Dynamic Channel Slot Allocation Scheme and Performance Analysis of Cyclic Quorum Multichannel MAC Protocol

In high diversity node situation, multichannel MAC protocol can improve the frequency efficiency, owing to fewer collisions comparedwith single-channelMACprotocol. And the performance of cyclic quorum-basedmultichannel (CQM)MACprotocol is outstanding. Based on cyclic quorum system and channel slot allocation, it can avoid the bottleneck that others suffered fromand can be easily realized with only one transceiver. To obtain the accurate performance of CQMMACprotocol, aMarkov chainmodel, which combines the channel-hopping strategy of CQM protocol and IEEE 802.11 distributed coordination function (DCF), is proposed. The results of numerical analysis show that the optimal performance of CQM protocol can be obtained in saturation bound situation. And thenwe obtain the saturation bound of CQMsystemby bird swarm algorithm. In addition, to improve the performance of CQMprotocol in unsaturation situation, a dynamic channel slot allocation ofCQM(DCQM)protocol is proposed, based onwavelet neural network. Finally, the performance of CQM protocol and DCQM protocol is simulated by Qualnet platform. And the simulation results show that the analytic and simulation results match very well; the DCQM performs better in unsaturation situation.


Introduction
IEEE 802.11Distributed Coordination Function (DCF) [1] has been widely used in mobile ad hoc networks.However, in high diversity node situation, the IEEE 802.11DCF suffers from many collisions, resulting in low frequency utilization [2].
Multichannel MAC protocol can help to share the traffic loads among different channels.Hence, the collisions singlechannel MAC protocols suffered from can be alleviated.In fact, IEEE 802.11b and IEEE 802.11a can support 3 and 13 nonoverlapping channels, respectively [2].This means that designing a multichannel MAC (MMAC) protocol is feasible and desirable in IEEE 802.11-based mobile ad hoc networks.
The great challenge of designing MMAC is how to allocate channels to node for transmitting information.And solutions to this problem can be classified into two patterns: (a) Channel negotiating pattern: channels allocated by negotiating through dedicated control slot or channel.(b) Channel-hopping pattern: nodes switch channels in a fixed pattern or random mechanism.
There are many protocols ( [3][4][5][6][7][8][9][10][11][12][13][14][15]) that belong to the channel negotiating pattern.In these protocols, some are equipped with at least two transceivers, such as protocols [3,7,[11][12][13][14].For these protocols, one transceiver is turned to a common control channel that is dedicated for negotiating the channel to be used next.Once the channel is selected, the other transceiver(s) will switch to the negotiated channel for data transmission.These protocols are referred to as the multitransceiver channel negotiating solutions.An undesirable feature of these protocols is high hardware cost.In addition, at one moment, at most one transmission pair can be handled, and the dedicated control transceiver is a bottleneck of the throughput of network.To solve these problems, some are equipped with only one transceiver, such as [4-6, 8-10, 15].Among them, protocols [5,6,9,15] use a dedicated control channel for control message exchange.In such methods, the dedicated control channel will be either overloaded or underutilized if the capacity of the dedicated control channel and the data channels is not properly distributed.Some other proposals [4,8,10] use a common control period, which is similar to the ATIM window concept in IEEE

Introduction of CQM Protocol
2.1.Cyclic Quorum System.Quorum systems have been widely used for MAC protocol designing in wireless networks [22,23].And a quorum system can be defined as follows.
Given a universal set  = {0, . . .,  − 1}, a quorum system  under  is a collection of nonempty subsets of , each called a quorum, which satisfies the intersection property  ∩  ̸ = : ∀,  ∈ . ( There are many quorum systems, such as the cyclic quorum system, the grid quorum system, and the torus quorum system.The cyclic quorum system has the elegant feature of rotation closure property, and it can provide equal opportunity for a node to transmit and to receive.The rotation closure property is as follows: ∩ rotate (, ) ̸ = ⌀: ∀,  ∈ ,  ∈ {0, . . .,  − 1} where rotate (, ) = {( + ) mod  |  ∈ } .
A cyclic quorum system can be constructed from a difference set.The definitions of a difference set and a cyclic quorum system are as follows.

CQM Protocol.
Based on cyclic quorum system, Chao and Tsai propose a cyclic quorum-based multichannel (CQM) MAC protocol [2].The CQM protocol does not need channel negotiating, so the bottleneck of channel negotiating mechanism can be avoided.In CQM protocol, nodes can communicate with others when they meet at the same channel and same channel slot.And it can provide equal opportunity for nodes to transmit and to receive through the cyclic quorum system.
In CQM protocol, time is divided into a series of cycles.Each cycle consists of default channel slots and switching channel slots, numbered from 0 to  − 1.The value of  is determined by the integer set from which the adopted difference set is derived.According to [2], CQM system

Default slot
Switching slot

Idle
Look up table Figure 1: The protocol processing of CQM protocol with two channels.
performs better under  6 .In this paper,  6 is adopted in the analysis of CQM system.Let  denote the channel slot length, to separate with system time slot .We assume that the length of channel slot  is long enough to transmit at least one data packet.At default channel slots, a node stays at its default channel, waiting for transmission requests.At switching channel slots, a node may switch to its intended receiver's default channel.We use a cyclic quorum   under   to identify a node's default slots.Specifically, for any node  ∈ , where  is the set of nodes in the network, th node's default channel (denoted as DC  ) and default slots (denoted as DS  ) are chosen as follows: where node ID  is the ID of th node.Figure 1 is an example of CQM operation under  6 with two channels (numbered from 0 to 1).Nodes 0, 1, and , with IDs 0, 1, and , respectively, are within each other's transmission range.Each node's default channel and default slots are shown in Figure 1, supposing that we choose the difference set {0, 1, 3} under  6 as  0 .The marked time slots are default channel slots.The number in each channel slot is the channel that should be switched to.
As is shown in Figure 1, when a packet arrives at a random time slot, the packet should wait in queue until all preceding packets are transmitted.And then the node looks up its channel-hopping table and checks whether it can meet its destination node at the current channel slot.If they meet each other at the current channel slot, the node can turn into the back-off stage.Otherwise, the node will turn into Wait 1 state to wait for the next channel slot available.During back-off stage, the back-off timer of a node is set to a random time according to 802.11 DCF scheme.In this paper, according to CQM protocol, when the channel is occupied by the other nodes or the current channel slot is empty, the back-off timer is assumed to be held to wait for the next channel slot available.And then, the channel slot remaining will be checked when back-off timer reaches zero.If the channel slot remaining is long enough for one packet transmission, the packet will be transmitted.Otherwise, the node should turn into Wait 3  ,0 state to wait for the next channel slot available.Finally, after each successful transmission or after having reached the maximum number of the retransmissions , if there is a packet to be transmitted in queue, the node enters into checking processing again.Otherwise, the node enters into the idle state. denotes the probability of having an empty queue.Take Node 0 for example; Table 1 shows average channel slots needed between twice meeting in one cycle in the situation that the node is at meeting state and waiting state.And the average meeting slots and waiting slots in one cycle are also shown in Table 1.  2. We consider the following assumptions for modeling network.(1) The network consists of  nodes moving in the range of transmission distance, and packets are transmitted from sources to destinations directly.(2) A total of ℎ channels are available for every node, and all of them have the same bandwidth.(3) Every node knows the IDs of its one-hop neighbors, and every node is equipped with onehalf-duplex transceiver, which is able to switch to any channel dynamically.(4) Every node is time synchronized and uses the IEEE 802.11DCF (RTS/CTS mode) as MAC protocol.(5) Packets arrive to a node according to a Poisson process with rate  packets/s.(6) The channel is assumed to be error-free.Packet transmission is considered to be successful if there are no other packets transmissions at the same time.

Performance Analysis of CQM Protocol
According to CQM protocol, each node has the same chance to transmit packet through different channels.So we can take one selected channel of a node into consideration to model the CQM protocol scheme at MAC layer.And then we assume that there are   = /ℎ nodes with packets rate  to content in one selected channel in a random time slot.The model consists of states that a node can reside in.The points  0 ,  1 ,  2 ,   0 , . . .,    represent connection points, which are not states.
During queuing stage, the arriving packet will wait in buffer, if there are other packets to be transmitted.And if there is no packet in buff, the node will turn into idle state.
If the packet is eligible to be transmitted, the node enters into checking stage.The channel-hopping table will be checked firstly.The node can meet its destination node with probability  meeting and turns into Wait 1 state to wait for next channel slot available with probability 1 −  meeting .
During back-off stage, we use the tuple (, ) to represent the different states. denotes the th back-off stage, and number  = 0, 1, . . .,   , . . ., , and  denotes the value of back-off timer in the range [0,   − 1] [24].  is the size of the CW at stage , which can be expressed as follow: where  denotes the maximum number of packet retransmissions before the packet is dropped.According to [25], the default value for   is 5 and it is 7 for .
When time slot  is idle and the current channel slot remaining is sufficient for once back-off timer decrease, the state (, ) will turn into (,  − 1) with probability    sufficient .Otherwise, the back-off timer will be held and the node will wait for next channel slot available.According to 802.11 DCF, the packet will be transmitted when node turns into (, 0) states.Different from that, in this model, only if channel slot remaining is long enough for one packet transmission, the packet will be transmitted at (, 0) states.Otherwise, the node will enter into Wait 3 ,0 state to wait for next channel slot available. , denotes the probability of state (, ).  success denotes the probability that a node transmits successfully in a random time slot and one selected channel.We use    to denote the probability that the node arrives at point   .
In order to obtain the expression of state-steady probabilities of a node, firstly, we need to express  , in terms of  0,0 .According to Figure 2, during back-off stage, we can obtain the following relations: where   sufficient and    sufficient denote the probability that the remaining channel time is enough for one packet transmission and once back-off timer decrease, respectively.They can be expressed as follows: Let    denote the probability that only  nodes out of  nodes transmit packets in a random time slot and one selected channel.Hence,   success can be expressed as follows: where  denotes the probability that a node transmits one packet in a random time slot and one selected channel. can be expressed as follows: Combining ( 9) with (10),  0,0 can be expressed with   success : And then, the    can be obtained as follows: where  meeting denotes the probability that a pair of nodes can meet each other in a random channel slot and a selected channel.According to analysis above,  meeting can be expressed as follows: Let  Wait states.According to Figure 2, they can be expressed as follows: where  traffic = 1 −  − denotes the probability of having packet to be transmitted in a random time slot  when the node is at Idle state. denotes the probability that there is no packet in the queue of a node after each successful transmission or after having reached the maximum number of the retransmissions . can be expressed as follows: And then (13) can be rewritten as follows: where [  ] denotes the average service time of one packet transmission (from the packet leaving the MAC buffer until it is successfully transmitted or reaches the retry limit).According to Figure 2, [  ] includes two section: the first one is the average time cost in checking stage ([ Wait 1 ]), and the other is the average time cost in back-off stage([ backoff ]): According to Figure 2, [ Wait 1 ] can be expressed as follows: To get the value of all states in Figure 2, the average time cost [ backoff ] in back-off stage should be obtained firstly.According to Figure 2, [ backoff ] can be expressed as follows: Combining ( 6) with (22), [ backoff ] can be expressed with   success Assume and then ( 23) can be rewritten as follows: where  denotes the average time between successive counter decrements in back-off stage.The time needed for successive counter decrements includes situations: only one time slot   is needed when all the other nodes have no packet to be transmitted,   +   needed when a packet is transmitted successfully by the other nodes, and   +   needed when a transmission collision occurs in the other nodes.Let    ,    +  , and    +  denote probabilities of these situations, respectively.Where   denotes the average time cost for once back-off timer decrease when the channel is idle.  can be expressed as follows: And then, we can get can be expressed as follows: where   is the time cost for a successful transmission and   is the average time the channel is sensed busy by each station during a collision.Let  = PHY ℎ + MAC ℎ be the packet header, and let  be the propagation delay.  and   are equal to Mathematical Problems in Engineering Based on this analysis, the value of  and   success should be obtained before all the state-steady probabilities of a node can be got.Firstly, the relation between them can be expressed based on (18) and (20): (30) In addition, the relation between  and   success also can be obtained by using the normalization condition The equation can be expressed as follows: Equations ( 30) and (32) are nonlinear and nonconvex.The equation set can be solved using arithmetic solution.And then, all the probabilities of  , ,    ,  Idle ,  Wait 1 ,  Wait 2 , , and  Wait 3 ,0 can be got too.

Throughput Analysis
. Now, we will analyze the throughput of CQM protocol.Let  denote the throughput of CQM system.In this paper, we assume the total of ℎ channels is available, and all of them have the same bandwidth.Hence, the throughput of CQM protocol can be expressed as follows: where [] denotes the average payload size per virtual slot in one selected channel.[] can be expressed as follows: And [slot] denotes the virtual slot duration.It contains the duration of an empty slot time , the time duration   due to a successful transmission, and the time duration   due to a collision, respectively.And then the average slot duration [lot] can be obtained: Finally, the normalized throughput of CQM protocol can be obtained: ) . (37)

Numerical Analysis of CQM Protocol.
To show the influence of parameters (, , , and ℎ) to the performance ([ tr ] and ) of CQM system obviously, we now present the relationship between them by numerical analysis when ℎ is set to 3. A summary of parameters is shown in Table 2.
The throughput versus node number and packet rate is shown in Figure 3, when the channel slot length is set to 100 ms.
As is shown in Figure 3(a), the throughput increases gradually with the increased node number with a certain packet rate, and it approaches a constant in the end.In a network, with the node number increases, more packets can be transmitted successfully, so the throughput of network increases.However, with the network size become much bigger, more and more nodes transmit packets in one channel with a certain bandwidth, more and more collisions will occur.In the end, the network will reach a balance state, and the throughout will approach a constant.As is similar to the influence of node number, the throughput has the same change trend with the increased packet rate.As is shown in Figure 3(b), with the increase of node number and packet rate, the throughput increases gradually.
When node number and packet rate reach a bound, the network will turn into saturation state, and throughput reaches its maximum value.In this paper, we call it saturation bound.
Figure 4 shows the relationship between throughput, node number, and channel slot length.This system consists of 3 channels, and the packet rate is set to 2 packets/s.As is shown in Figure 4, on the one hand, the throughput increases with the increase of node number in a certain channel slot length, and it approaches a constant value when the network is at saturation state.On the other hand, the throughput changes slowly with the increase of channel slot length in a certain node number.
The relation between parameters (, , ) and  can be revealed by numerical analysis.The most maximum throughput can be obtained when parameters (, , ) break through the saturation bound.And then, the change trend of average packet delay with the change of parameters (, , ) can be shown in Figures 5(a As is shown in Figure 5(a), with a given  = 100 ms, the average packet delay increases sharply with the increase of node number in oversaturation case.The increased packet rate has little influence on the average packet delay.However, the packet dropping rate will increase sharply with the increase of packet rate in oversaturation case.Figure 5(b) shows that, with the given  = 8 and  = 36, the maximum throughput and minimum average packet transmission delay can be obtained when channel slot length is set to 0.1s.That is to say, for a given  and , the network can reach the saturation situation only when the channel slot length reaches one certain value.
Based on the analysis in this section, for a network with a certain channel slot length, the maximum throughput, minimum average packet delay, and minimum drop rate can be obtained only in the saturation bound case.And we will   find the saturation bound of CQM system based on bird swarm algorithm in Section 5.

Bird Swarm Algorithm Based Saturation Bound
In this section, we will find the saturation bound of CQM system.According to analysis in Section 3, the best performance of CQM system can be obtained when the network is in saturation bound case.In this way, the problem can be considered to be an optimization problem.The goal is to find pairs of value of  and  in saturation bound case with a certain .
For this optimization problem, to get the less average packet transmission delay and less drop rate under the situation with the most maximum throughput, we set the objective function as follows: And the constraint conditions are as follows: According to (38) and (39), this optimization problem is nonlinear and nonconvex.To attack this optimization problem, bird swarm algorithm (BSA) is adopted.
BSA has elegant properties of effectiveness, superiority, and stability to solve nonlinear and nonconvex problem, proposed by Meng et al. in 2015 [26].It is based on the three kinds of behaviors of bird: foraging behavior, vigilance behavior, and flight behavior.The BSA concludes four search strategies associated with five simplified rules.
(a) Foraging Behavior.Each bird searches for food according to its experience and the swarms' experience.This behavior can be expressed as follows: where   , denotes the position of the th bird at time step .rand(0, 1) denotes independent uniformly distributed numbers in (0,1).Cog and Soc are two positive numbers, which can be, respectively, called cognitive and social accelerated coefficients. , denotes the best previous position of the th bird and   denotes the best previous position shared by the swarm.
(b) Vigilance Behavior.Birds would try to move to the centre of swarm, and they would inevitably compete with each other.Thus, each bird would not directly move towards the centre of the swarm.These motions can be formulated as follows: where  is a positive integer, which is randomly chosen between 1 and .1 and 2 are two positive constants in [0, 2].Fit  denotes the th bird's best fitness value and sumFit represents the sum of the swarms' best fitness value.mean  denotes the th element of the average position of the whole swarm.And  is the smallest constant in the computer.
(c) Flight Behavior.Birds may fly to another site in response to predation threat, foraging, or any other reasons.The behaviors of the producers and scroungers can be described mathematically as follows, respectively: where rand (0, 1) denotes Gaussian distributed random number with mean 0 and standard deviation 1. FL means that the scrounger would follow the producer to search for food.Based on BSA algorithm, for a certain channel slot length , we can get the tuple (, ) at the saturation bound.The parameter values of BSA algorithm in this section are given in Table 3.
In this section, the channel slot length  is selected in range of [0.01, 1].And Figure 6(a) shows the results of BSA algorithm with 3 channels.Figure 6(b) is the smooth result of Figure 6(a).
The surface in Figure 6(b) can denote the saturation bound of CQM system obviously.The point on the surface denotes one possible tuple (, , ) in the saturation bound case.As is shown in Figure 6(b), the packet rate changes against the changes of node number with a certain channel slot.
When  is set to 100 ms, the relationship between node number and packet rate for different channel number in the saturation bound case can be illustrated in Figure 7.And the normalized throughput for different node number with  = 8 can be shown in Figure 8.
As is shown in Figure 7, in saturation bound case, the node number decreases with the increase of packet rate with  = 100 ms for different channel number.And the node number needed increase with the increase of channel number in a certain packet rate.That is to say, only when the system load is larger than capacity of channel, the network can reach the saturation bound state.

Traffic Prediction Based DCQM Protocol
According to the analysis in Section 4, the accurate performance of CQM MAC protocol is obtained.The metrics (throughput and average packet transmission delay) are calculated in performance analysis, with respect to node number, packet rate, channel slot length, and channel number.
In CQM protocol, owing to its equal opportunity for nodes to transmit and to receive, the optimal performance of CQM protocol can be obtained in saturation bound situation.
However, in unsaturation situation, in a random time slot, some nodes have packets to be transmitted, while others have no packet to be transmitted.In this situation, the channel slots can not be utilized effectively, due to the fixed slot allocation scheme of CQM protocol.
To get the optimal performance in both unsaturation and saturation situations, a dynamic time slot allocation scheme of CQM protocol is proposed, based on traffic prediction.In traffic prediction slot, each node predicts the real time arrival traffic  tra by wavelet neural network.And then, in allocation slot, the next channel slot is allocated according to the predicted traffic of network.

The Prediction Model of Wavelet Neural Network.
By contrast with the traditional neural network, WNN shows a higher accuracy, faster convergence, and better fault tolerance to complex nonlinear, uncertain, and unknown system.Wavelet neural network takes the topological structure of BP neural network as the foundation and selects the Morlet wavelet basis function as the transfer function of the hidden layer [27,28].As a feed-forward network, BP neural network includes the forward propagation of signal and the backpropagation of error.While the network is in the training and learning process, the weight is continuously adjusted to obtain the minimum total error which is relevant to the appropriate output of the network.The  −  − 1 prediction model of WNN is shown in Figure 8.
As is shown in Figure 8, where   ,  = 1, 2, . . ., , is the input parameter, x+1 is the predicted output value in  + 1 moment,   is the layer weight from input layer to hidden layer, and   is the layer weight from hidden layer to output layer, where  denotes the node number in hidden layer;  is the expansion parameter of the wavelet function;  is the translation parameter of the wavelet function.The Morlet wavelet basis function can extract the amplitude and phase information of the analyzed signal.Here the Morlet wavelet basis function as the activation function is shown as follows: The wavelet neural network adopts the gradient descent algorithm [29] to correct the connection weight.The error function  = ( +1 − x+1 ) is used to correct the connection weight, so as to minimize the network error.

The Dynamic Time Slot Allocation Scheme.
To get the optimal performance in both unsaturation and saturation situation, the DCQM protocol is proposed.Based on CQM protocol and WNN, the traffic prediction slot and allocation slot are added in CQM protocol.Figure 10 is an example of DCQM operation under  6 with two channels (numbered from 0 to 1).Nodes 0, 1, and , with IDs 0, 1, and , respectively, are within each other's transmission range.The protocol processing of DCQM protocol is shown in Figure 9.
As is shown in Figure 9, the traffic prediction slot and allocation slot are added in front of each channel slot.In the end of a channel slot, number of packets transmitted in channel slot and that in the former channel slots are sent to WNN prediction processing.In traffic prediction slot, the predicted traffic to be transmitted in next channel slot of each node can be obtained.And during the allocation slot, if the predicted traffic is 0, the next channel slot is turned to default slot.Otherwise, nodes will broadcast their predicted traffic in their current channel in a random slot.Each node can get the predicted traffic of nodes in same channel, which can denote the traffic of network.And then, the next channel slot of each node can be allocated, according to one judgment criteria.
According to analysis of Figure 9, the judgment criteria are the key to allocate the channel slot.To utilize the channel efficiently, the switching channel slot should be preferentially allocated to the nodes that having packets to be transmitted.However, when more and more nodes have packets to be transmitted, if all of them are allocated to switching channel slot, the problem of missing destination node exists.To avoid this problem, the probability  allo switch that the switching channel slot is allocated to a node is introduced.And let   traffic denote the ratio of busy node number to network node number.And  allo switch should meet the conditions as follows: As is shown in (44),  allo switch is inversely proportional to  traffic .And  traffic is obtained through broadcast in allocation slot.After traffic prediction slot, each node obtained their predicted packet number by WNN algorithm.During allocation slot, the nodes that having packets to be transmitted broadcast their predicted packet number in random slot.In this way, each node can obtain the approximate  traffic of network.And then, each node will turn to switching channel slot according to corresponding  allo switch .
To obtain the optimal  allo switch that meets the condition in (44), lots of Monte Carlo simulations are adopted, with ℎ = 3, 5, 7, and 60 nodes considered.For one unsaturation situation ( traffic ∈ [0.1, 1]), lots of value of  allo switch ∈ [0.01, 1] are considered.The optimal  allo switch is obtained when the throughput of network reaches its maximum.The relationship between  allo switch and  traffic is revealed in Figure 10.
As is shown in Figure 10,  allo switch is inversely proportional to  traffic , which meets the condition in (44).And for the same  traffic ,  allo switch increases with the increase of channel number.With more channel numbers, the probability that nodes meet their destination nodes becomes bigger.And the utilization rate of frequency increases with the increase of channel number.

Performance Evaluation
To verify our analytical results, we compared analytic results with simulation results obtained from Qualnet simulator.In addition, the performance of CQM and DCQM protocols is also compared through Qualnet simulator.Qualnet simulator is the only parallel and message level network simulation tool, developed by Scalable Networks Technologies.It has the faster running speed, higher accuracy, and better extensibility and is suitable for development and simulation of ad hoc network and wireless sensor networks.
In our simulations, nodes are uniformly placed in an area of 170 m × 170 m.The transmission range of a node is 250 m.In this way, all nodes can stay in the transmission range of others.A node keeps a separate FIFO queue for each of its neighbors.Each node may act as a sender where the destination is chosen from its one-hop neighbors.The packet rate is selected in [2,6].And the channel slot is set to 100 ms.To get the performance of different channel number, every node is equipped with several interfaces.The interface can be assumed to be different channels, and the CQM channelhopping strategy is used in our simulations.The number of interface is set to 3, 5, and 7.The system parameters are the same as the numerical analysis in Section 3.
Firstly, we will verify the saturation bound of analysis results. Figure 11 shows results comparison between numerical analysis and simulation when  is set to 2, 3, 4, 5, 6, 7, and 8.
As is shown in Figure 11, the numerical analysis results can be verified by simulating.In addition, the more nodes can be accommodated with the increase of channel number.It can be verified that the multichannel system can perform better than the single system in high diversity node situation.
And then, we present the aggregate throughput between the CQM and proposed DCQM protocol as shown in Figure 12.The simulation parameters of DCQM protocol are the same as that of the CQM protocol.In addition, for DCQM,  prediction and  allocation denote the time in the traffic prediction stage and allocation stage, respectively.In this simulation,  prediction is set to 1ms, and the  allocation is set to 5 ms.Each traffic flow in the network uses the constant bit rate (CBR) traffic model, the packet size is 1024 bytes, and the packet rate is set to 8. As is shown in Figure 12, for CQM and DCQM protocols, with different channel number, the normalized throughput increases with the increase of packet rate.And then, it reaches its maximum value when node number reaches one certain value.Finally, it decreases with the increase of node number gradually.In addition, in unsaturation situation, the normalized throughput of DCQM is bigger than that of CQM protocol.This is because the utilization of frequency increases due to dynamic channel slot allocation.And in saturation situation, the performance of CQM protocol is slightly better than DCQM protocol.For DCQM protocol, in saturation situation,  allo switch is almost 0, and the channel slot allocation is the same as CQM protocol.However, the additional overhead is needed in DCQM protocol because of the additional traffic prediction slot  prediction and allocation slot  allocation .

Conclusions
IEEE 802.11DCF suffers from many collisions in high diversity node situation.Multichannel MAC protocol can help to share the traffic loads among different channels.And the CQM protocol performed better among MMAC protocols with only one transceiver.However, the performance of CQM protocol is not analyzed theoretically.And the performance is not optimal for the fixed channel slot allocation scheme in unsaturation situation.
In this paper, a Markov chain model is proposed to analyze the performance of CQM protocol theoretically.The throughput and average packet transmission delay of CQM system are revealed too.And the saturation bound of CQM protocol is obtained based on BSA algorithm.In addition, to obtain the optimal performance of CQM protocol in unsaturation situation, a traffic prediction based dynamic channel slot allocation scheme of CQM protocol is proposed based on WNN prediction model.In the end, the performance theoretical analysis of CQM protocol is verified by simulating on Qualnet platform.And the performance comparison of CQM and DCQM protocol is simulated too.The results show that the simulation results and analytical results match very well, and the DCQM protocol performs better than CQM protocol in unsaturation situation.

Figure 3 :Figure 4 :
Figure 3: Throughput versus node number and packet rate with  = 100 ms.
ck et ra te (p ac ke ts /s ) Average packet transmission delay (s) Average packet transmission delay of CQM system with  = 100 ms (3D)

Figure 5 :
Figure 5: Average packet transmission delay in oversaturation case.

Figure 6 :
Figure 6: The saturation bound results obtained by BSA algorithm.

Figure 7 :
Figure 7: The saturation bound of CQM system with different channel number.

Figure 8 :
Figure 8: The prediction model of WNN.

Figure 9 : 7 Figure 10 :
Figure 9: The protocol processing of DCQM protocol with two channels.

Table 1 :
Average channel slots analysis of node 0.

Table 2 :
CQM system parameters in numerical analysis.

Table 3 :
The parameter values of the BSA algorithm.