6,30,and64nodes in Fig. 4(a),(b)and(c)respectively.When the network load is low,i.e.the network is not saturated,all protocols perform similarly.As the network load draws near sat-uration,MMAC performs signi?cantly better than IEEE 802.11,and also does better than DCA.Since there are 3channels,DCA uses1channel for control packets and other2channels for data.By using this separate control channel,DCA achieves almost100%throughput improvement over IEEE802.11.But as the number of channel increases,the throughput improvement of DCA for the added channel becomes less,because of bottleneck on control channel,as we will see later. MMAC uses all3channels for data exchange,but cannot achieve200%improvement over IEEE802.11,because of its overhead for channel negotiation.The overheads in MMAC are periodic beacon transmissions and ATIM packets.As the graphs show,MMAC performs20%-30%better than DCA.The throughput improvement of MMAC over DCA may not be dramatic,but it is impor-tant that MMAC achieves this throughput using only a single transceiver for each host.Thus,the improvement is achieved using simpler hardware.

Fig.5shows the average packet delay of the protocols as the network load increases.The difference between IEEE802.11and other protocols in delay is due to the fact that with only one channel,a packet has to wait longer to occupy the channel when the network load is high.When comparing DCA and MMAC,MMAC shows higher delay in the network scenario with6 nodes.Then the delay of two protocols becomes similar with30nodes,and MMAC outperforms DCA in64-

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Aggregate Throughput vs.Packet Arrival Rate in a wireless LAN.

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Fig.5.

Average Packet Delay vs.Packet Arrival Rate in a wireless LAN.

node scenario.In 6-node scenario,MMAC shows higher delay even though it achieves higher throughput.This is because only ATIM packets are allowed to be exchanged in ATIM windows.For 20ms in every 100ms,packets have to wait for channel negotiation,whether or not the channel is idle.But when the number of nodes becomes large,DCA suffers from high contention at the control channel which results in high packet delay.MMAC does not have this problem,because it does not maintain a separate channel for control messages.Since Fig.5shows the delay for a wide range of network load,the difference in delay when the network load is low is not shown clearly.Fig.6shows the aggregate throughput and average packet delay of the protocols only when the network load is low.We can see from Fig.6(b)that MMAC has signi?cantly larger packet delay than other protocols,even though all the protocols achieve almost the same amount of throughput.

In Fig.7,we simulated the protocols using different packet sizes.We have ?xed the packet arrival rate of

each ?ow to be 100packets/sec,so the network is already being saturated.In general,aggregate throughput is higher when packet size is large,mainly because of less control overhead.With larger packets,larger amount of data is transmitted for one RTS/CTS exchange,and thus contending over the channel occurs less frequently.we can observe from Fig.7that for DCA,throughput is close to IEEE 802.11when the packet size is smaller than 256bytes,but shows sharp increase when the packet size is greater than 256bytes.Recall that DCA uses a common channel for all nodes to exchange control messages.When packet size is too small,control channel becomes a bottleneck so that available data channels cannot be utilized to its maximum.This indicates that as the number of channels increase,the packet size should also increase in DCA to fully utilize the data channels.MMAC does not have this bottleneck problem,since there is

Now we look at results from multi-hop network.As stated in the previous section,in our multi-hop network

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Aggregate Throughput and Average Packet Delay when the network load is low,in a wireless LAN.

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100 1000

A g g r e g a t e T h r o u g h p u t (K b p s )

Packet Size (Kbytes)Aggregate Throughput vs. Packet Size, 3 Flows

802.11DCA MMAC

(a)6nodes

05001000150020002500

3000

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1000

A g g r e g a t e T h r o u g h p u t (K b p s )

Packet Size (bytes)Aggregate Throughput vs. Packet Size, 15 Flows

802.11DCA MMAC

(b)30nodes

500

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1001000

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Fig.7.

Aggregate Throughput vs.Packet Size in a wireless LAN.

simulations,a node can be a source for multiple destina-tions,or it can be a destination for multiple sources.Fig.8shows the aggregate throughput of different protocols as the network load increases.3and 4channels are used in Fig.8(a)and 8(b)respectively.In 8(a),MMAC performs better than DCA,but the difference is smaller than in wireless LAN case.This is due to the following reasons.First,in a multi-hop network,all 3channels may not be fully utilized in the entire area.In the region where the network can bene?t from having the third channel,MMAC does better than DCA.But in the region where only 2channels are needed,DCA does better than MMAC because it can utilize 2data channels without ATIM window overhead.Second,in MMAC,if a node has ?ows to two different destinations,each destination may choose a different channel,and one ?ow may have to wait for an entire beacon interval to negotiate the channel again.Also,if a node is a destination for two ?ows from other sources,these two ?ows must be transmitted on the same channel,diminishing the bene?t of having multiple channels.As the network load becomes very high,throughput of DCA drops faster than MMAC.This is because a single control channel is shared by every node in DCA.When the network load is very high,the collision rate of control packets increases,degrading the throughput.We call this control channel saturation .

The impact of control channel saturation is also shown in Fig.8(b).MMAC gains signi?cant bene?t from not having a dedicated control channel.As mentioned in section II,the maximum number of channels that can be fully utilized using DCA is ,given that is the data packet size and is the control packet size.But even when the number of channels is less than ,the throughput suffers from contentions among the control packets if the number of channels is close to this value.This control channel bottleneck can be removed if we use larger packets.The results using large packets are shown in Fig.9(a)and 9(b).Here we used 1024bytes as the packet size.As the results

200400600800100012001400

100

1000

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(a)3channels

500

1000

1500

2000

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Aggregate Throughput, 40 Flows, 4 Channels

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(b)4channels

Fig.8.

Aggregate Throughput vs.Packet Arrival Rate in a multi-hop network.Packet size is 512bytes.

0200400600800100012001400160018001

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(a)3channels

500

1000

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1101001000

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802.11DCA MMAC

(b)4channels

Fig.9.

Aggregate Throughput vs.Packet Arrival Rate in a multi-hop network.Packet size is 1024bytes.

show,MMAC only does slightly better than DCA,both with 3and 4channels.However,MMAC achieves this improvement with simpler hardware than DCA.Fig.10(a)and 10(b)shows the average packet delay of the protocols as the network load increases.Packet size is again 512bytes in these graphs.With 3channels,MMAC shows higher delay than DCA,even though MMAC achieves higher throughput.This is due to the same reasons explained in wireless LAN scenario.However,when 4channels are available,MMAC shows lower delay than DCA.We can see that the average packet delay of DCA is almost the same with 3and 4channels.This is because DCA does not bene?t from having one more channel because of control channel saturation,as mentioned above.But MMAC bene?ts from having the fourth channel and the average delay becomes lower.ATIM window overhead in MMAC does not increase with the number of channels,as long as the ATIM window is long enough to exchange all the ATIM

messages necessary.

We have ?xed the ATIM window size to 20

so far in this paper.But this may be undesirable due to the following reason.When there are small number of ?ows in the network,using 20%of each beacon interval for exchanging ATIM messages is wasteful.Much of the time the channel will be left as idle,because data packets are not allowed to be transmitted in this interval.On the other hand,if there are very large number of ?ows in the network,a longer ATIM window would be needed to exchange all the ATIM messages between nodes to negotiate channels.Thus the ATIM window size affects the throughput of MMAC protocol 4.To study this impact,aggregate throughput is measured using different ATIM window sizes.Fig.11shows the result.For this network scenario,an ATIM window

A similar observation about impacts of ATIM window on IEEE 802.11power saving mechanism is reported in [19].

246810121416

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246810121416

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(b)4channels

Fig.10.

Average Packet Delay vs.Packet Arrival Rate in a multi-hop network.

size of around 15-20is shown to be the best for throughput.When the ATIM window size is less than 15,not all nodes can exchange ATIM messages and negotiate channels during this interval.Nodes that have not successfully exchanged ATIM messages stay in the default channel.So the multiple channels cannot be fully utilized,resulting in degraded throughput.If the ATIM window is longer than 20,the throughput decreases because while the overhead increases,no more ATIM

messages are exchanged after 20

and thus cannot bene?t from having a longer ATIM window.The optimal ATIM window size depends mainly on the number of ?ows in the beacon interval,because an ATIM packet exchange is required for each ?ow.Since the number of ?ows is often dynamically changed,it is desirable to also make the ATIM window size change dynamically.Changing ATIM window size dynamically to achieve maximum throughput is left as a future work.

700

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2565121024

Fig.11.Aggregate Throughput vs.ATIM Window Size in a multi-hop network.

Finally,we measured the throughput of different pro-tocols varying number of channels.This simulation was done for a wireless LAN with 30nodes.We used 512bytes for packet size,and the number of channels vary from 3to 6.The results are shown in Fig.12.In the graphs,“MMAC-3”indicates MMAC protocol with 3channels,and “DCA-4”refers to DCA protocol with 4channels.The throughput of IEEE 802.11is also shown in the graphs.Because of control channel saturation,DCA does not bene?t from having additional channels when the number of channels becomes larger.MMAC does better than DCA with the same number of channels,when the network load is high.

DCA and MMAC have their own ways to avoid the hidden terminal problem and access multiple channels dynamically.DCA uses one separate channel to ex-change control packets,whereas MMAC uses ATIM windows to negotiate channels.In DCA,the bandwidth of control channel has a major effect on the performance.In MMAC,the ATIM window size takes the role.As the results show,MMAC can achieve better throughput than DCA,with simpler hardware.

VI.D ISCUSSION

In this section,we discuss some issues to be consid-ered regarding our scheme and possible ways to improve it.

When a node is sending packets to two different destinations,these two destination nodes may select a different channel.For example,suppose that we have nodes A,B and C in the network,as in Fig.13.Node A has packets destined for B,and also packets destined for C.During channel negotiation,node B selects channel 1and node C selects channel 2.If A selects channel

A g g r e g a t e T h r o u g h p u t (K b p s )

Packet Arrival Rate per flow (packets/sec)Aggregate Throughput, DCA

(a)DCA

A g g r e g a t e T h r o u g h p u t (K b p s )

Packet Arrival Rate per flow (packets/sec)

Aggregate Throughput, MMAC

(b)MMAC

Fig.12.

Aggregate Throughput vs.Packet Arrival Rate in a wireless LAN (30nodes).

1,it can only transmit packets destined for B,and all the packets destined for C must wait until next beacon interval to negotiate the channel again.This behavior of MMAC protocol raises several issues.First,to avoid head of line blocking problem,the packets that cannot be transmitted because of channel mismatch must be kept in a separate buffer,and be restored to the front of the buffer at the end of the beacon interval.This complicates the queue management.Also,it is possible that the same channels are selected by each node in the subsequent beacon intervals,starving the ?ow from A to C.In our scheme,if node A has to send ATIM packets to B and C,A chooses randomly

which one to send the packet to ?rst.This randomness will prevent complete starvation,although there can be short-term unfairness among the ?ows.Instead of randomly choosing among the destinations,A can send an ATIM packet ?rst to the destination which is the target node of the ?rst packet in its queue.This modi?cation will improve the fairness of the protocol.

In addition to the problems stated above,this situation might also have impact on the throughput.Suppose that A had only a few packets for B.Then after sending all the scheduled packets,A becomes idle for the rest of the beacon interval.But A cannot send packets to C,even though A has received C’s ATIM-ACK during ATIM window and knows which channel C will be listening on.To avoid waste of bandwidth,we can extend MMAC to allow nodes to switch channels inside the beacon interval.A node may switch channels according to the following rules.

If node A ?nishes sending packets on its selected

Channel 1

Channel 2

Fig.13.An example network scenario.Assume there are other nodes in the vicinity of these three nodes,that affect the PCL of these three nodes.Node A has packets for B,and also packets for C.A exchanges ATIM messages with B ?rst,and both select channel 1.After that,A sends an ATIM packet to C,and C selects channel 2.Since A will stay in channel 1for the beacon interval,packets for C must be deferred until the next beacon interval.

channel,and does not know of any node that is planning to send packets to A,A may switch its channel.

If A has received any ATIM packet during the ATIM window,A must stay on the selected channel for the entire beacon interval.

After switching to another channel,node A must wait for one packet transmission interval before transmitting a packet,to gather information on condition of the new channel.This delay is required to avoid collision,because A does not have NA V (Network Allocation Vector)information for the new channel at the time it switches channels.

In our example,A can switch to channel 2after sending all the scheduled packets to B,because it has not received any ATIM packets during the ATIM window.C

stays in channel2for the entire beacon interval,because it has received ATIM packet from A.So the commu-nication between A and C can take place in channel 2correctly.This extended scheme might increase the throughput,and the performance of this scheme will be studied in the future work.

Another issue is that in MMAC,a node counts the usage of a channel based on the ATIM-ACK or ATIM-RES packets it overhears,and selects the channel with the least count to balance the channel load.It means that the node is counting the number of source-destination pairs.The assumption here is that every?ow has the same amount of traf?c ready to be transmitted in the beacon interval,which may not be true.Different?ows may have different number of packets pending to be sent.So it may be better to count the number of pending packets rather than number of source-destination pairs.This could be easily achieved.The source counts the number of pending packets for the destination and include the value in the ATIM packet.This number is echoed in the ATIM-ACK and ATIM-RES packet,so that the nodes in the vicinity of the source or destination can obtain the information.When selecting a channel,the node selects a channel with the least number of packets scheduled on the channel.This selection mechanism will achieve a better load balancing than the original scheme.

VII.C ONCLUSION AND F UTURE W ORK

In this paper,we have presented a multi-channel MAC protocol that utilizes multiple channels to im-prove throughput in wireless networks.The proposed scheme requires only one transceiver for each host,while other multi-channel MAC protocols require multiple transceivers for each host[3],[8],[9].The nodes in the network are synchronized by beacons,and the channels are negotiated in the ATIM window using ATIM packets. After the ATIM window,nodes switch to their selected channel and exchange messages on that channel for the rest of the beacon interval.Since multiple transmissions occur at the same time,MMAC improves the throughput of a wireless network signi?cantly,even with small number of channels.

Simulation results show that MMAC performs signif-icantly better than https://www.wendangku.net/doc/9714771866.html,pared with DCA, MMAC performs better in terms of throughput,but often somewhat worse in terms of packet delay.It is important that MMAC achieves a comparable performance using simpler hardware than DCA.Also,since the ATIM windows are already speci?ed in IEEE802.11PSM,if PSM is used,MMAC can be easily integrated to achieve multi-channel accessibility without further overhead.

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[2]J.Monks,V.Bharghavan,W.Hwu,“A Power Controlled

Multiple Access Protocol for Wireless Packet Networks,”in IEEE INFOCOM,April2001.

[3] A.Nasipuri,S.Ye,J.You and R.Hiromoto,“A MAC Protocol

for Mobile Ad Hoc Networks using Directional Antennas,”in IEEE Wireless Communications and Networking Conference (WCNC),Chicago,IL,September2000.

[4]R.Roy Choudhury,X.Yang,R.Ramanathan and N.H.Vaidya,

“Using Directional Antennas for Medium Access Control in Ad Hoc Networks,”in ACM MOBICOM,Atlanta,GA,September 2002.

[5]Y.-B.Ko,V.Shankarkumar and N.H.Vaidya,“Medium Access

Protocols using Directional Antennas in Ad Hoc Networks,”in IEEE INFOCOM,March2000.

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[7] A.Nasipuri,J.Zhuang and S.R.Das,“A Multichannel CSMA

MAC Protocol for Multihop Wireless Networks,”in IEEE Wire-less Communications and Networking Conference(WCNC), September1999.

[8]N.Jain and S.Das,“A Multichannel CSMA MAC Protocol

with Receiver-Based Channel Selection for Multihop Wireless Networks,”in Proceedings of the9th Int.Conf.on Computer Communications and Networks(IC3N),October2001.

[9]S.-L.Wu,C.-Y.Lin,Y.-C.Tseng and J.-P.Sheu,“A New Multi-

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Channel MAC Protocol with Power Control for Multi-Hop Mobile Ad Hoc Networks,”The Computer Journal,vol.45, pp.101–110,2002.

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and Resolution Multiple Access for Multichannel Wireless Networks,”in IEEE INFOCOM,2000.

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mechanisms in Emerging Standards for Wireless LANs:The MAC Level Perspective,”IEEE Personal Communications,June 1998.

数据分析中常用的10种图表及制作过程

数据分析中常用得10种图表 1折线图折线图可以显示随时间(根据常用比例设置)而变化得连续数据,因此非常适用于显示在相等时间间隔下数据得趋势。表1家用电器前半年销售量月份冰箱电视电脑平均销售量合计 1月68 45 139 84 252 2月33 66 166 88 265 3月43 79 160 94 282 4月61 18 115 65 194 5月29 19 78 42 126 6月22 49 118 63 189 图1 数点折线图图2堆积折线图

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好看的图表制作软件导语：好看的图表制作软件，专业的图表能够帮助你简化沟通，漂亮的图表却能让人眼前一亮，瞬间吸引众人的目光。这就是为什么有人即便已经学会了如何用Excel制作图表，却依然走在美化图表的路上的原因。免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 当数据变得易于阅读和理解时，我们就容易记住它，并在以后使用到这些数据，充分发挥数据的影响力。而且，建立起各数据之间关系之后，可以从中发现仅阅读原始数据无法发现的一些信息，更有利于在管理决策过程中使用。什么软件可以制作出好看的图表？图表制作通常我们会使用Excel、Word制作，但一些稍复杂的图表使用这些软件制作便有些吃力，或者说又要借助其他软件才能绘制。亿图图示，一款专业绘制各类图表的软件。软件可以绘制柱状图、饼图、条形图、雷达图、气泡图等

一系列图表，操作使用简单，无需特意学习便可绘制，图种齐全，是绘制图表的不二选择。使用亿图图示专家绘制图表有何优势？ 1.可以通过模板、例子，快速创建出专业的图表; 2.图表数据可以进行实时修改； 3.自带多种主题、样式，可以一键更改整个主题风格; 4.可以通过导入数据快速创建图表； 5.可以将图表中的数据直接导出为Excel； 6.支持跨平台操作，可用于windows、Mmac以及 linux系统;

7.可以一键导入导出为visio，以及导出PDF、SVG、office、PowerPoint、图片格式的文件; 8.支持云储存，个人云和团队云; 9.所见即所得的打印方式。丰富的模板和例子：

EXCEL怎么制作漂亮的柱状图

柱状图是经常需要绘制的图，本文讲解如何在软件绘制的默认的柱状图的基础上对柱状图进行美化设计，得到一张漂亮的柱状图。 1、录入数据。 2、选择数据，插入柱状图，得到软件默认的柱状图。 3、设计标题。在图表工具中选择图表标题;图表上方，然后输入需要的标题文字。设置标题字体和字号。选用笔划较粗的字体，使用大字号。 4、设计图例。选择在顶部显示图例，设置图例字体和字号。 5、设计柱形填充颜色。点选相同系列柱形，在图表工具;格式;形状填充中选择颜色。 6、设计数据标签。每一张图都有想说明的重点，所以不必将每个系列的数据标签都显示出，本例显示出第二系列的数据标签。选择数据标签外，显示出数据标签，并对数据设置字体和字号，并选用与系列柱形相同的颜色。 7、设计坐标轴。为了强化逐渐增加的趋势，可以将纵坐标轴的最大和最小刻度进行更改。因为已经显示出了数据标签，所以没必要再需要纵坐标轴，点击选择纵坐标轴，将其删除。点选横坐标轴，更改字体和字号。 8、设计网格线。无需网格线，将其删除。 9、整体再设计。这一步需要具体问题具体分析。本图因为是逐渐增加的风格，所以需要强化这个增加的趋势。把标题更改为居中覆盖标题，那么柱形将进一步扩大。同时手动将标题和图例移动到左边的空白区域，使整个图更显稳重。 10、增加对图形的说明。因为绘制图形的目的就是为了说明图形所要表达的意义，充分利用左边的空白区域，添加本图需要表达的意义。 11、设计柱形之间的间隔距离。双击柱形，弹出格式设置对话框，拖动滑块改变系类重

叠和分类间距的值。 12、再为图增加一个边框。在格式;形状轮廓中选择颜色，选择边框的粗细和线型。可以适当宽点。得到最终美化的柱形图。注意事项:整体上保持简约，颜色不宜过分鲜艳，不宜太过花哨。

图表制作软件哪个好

图表制作软件哪个好导语：图表制作软件哪个好？Excel是大家经常会用到的一款办公软件，当数据比较多的时候，我们该如何让数据更直观的在Excel中表现出来呢？免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 数据图表可以仿版地查看数据的差异和预测趋势，使数据比较或数据变化趋势变得一目了然，有助于快速、有效地表达数据关系。图表是生成它的工作数据相链接的。制作图表用什么软件比较好？亿图图示拥有一套齐全的商务市场分析图符号，主要包括：基本图表、营销图表和营销形状。这些多样的符号，可以帮助使用者在较短的时间内完成市场分析图的绘制。除此以外，软件里的符号精致美观，对提升市场分析的演示报告，也是另外一种提升。运用合适的符号，能够有效提升市场分析图的质量。

使用亿图图示专家绘制图表有何优势？ ●可以通过模板、例子，快速创建出专业的图表; ●图表数据可以进行实时修改； ●自带多种主题、样式，可以一键更改整个主题风格; ●可以通过导入数据快速创建图表； ●可以将图表中的数据直接导出为Excel； ●支持跨平台操作，可用于windows、Mmac以及linux系统; ●可以一键导入导出为visio，以及导出PDF、SVG、office、PowerPoint、图片格式的文件; ●支持云储存，个人云和团队云; ●所见即所得的打印方式。

丰富的模板和例子：

1、柱状图：是网站分析中常见的一种图表。主要是用来展示在某一段时间内，各数据间的变化或者各数据间的比较情况。但是仅限于数据较少的情况，因为数据过多会导致柱间空隙很小，会影响数据的展示和分析。 2、条形图：常用于对比两类事物在不同特征项目的数据情况，显示各个项目之间的比较情况，能够清晰、直观的表示数据。

如何做一个简单漂亮的图表

如何做一个简单漂亮的图表导语：如何做一个简单漂亮的图表？相信对于Excel我们并不陌生，尤其是需要进行各种数据处理、分析、统计的职场人士来说。Excel中的图表，能够让数据信息展示更清晰，更易于理解。但是Excel也有其不完美之处，用Excel中的数据转成图表，其样式、效果都相对比较单调，不够生动。那么，有什么方法，可以让Excel中的图表更专业、漂亮呢？免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 有时候我们需要对数据进行对比，比如说我们在需要同一种产品的时候，关于这些产品的某一个方面的属性，不同的供应单位会有不同的数据，市场上也会做出不同的反映，此时我们就要通过横向以及纵向的对比来决定究竟选择哪一个供应方提供的产品，这样不管是节约成本还是提高产品的质量，都是更为有利。专业的图表制作软件

一般制作商务图表制作通，我们会使用Excel、Word制作，但一些稍复杂的图表使用这些软件制作便有些吃力，或者说又要借助其他软件才能绘制。亿图图示，一款专业绘制各类图表的软件。软件可以绘制柱状图、饼图、条形图、雷达图、气泡图等一系列图表，操作使用简单，无需特意学习便可绘制，图种齐全，是新手绘制商务图表的不二选择。使用亿图图示专家绘制图表有何优势？ 1.可以通过模板、例子，快速创建出专业的图表; 2.图表数据可以进行实时修改； 3.自带多种主题、样式，可以一键更改整个主题风格; 4.可以通过导入数据快速创建图表； 5.可以将图表中的数据直接导出为Excel； 6.支持跨平台操作，可用于windows、Mmac以及 linux系统;

零基础如何制作一份个性化的信息图表

零基础如何制作一份个性化的信息图表导语：信息图表的价值性不言而喻，它是一种将文字、数据或知识等信息进行可视化的工具，使一些难以准确表达的复杂信息得以简化。每个人都可以制作出一份个性化的信息图表，我们一起来学习一下！免费获取信息图软件：https://www.wendangku.net/doc/9714771866.html,/infographics/ 有哪些适合新手的信息图制作软件？

信息图的制作相比一般的排版设计还要麻烦一些，又是图表的展示又是文字图片。貌似要切换几个软件制作，无法使用一个软件搞定。但其实一个亿图信息图就可以，并且新手也能够上手制作。亿图信息图可以很容易地创建各种美观的信息图表、平面设计图、小册子、海报、证书，软件的特点是易于排版，多种标题可以选择，对信息图起到至关重要的作用。导出格式支持多种图片格式，也支持导为Html，PDF，SVG，Microsoft Word, PowerPoint，Excel等，方便打印。零基础如何用亿图制作个性化的信息图表首先需要现在电脑上下载安装好亿图信息图软件

亿图信息图软件支持绘制：信息图、海报、地图、图表、宣传单、卡片、宣传册、流程图、时间线、新闻稿、横幅、PPT演示文稿等图。安装完成后，打开软件，在新建“预定义模板和例子”中，选择你需要的绘图类型，双击即可快速开始绘图。添加形状在绘图页面的左侧，有一个符号库，里面放着很多漂亮实用的图形，双击图形或者用鼠标拖拽到绘图页面即可。

信息图软件中内置丰富的图形符号，包含常用的基本符号、基本图表、地图标记、人物等精美的素材。修改形状样式打开软件右侧的工具栏，可以对形状的颜色、线条、形状属性、图层等进行详细的设置。

论文图表制作软件

论文图表制作软件导语：如何在论文中优雅的插入各种图表？为了更加直观的传统信息，我们常常喜欢把文本数据的内在关系梳理成图形的形式，达到“一图胜千言”的效果。那么，面对复杂、单调的数据，怎样轻松的将这些数据展现在论文中呢？免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 在科研论文中，图表是研究结果最为直观的显示方式，表格和图片可以更加清楚直观地表现一些复杂的信息，比如复杂系统之间的关系以及事件发生的顺序等。那么，这种直观的图表是怎么绘制的呢？专业的论文图表制作软件图表制作通常我们会使用Excel、Word制作，但一些稍复杂的图表使用这些软件制作便有些吃力，或者说又要借助其他软件才能绘制。亿图图示，一款专业绘制各类图表的软件。软件可以绘制柱状图、饼图、条形图、雷达图、气泡图等一系列图表，操作使用简单，无需特意学习便可绘制，图种齐全，是绘制图表的不二选择。

使用亿图图示专家绘制图表有何优势？ 1.可以通过模板、例子，快速创建出专业的图表; 2.图表数据可以进行实时修改； 3.自带多种主题、样式，可以一键更改整个主题风格; 4.可以通过导入数据快速创建图表； 5.可以将图表中的数据直接导出为Excel； 6.支持跨平台操作，可用于windows、Mmac以及linux系统; 7.可以一键导入导出为visio，以及导出PDF、SVG、office、PowerPoint、图片格式的文件; 8.支持云储存，个人云和团队云; 9.所见即所得的打印方式。

丰富的模板和例子：

高级漂亮图表制作

高级漂亮图表制作导语：高级漂亮的图表总能让你的数据显得更加的专业，更加吸引目光。不熟悉Excel制作图表的朋友可能会认为Excel中图表都不是很好看。但是，如果经过一番美化后，那又是不同的效果了。这里小编给你分享一种简单、实用的数据图表制作方法，让你更轻松地制作出专业好看的图表。免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 数据分析的过程和结果的呈现最直观的是采取图表的形式，图表直观有冲击力。只有正确地使用图表，才可以向业务方讲好数据故事，从而来支撑业务发展。什么软件可以制作出高级漂亮的图表？图表制作通常我们会使用Excel、Word制作，但一些稍复杂的图表使用这些软件制作便有些吃力，或者说又要借助其他软件才能绘制。亿图图示，一款专业绘制各类图表的软件。软件可以绘制柱状图、饼图、条形图、雷达图、气泡图等

EXCEL高逼格商务图表制作

EXCEL高逼格商务图表制作 ======================= 目录一、商务图表制作核心理念和方法 1.突破Excel的图表元素 2.突破Excel的图表类型 3.布局与细节二、“商务范”图表制作实例 1.日期坐标轴妙用 2.堆积柱形图妙用 3.漏斗图-利用辅助列占位 4.自定义Y轴刻度间距 5.含加粗边缘的面积图 6.图表覆盖妙用- 横网格线覆盖于图表之上 7.为Pie图加背景图片 8.仪表盘 9.多数量级的几组数据同时比较 10.手风琴式折叠bar图

11.Water Fall 瀑布图 12.不等宽柱形图 13.滑珠图 14.动态图表1 15.动态图表2 16.Bullet图-竖直三、配色方案 1.Nordri设计公司分享的配色方案 2.ExcelPro分享的方案正文一、商务图表制作核心理念和方法 1. 突破Excel的图表元素不要仅用“图表”做图表，而是用“图表＋所有Excel元素（如单元格，填充色，文本框）”去做图表。

左上图，只有B4单元格是图表区域，标题利用的是B2；B3－B5填充浅色，"index"和"data"分别在B3、B5。右上图，B2为图表序号，C2为图表标题，填深绿色，B3为副标题，图例放在C4，图表在C5，B2到C5填充淡色，B6、C6合并填写注释。左上图，标题在C2－H2居中，图表在C3－H3，利用Excel单元格的数据表在C6－H8。右上图，B2填红色装饰，标题和副标题分别在B2、B3，图表在D4－F4，数据来源在D5，标号2为矩形框，整个区域有边框。

2. 突破Excel的图表类型左上图，先用所有数据做曲线图或柱形图，然后选中相应的序列，更改图表类型，有时还需要用到次坐标轴。右上图，先做好面积图，然后将该数据序列再次加入图表，修改新序列的图表类型为曲线图，调粗线型。 3. 布局与细节布局下图从上到下可以分为5个部分：主标题区、副标题区、图例图、绘图区、脚注区。特点有：完整的图表要素；突出的标题区；从上到下的阅读顺序。

制作商务图表用什么软件

制作商务图表用什么软件导语：在职场上，你是不是经常要和各类图表打交道呢？比如条形图、蜘蛛图、饼状图等。有时候我们不仅需要看得懂图，还需要自己亲手绘制。因此，我们将在本文教你如何使用软件绘制专业的商务图表。免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 商务图表一般用什么软件绘制？亿图图示拥有一套齐全的商务市场分析图符号，主要包括：基本图表、营销图表和营销形状。这些多样的符号，可以帮助使用者在较短的时间内完成市场分析图的绘制。除此以外，软件里的符号精致美观，对提升市场分析的演示报告，也是另外一种提升。运用合适的符号，能够有效提升市场分析图的质量。

配置需求 Windows? 2000, Windows? XP, Windows 2003, Windows Vista, Windows 7,Windows 8, Windows 10 Mac OS X 10.7 + Linux Ubuntu 14 + 表格制作软件特色 ●支持多个系统：同时支持支持Windows，Mac和Linux，并且版本同步更新。 ●智能化操作：拥有自动设置，根据条件为主题进行颜色填充，添加图形，排版，用户只需关心形状的关系，其他的软件会自动搞定。 ●操作界面简单：涵盖内容一目了然，操作简单易懂，添加，删除，修改全是可视化操作，最大程度提高绘制效率。 ●模板多：内置一系列优秀的各类表格模板，还有免费的在线模板可以随时被下载编。 ●导出格式多：一键导出你的项目图到各种格式的图片，Html，PDF，SVG， Microsoft Word, PowerPoint，Excel，以及Visio，实时预览功能，所见即所得。让您的图表清晰内容透明。

excel图表工具技巧

excel图表工具技巧导语：相信对于Excel我们并不陌生，尤其是需要进行各种数据处理、分析、统计的职场人士来说。Excel中的图表，能够让数据信息展示更清晰，更易于理解。但是Excel也有其不完美之处，用Excel中的数据转成图表，其样式、效果都相对比较单调，不够生动。那么，有什么方法，可以让Excel中的图表更专业、漂亮呢？免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 当数据变得易于阅读和理解时，我们就容易记住它，并在以后使用到这些数据，充分发挥数据的影响力。而且，建立起各数据之间关系之后，可以从中发现仅阅读原始数据无法发现的一些信息，更有利于在管理决策过程中使用。专业的图表制作软件一般制作商务图表制作通，我们会使用Excel、Word制作，但一些稍复杂的图表使用这些软件制作便有些吃力，或者说又要借助其他软件才能绘制。亿图图示，一款专业绘制各类图表的软件。软件可以绘制柱状图、饼图、条

形图、雷达图、气泡图等一系列图表，操作使用简单，无需特意学习便可绘制，图种齐全，是新手绘制商务图表的不二选择。使用亿图图示专家绘制图表有何优势？ 1.可以通过模板、例子，快速创建出专业的图表; 2.图表数据可以进行实时修改； 3.自带多种主题、样式，可以一键更改整个主题风格; 4.可以通过导入数据快速创建图表； 5.可以将图表中的数据直接导出为Excel； 6.支持跨平台操作，可用于windows、Mmac以及 linux系统; 7.可以一键导入导出为visio，以及导出PDF、SVG、office、PowerPoint、图片格式的文件;

适合新手用的图表制作软件

适合新手用的图表制作软件导语：适合新手用的图表制作软件有哪些？精美的图表总能让你的数据显得更加的专业，更加吸引目光。不熟悉Excel制作图表的朋友可能会认为Excel中图表都不是很好看。但是，如果经过一番美化后，那又是不同的效果了。这里小编给你分享一种简单、实用的数据图表制作方法，让你更轻松地制作出专业好看的图表。免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 在日常工作中，数据图表作为用来表达数据的各类形态，丰富的图表样式中适合表达的数据和说明。数据图表可以非常清晰的表达不同项目之间的差距和数值，绘制好的图表更能直观全面分析内部各个组成部分对事件的影响。适合新手用的图表制作软件？亿图图示拥有一套齐全的商务市场分析图符号，主要包括：基本图表、营销图表和营销形状。这些多样的符号，可以帮助使用者在较短的时间内完成市场分析图的绘制。除此以外，软件里的符号精致美观，对提升市场分析的演示报告，也是另外一种提升。运用合适的符号，能够有效提升市场分析图的质量。

22个实用在线制作图表工具

22个实用在线制作图表工具习惯了ms office制作图表，也习惯了为它断断续续打补丁。在线制作图表工具用得不多，在信息终端越来越多元化的现在，在线工具的作用会越来越大。下面是我们翻译的文章：你有过需要制作简洁美观的图表，但却只有浏览器这个工具的遭遇吗？图表能有效地展示事物之间的联系，但是手上没有你喜爱的制作软件时，怎样制作会是大挑战。此文中，我们选出一些最好的在线图表制作应用工具，其能快速地创作出各种各样的图表。它们大部分易上手，也不用担心显示效果。输出结果就像下面的示意图一样精彩。 Rich Chart Live 在你的浏览器上创造出精彩悦目的flash图表

DIY Chart DIY（do it yourself/自己制作) chart（图表）是一个简单高效的在线工具，可以用任何脚本语言将静态或动态数据生成交互图表。 Online Chart Generator 最好的在线生成图表工具，可以快速地制作出迷人的3D效果

https://www.wendangku.net/doc/9714771866.html, https://www.wendangku.net/doc/9714771866.html,把在线数据可视化的复杂性拆卸了。它提供简单常见互动的在线图表生成器。 ChartGo chartGo通过让用户粘帖数据到图表数据区并点击生成按钮来快速在线制作图表。

Create A Graph 在这个网站上你可以制作一个细节丰富的图表，可预览，可打印，可下载，可email你的作品。

JS Charts JS charts是一个javascript图表生产工具（需要或不需要编写代码的知识）。用JS charts在各种条形图、饼形图、简单的线性图模板中可很容易地制作出图表。 Pie Chart Tool Pie Chart Tool根据你提供的数据生产一个饼形图。你所需做的是输入数据和类别名。 Piecolor Piecolor是各种颜色制作饼形图的工具。

Excel精美图表制作

Excel精美图表制作导语： Excel的优势在于，它不需要过多的文字表达，只需要一个简简单单的图表，就能将复杂的数据信息清晰的展现出来。让人一眼就能了解数据信息，并找到想要的答案。这就是图表所带来的魅力。免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 图表与表格比较，优点在于图表能更形象化地表示数据之间的关系，图表有若干种类型如普通的柱、饼形图，柱形可以比较数据的差距，而饼形能体现出占比成份等，表格呢，只能通过颜色、格式等表达数据的特殊。 Excel中那些精美的图表是怎么制作出来的？亿图图示拥有一套齐全的商务市场分析图符号，主要包括：基本图表、营销图表和营销形状。这些多样的符号，可以帮助使用者在较短的时间内完成市场分析图的绘制。除此以外，软件里的符号精致美观，对提升市场分析的演示报告，也是另外一种提升。运用合适的符号，能够有效提升市场分析图的质量。

丰富的模板和例子：

15款经典图表软件推荐创建最漂亮的图表

15款经典图表软件推荐创建最漂亮的图表 2011-04-06 09:35 | 5290次阅读| 来源：开源中国社区【已有14条评论】关键词：| 作者：老枪| 在这篇文章中，我将列出图表，图形和数据可视化的最佳软件，从创建基本的2D图表到产生复杂的数据集的数据可视化，这些PHP，Javascript、Flash的图表，对于任何一个严谨的开发者都是必须一览的。 1. FusionCharts v3帮助创建Web或企业应用的动画/交互的图表。企业级图表组件支持PCs, Macs, iPads, iPhones，以及大量其他的手机设备。 2.

bXML/SWF图表是个简单、强大的工具，支持XML数据创建吸引人的图表。XML提供灵活的数据生成，而Flash提供最好的图像质量。 3. JpGraph是面向对象的PHP图形创建库。该库完全PHP所写，可用作任何PHP脚本。 4. Open Flash Chart，是个开源软件，用来生成Flash的图表的组件。

5. FusionCharts是完全免费和开源的Flash图表组件。可创建动画、交互的图表web 应用、桌面应用等。FusionCharts支持PHP,,JSP, ColdFusion,Python,RoR,简单的HTML页面，甚至是PowerPoint演示。 6. PHP图形脚本可非常简单的嵌入动态生成图形和图表到PHP应用或HTML页面中。该图形软件使用简便，可几分钟内制作专业水准的实时图形。

7. jQuery Visualize Plugin是一个根据HTML表格的内容生成图表的插件。 8. Highcharts是纯粹的JavaScript写的图表库，提供简单的方式添加交互图表到站点或web应用，支持各种图表类型。

如何从零开始制作数据可视化图表

如何从零开始制作数据可视化图表导语：在以往，想要从零制作一张可视化图表，还是相对比较复杂，经过的环节分别是：数据整理、确定总体设计方案、排版、内容填充、细节调整以及最终的校对。而有了专业的可视化图表软件，就会让制作过程显得十分容易。免费获取信息图软件：https://www.wendangku.net/doc/9714771866.html,/infographics/ 零基础用什么软件制作信息图？

做信息图的软件通常听说的都是AI、PS，一般人要做的话需要花时间去学，并且学了也不一定运用得很好。专业的制图软件除了这些，还有零基础也能操作的亿图信息图软件。软件里有大量的信息图模板和矢量素材可以免费使用，还有智能的排版布局、一键更换主题，省时且高效；一键导出你的图表作品到各种格式的图片、Html、PDF、SVG、office等。零基础如何制作出数据可视化图表首先需要现在电脑上下载安装好亿图信息图软件

导入Excel文件快速生成图表以柱状图为例，点击形状右上角的浮动按钮，选择“从文件加载数据”。就能将Excel文件中的数据快速导入到软件中，并自动生成相应的柱状图。如果需要在软件中对已经生成的柱状图进行修改，只要点击动作按钮中的“编辑图表数据”即可进行修改。

如何做一个漂亮又实用的图表型PPT

如何做一个漂亮又实用的图表型PPT? 导语：如何做一个漂亮又实用的图表型PPT?在制作PPT时我们经常需要插入图表，但是直接从Excel/PPT中复制过来的图表太丑没办法直接用。今天，小编就教你一种方法，可以助你轻松绘制出专业又不失美感的数据图表！免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 图表的作用就是让数据可视化，我们通过各种途径和渠道收集到的数据是杂乱无章的，即使是其中含有一定的规律性也都是无法直接看出来，图表的作用就在于能够以一种视图的方式来展现数据，如果数据的演变中还有一定的规律，就能够将这种规律呈现出来，从而使用户更清楚的筛选到自己需要的信息，在决策的时候也能够以这些数据为依据。专业的图表制作软件一般制作商务图表制作通，我们会使用Excel、Word制作，但一些稍复杂的图表使用这些软件制作便有些吃力，或者说又要借助其他软件才能绘制。亿图图示，一款专业绘制各类图表的软件。软件可以绘制柱状图、饼图、条

漂亮的图表制作软件

漂亮的图表制作软件导语：精美的图表总能让你的数据显得更加的专业，更加吸引目光。不熟悉Excel 制作图表的朋友可能会认为Excel中图表都不是很好看。但是，如果经过一番美化后，那又是不同的效果了。这里小编给你分享一种简单、实用的数据图表制作方法，让你更轻松地制作出专业好看的图表。免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 图表是Excel中一种功能强大的数据分析工具，使用图表可以直观地表现数据之间的各种关系，更为清晰地表达各种信息。Excel提供了多种标准图表类型，包括柱形图、条形图、折线图、饼图和XY散点图等，每种图表类型又包含若干小类。根据数据的不同和使用要求的不同，用户可以创建不同类型的图表以满足需要。

专业的图表制作软件一般制作商务图表制作通，我们会使用Excel、Word制作，但一些稍复杂的图表使用这些软件制作便有些吃力，或者说又要借助其他软件才能绘制。亿图图示，一款专业绘制各类图表的软件。软件可以绘制柱状图、饼图、条形图、雷达图、气泡图等一系列图表，操作使用简单，无需特意学习便可绘制，图种齐全，是新手绘制商务图表的不二选择。使用亿图图示专家绘制图表有何优势？ 1.可以通过模板、例子，快速创建出专业的图表; 2.图表数据可以进行实时修改； 3.自带多种主题、样式，可以一键更改整个主题风格; 4.可以通过导入数据快速创建图表； 5.可以将图表中的数据直接导出为Excel；

6.支持跨平台操作，可用于windows、Mmac以及 linux系统; 7.可以一键导入导出为visio，以及导出PDF、SVG、office、PowerPoint、图片格式的文件; 8.支持云储存，个人云和团队云; 9.所见即所得的打印方式。丰富的模板和例子：

常见的图表处理工具软件有哪些

常见的图表处理工具软件有哪些导语：你还在为Excel图表怎么制作而苦恼吗？今天小编教你常用的图表处理工具及方法，助你能够更轻松、更高效地制作出专业、美观的数据图表，让你告别Excel图表制作单调、不专业的烦恼！免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 合理的数据图表，会更直观的反映数据间的关系，比用数据和文字描述更清晰、更易懂。将工作表中的数据转换成图表呈现，可以关注我们更好地了解数据见的比例关系及变化趋势，对研究对象做出合理的推断和预测。常见的图表处理工具软件有哪些？亿图图示拥有一套齐全的商务市场分析图符号，主要包括：基本图表、营销图表和营销形状。这些多样的符号，可以帮助使用者在较短的时间内完成市场分析图的绘制。除此以外，软件里的符号精致美观，对提升市场分析的演示报告，也是另外一种提升。运用合适的符号，能够有效提升市场分析图的质量。

丰富的模板和例子：

图表制作软件那个好

图表制作软件那个好导语：在日常工作中，有时候会需要绘制各种图表，将数据用一些可视化的图表来展示，似乎越来越成为一种趋势。那你知道这些图表是怎么制作的呢？当然需要借助一些好用的软件。本文将为你介绍讲解这些软件。免费获取商务图表软件：https://www.wendangku.net/doc/9714771866.html,/businessform/ 图表制作软件有哪些？图表制作通常我们会使用Excel、Word制作，但一些稍复杂的图表使用这些软件制作便有些吃力，或者说又要借助其他软件才能绘制。亿图图示，一款专业绘制各类图表的软件。软件可以绘制柱状图、饼图、条形图、雷达图、气泡图等一系列图表，操作使用简单，无需特意学习便可绘制，图种齐全，是绘制图表的不二选择。

使用亿图图示专家绘制图表有何优势？ 1.可以通过模板、例子，快速创建出专业的图表; 2.图表数据可以进行实时修改； 3.自带多种主题、样式，可以一键更改整个主题风格; 4.可以通过导入数据快速创建图表； 5.可以将图表中的数据直接导出为Excel； 6.支持跨平台操作，可用于windows、Mmac以及 linux系统; 7.可以一键导入导出为visio，以及导出PDF、SVG、office、PowerPoint、图片格式的文件;

8.支持云储存，个人云和团队云; 9.所见即所得的打印方式。丰富的模板和例子：

1、柱状图：是网站分析中常见的一种图表。主要是用来展示在某一段时间内，各数据间的变化或者各数据间的比较情况。但是仅限于数据较少的情况，因为数据过多会导致柱间空隙很小，会影响数据的展示和分析。

那些看起来很棒的信息可视化图表是怎么设计出来的

那些看起来很棒的信息可视化图表是怎么设计出来的导语：在生活中，有时候需要绘制各种图表，将数据用一些可视化的图表来展示，这样的图表看起来非常舒服，也很直观。当然，越棒的信息可视化图表其设计的复杂度越高。本文将带你来学习如何设计这样的可视化图表。免费获取信息图软件：https://www.wendangku.net/doc/9714771866.html,/infographics/ 专业的信息可视化图表是用什么软件设计的？

做设计首选当然是专业软件PS、AI等，但可视化图表还涉及到了数据的展示，数据上相对较为严谨，所以单单是有PS这些软件还不能完全做出来。那是否没有一个软件可以很好的符合这个可视化图表的需求呢？当然不是，亿图信息图可以了解一下~可以让零基础的你也能设计出精湛的可视化信息图。软件不需特地去学，简单操作即可上手，软件内置各种可视化数据图形图表，还有丰富的设计素材和模板，可用于参考、使用、激发灵感。如何用亿图信息图软件设计出好看的可视化图表首先需要现在电脑上下载安装好亿图信息图软件

制作一个漂亮的表格html代码

Company	Contact	Country
Apple	Steven Jobs	USA
Baidu	Li YanHong	China
Google	Larry Page	USA
Lenovo	Liu Chuanzhi	China
Microsoft	Bill Gates	USA
Nokia	Stephen Elop	Finland