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A connectivity resilient dynamic multi-channel assignment method for VANET


  • Tong Zhao,

    Corresponding author
    1. State Key Laboratory of Software Development Environment, Beihang University, Beijing, China, 100191
    2. School of Electronics Engineering and Computer Science, Peking University, Beijing, China, 100871
    • Correspondence: Tong Zhao, State Key Laboratory of Software Development Environment, Beihang University, Beijing, China, 100191.

      E-mail: zhaotong@gmail.com

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  • Shanbo Lu,

    1. School of Electronics Engineering and Computer Science, Peking University, Beijing, China, 100871
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  • Wei Yan,

    1. State Key Laboratory of Software Development Environment, Beihang University, Beijing, China, 100191
    2. School of Electronics Engineering and Computer Science, Peking University, Beijing, China, 100871
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  • Xiaoming Li

    1. School of Electronics Engineering and Computer Science, Peking University, Beijing, China, 100871
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Multi-interface multi-channel can be used to reduce the channel interference and improve the network capacity for multi-hop wireless ad-hoc networks, but using multi-channel will impact the network connectivity, which is an important quality of service factor in VANET. The basic multi-channel assignment scheme in our paper keeps the network connectivity resilient to the mobility. On the basis of this method, we design a dynamic channel assignment algorithm that can dynamically switch the channels to the less busy ones by monitoring the channel usages. In order to survive the highly mobile scenarios in VANET, the algorithm is designed in a fully distributed way with low overhead. Simulations show that our method can notably improve the throughput of VANETs. And the performance keeps steady with various network configurations. Copyright © 2014 John Wiley & Sons, Ltd.

1 Introduction

Vehicular ad-hoc network, is confronted with the same problems of inter-link interference and low capacity [1]. Multi-channel technology can alleviate the interference [2]. However, channel diversity and network connectivity are two conflicting factors. The formerly interfered links can work concurrently when different channels are assigned. But the formerly connected nodes are disconnected when they are on different channels. Figure 1 is an example. All the four nodes are within direct communication distance. The topology with a single channel is originally a four-node fully connected graph (Figure 1(a)). When links (1,4) and (2,3) are working on different channels, the network is partitioned to two parts (Figure 1(b)). If the nodes can work on two channels concurrently with two interfaces, a topology in Figure 1(c) can be formed. If the nodes equip as many interfaces as channels, they can freely select the channels to avoid interference while assuring connectivity. However, there are 12 orthogonal channels in 802.11a, three in 802.11 b/g [3] and seven channels for dedicated short-range communications (DSRC) [4]. Equipping three interfaces on each node seems possible, but mounting 7 or 12 interfaces is a bit too cumbersome.

Figure 1.

An example of connectivity degradation in multi-channel mobile ad hoc network. The configurations are as follows: (a) one channel; (b) two channels, one interface for each node; and (c) four channels, two interfaces for each node.

Most existing works on multi-channels have much fewer interfaces than channels [5-12]. An optimal channel assignment method in this condition needs to take the routing strategy and network load into consideration, and sacrifice some connectivity for the channel diversity. This channel assignment problem is proved to be Non-deterministic Polynomial-time (NP) hard [13]. The highly mobile character of VANET makes the problem even harder. In [14], the authors evaluated the quality of service (QoS) indicators of VANET through simulations. They found that delay and jitter are usually within tolerance, but delivery ratio and connection lifetime are difficult to meet the QoS requirements. Thus, sacrificing connectivity for the channel diversity seems not suitable for VANET. On the other hand, vehicles have much fewer energy and hardware constraints than handheld mobile devices. Consequently, we attempt to preserve the VANET connectivity while relaxing the energy and hardware constraints. A connectivity resilient multi-channel assignment protocol can not only benefit the VANET QoS but also make the other protocol design independent to the multi-channel method and preserve the layered network architecture.

In our previous work [15], we proposed a multi-channel assignment method on the basis of road topology (multi-interface multi-channel (MIMC)-Road), which in theory, can keep the same connectivity as single channel network. In this paper, we first generalize the previous solution by answering how to achieve the connectivity invariant/resilient using the pigeonhole principle. We further present a channel usage-based dynamic channel assignment method to use the channel resources efficiently. Each node monitors the channel usages of its own active channels and exchanges the channel usage information with the neighbors. With the collected channel usage information, the node can switch from a crowded channel to a channel with sparse nodes, while it still keeps the connectivity. The method is fully distributed and insensitive to the mobility, which makes it suitable to be used in VANET.

In the rest of the paper, after reviewing the related work in Section 2, we discuss how to keep the network connectivity invariant/resilient with multi-channel and mobility in Section 3. In Section 4, we describe the details of the channel usage-based multi-channel assignment method. The evaluations are presented in Section 5, and the conclusion is in the last section.

2 Related Work

A lot of papers have studied the single interface multi-channel (SIMC) protocols in MANET using channel hopping methods. A fast switching and time synchronization is usually required to make the channel hopping efficient. And the protocols are tightly bounded with the medium access control (MAC) protocols. These shortcomings make the SIMC methods difficult to deploy in reality. A comparison of these works in MANET is given in [16].

In VANET, there are also some SIMC MAC protocol designs [17-19]. In this paper, our main concern is the multi-channel problem with multi-interface architecture (MIMC), which is independent of MAC protocols, and more efficient than single interface architecture [2]. The MIMC algorithms can be divided into the follo- wing categories.

2.1 Fixed multi-channel assignment

The algorithms of fixed multi-channel assignment will not change the assignment within a quite long period after an assignment is determined. These algorithms are suitable for networks with static topologies and known traffic profiles. In [20], the authors proposed a centralized channel assignment algorithm for mesh networks. The algorithm assumes that the traffic load is known in advance. The channel with few conflicts is assigned to link with high load. This algorithm cannot adapt to dynamic topology and traffic. When some links that need to re-allocate the channels, they may cause the ripple effect [20]. In [21], the authors presented a new multi-channel assignment algorithm based on a connectivity graph and a conflict graph in mesh network. This algorithm does not cause ripple effect, but it does not take the traffic load into consideration.

2.2 Dynamic multi-channel assignment

In this sort of algorithms, the interfaces can switch dynamically between available channels to adapt to the dynamic traffic load. In [12, 22], the authors proposed a mechanism to allocate channels dynamically on the basis of the spanning tree in mesh network. The gateway node is treated as the root of the tree. A centralized algorithm configures the spanning tree dynamically according to the traffic from and to the gateway.

2.3 Mixed multi-channel assignment

This sort of algorithms combine the aforementioned two assignment strategies. Some representative algorithms are in [5, 8]. In [5], each node's interfaces are divided into fixed interfaces and switchable interfaces. The fixed interfaces only receive packets. The switchable interfaces switch to the fixed listening channels of the neighbors to send the packets. The connecitivity is dynamically maintained by exchanging the listening channels of the nodes. In [8], the channels are assigned on the basis of clusters. By selecting the vehicles with the same moving directions, quite steady clusters may be formed. The DSRC channels are then partitioned into intra-cluster and inter-cluster channel sets. Neighboring clusters select channels by observing the busy status of channels.

2.4 Optimization models of multi-interface multi-channel

Besides the aforementioned heuristic design, there are also theoretical analysis and optimization models of using MIMC architecture [6, 7, 11]. These models usually require the topology and traffic to keep steady for the algorithms to converge. This makes them only fit for mesh network with static topology and known traffic pattern. And they will have difficulty in highly dynamic scenarios, such as in VANETs.

In mobile scenarios, channel assignment is usually solved using heuristics (such as in [5, 8]). Our work is also a heuristic design. But by first clarifying the connectivity invariant condition, we design the dynamic channel assignment method with simplicity and efficiency. The detail analysis and design are given in the following two sections.

3 Connectivity Invariant/Resilient Condition

In our previous work, we have designed a multi-channel assignment method on the basis of road map topology (MIMC-Road) [15]. The road is divided into multiple channel segments in a staggered pattern (as shown in Figure 2). This staggered pattern can guarantee that any two vehicles within the communication range will sit in one of the common channel segments. Thus, the network connectivity with the multi-channel configuration is identical to the single channel network. The vehicles select their active channels according to the position information and switch the channels when they move to the other channel segments. But this method has the following shortcomings. First, the channel assignment is static according to the position and the static road topology. Although it eliminates the assignment coordination overheads other than those in [5, 8], it cannot adaptively switch the channels when the density is high and several vehicles are in the same channel segment. Second, for those idle vehicles that are not communicating, they also need to switch the channels when they move across the channel segment boundaries. The connectivity invariance is based on the assumption that all the interfaces have the same communication range and there is no channel switching delay. In practice, it is not exactly connectivity invariant, but it is more resilient in the multi-channel and mobile environment.

Figure 2.

A MIMC-Road example of three channels and two interfaces of each node.

As discussed in Section 1, connectivity invariant property is valuable to the VANET QoS and layered network protocol design [14]. Here, we want to preserve the connectivity invariant property from MIMC-Road and overcome its shortcomings. Generally, the connectivity invariance can be achieved by insuring that there always exists at least one common channel between any two nodes within the communication range. In MIMC-Road, this is guaranteed by arranging the channels geographically. But more generally, for a network with C available channels, we can insure the common channel between nodes by equipping at lease math formula interfaces for every node. Letting these interfaces work on different channels and the existence of common channels are insured by the pigeonhole principle. This condition constrains the interface number of the vehicles. Considering that there are fewer hardware and energy limitations on the vehicles than on the conventional mobile devices, the requirement can be satisfied with reasonable costs. Specifically, for three channels in 802.11 b/g, seven channels in DSRC and 12 channels in 802.11 a, the required number of interfaces are 2, 4, and 7. It is suitable for a vehicle to equip two or four interfaces. Seven interfaces per vehicle look a bit too costly. But considering that MIMC architecture does not need to modify the MAC and the connectivity invariance can keep the layered network protocol architecture, we can obtain the hardware off the shelf and reduce the protocol implementation cost. The total cost may not be as much as one would expect at first glance. Furthermore, for networks with large number of channels, we can divide the channels into two groups. One group is dedicated for interfaces working in the multi-channel mode. The other group is for the interfaces in legacy mode. With this configuration, the conventional nodes with only one interface can join this multi-channel network as well. For example, we can divide 12 channels in 802.11 a into five channels for multi-channel networking and seven channels for conventional networking. Vehicles can be equipped with four interfaces (three for the multi-channel networking and one for the conventional networking) or only one interface. The four-interface vehicles can work in the high performance multi-channel network as well as the one-interface legacy VANET. Although the one-interface vehicles cannot join the high performance multi-channel network, they can still obtain services for the legacy VANET with their single interface. In this way, the multi-channel network can also be deployed gradually in the one-interface network. How to communicate in the conventional VANET with one interface is out of discussion in this paper.

In practice, when there are channel switching delays, the connectivity may not be invariant, but still, the previously discussed connectivity invariant condition can make the network connectivity nearly identical to that of the single channel network, and more resilient to the multi-channel and mobile environment. There are no constraints of using channels geographically as MIMC-Road did or timely as channel hopping methods did. Idle nodes will not be required to switch the channels to keep the connectivity anymore. For the dense networks, the nodes can freely switch their channels to find unbusy channels. This gives nodes the opportunity to use more channels for a better performance in a small area than MIMC-Road. The channel usage-based dynamic multi-channel assignment method in Section 4 achieves this. Moreover, only the interfaces on the same node are required to have the same communication ranges. The interfaces of different vehicles are no longer required to be identical. Different vehicles can equip hardwares from different manufacturers with various characters. This also simplifies the VANET deployment.

4 Channel Usage based Dynamic Multi-Channel Assignment

Intuitively speaking, when vehicles encounter high communication conflicts, they can switch interfaces from busy channels to spare ones to improve the performance. This is the design philosophy of channel usage-based assignment. On the basis of the connectivity invariant/resilient condition in Section 3, we do not need to worry about the connectivity and can concentrate our attention on the channel usage conditions. In the following subsections, we first give out the mathematic expression of channel usage in Section 4.1. Then, the design of the dynamic channel assignment algorithm is described in detail in Section 4.2.

4.1 Channel usage model

Before discussing the channel usage, we make the following assumptions and definitions. There are C available channels in the network. Each node equips K network interfaces that work on K different channels. math formula, which satisfies the connectivity invariant/resilient condition. The transmission probability of node n on channel c is P(n,c). The neighbors of node n is defined as B(n).

There are no communication conflicts on channel c only if there is no node transmitting or one node transmitting. The probability that only one node is transmitting around node n is

display math
display math

And the probability that no node is transmitting is

display math

Then, the conflicting probability is one minus the aforementioned two parts. Thus,

display math(1)

Assume that

display math

q can be considered as the total channel usage. Usually, if all the nodes access the channel on the basis of CSMA/CA and there is no hidden terminal, q will be ≤ 1. If there are hidden terminals, q can be > 1. Because the transmission probability of each node is ≤ 1, q is always ≤ m. Intuitively, we can guess that the conflict probability grows with the growing of the node number and transmission probability. We describe the monotonic properties of conflict probability by proving the following theorems.

Theorem 1. Given

display math

with math formula and 0 ≤ pi,q ≤ 1, function F(p1, p2,...,pm) reaches maximum at

display math

The maximum value of F(p1,p2,...,pm) is

display math(2)

Proof 1. Using the Lagrange multiplier method, let G(p1, math formula, and we have L(p1,p2,...,pm,λ) = F(p1,p2,...,pm) + λG(p1,p2,...,pm). Then, calculate the partial derivatives of L, and we obtain

display math

for i = 1,2,...,m, and

display math

Solve the equations of

display math

we obtain

display math


display math

Next, we will prove that math formula is the maximum point of F(p1,p2,...,pm).

Consider the second-order derivatives on pi,

display math


display math


display math

then the second-order judgment matrix M for the extreme point is

display math

From math formula, we have

display math

Then, HMHT = − xR, where R is

display math

R is a positive definite matrix. x > 0 when 0 ≤ q ≤ 1. So HMHT = − xR is a negative definite matrix. Thus, when math formula, F(p1,p2,...,Pm) achieves the maximal value in Equation (2).

From Theorem 1, we can conclude that under the condition math formula, the conflict probability defined in Equation (1) reaches the maximum value in Equation (2).

Next, we are going to discuss the monotonic properties of the maximum conflict probability. Theorem 2 states that the maximum conflict probability is monotonically increased with the transmission probability when the node number is fixed.

Theorem 2. For a fixed m (m ≥ 1), function

display math

is monotonically decreased with increasing q ( 0 ≤ q ≤ m).

Proof 2. The derivative of fm(q) is

display math

For m ≥ 1 and 0 < q ≤ m, we have math formula, which proves the theorem.

From Theorem 2, we know that the maximum conflict probability 1 − fm(q) is increased with increasing transmission probability.

The next theorem presents the monotonic increasing property of conflict probability with increased nodes when there are no hidden terminals.

Theorem 3. For a given q ( 0 ≤ q ≤ 1), function

display math

is a monotonically decreasing function when m ≥ 2.

Proof 3. when m ≥ 2 and 0 ≤ q ≤ 1,

display math

The natural logarithm of gq(m) is

display math

Obtaining the derivative of the aforementioned formula and denoting it as h(m), we have

display math

Because gq(m) > 0, we only need to show that h(m) < 0 to prove math formula.

We calculate h ′ (m) and obtain the following equation:

display math

For m ≥ 2 and 0 ≤ q ≤ 1, we have h ′ (m) > 0, which means h(m) is a strictly monotonically increasing function. By evaluating the h(m) when m → + ∞ , we obtain

display math

Therefore, we can conclude that h(m) < 0 for m ≥ 2 and 0 ≤ q ≤ 1. This proves the theorem.

So, 1 − gq(m) is monotonically increasing with increased m when 0 ≤ q ≤ 1 and m ≥ 2. Thus, the conflict probability is increased with increased neighbors when there are no hidden terminals. If hidden terminals exist and q > 1, gq(m) is no longer monotonic. The values of 1 − gq(m) is calculated in Table 1 with 0 < q ≤ 2 and m from 2 to + ∞ . For m = + ∞ , we calculate the conflict probebility as in the succeeding text. First, we can derive 1 − gq(m) as follows:

display math


display math

therefore, we have

display math

It is shown in Table 1 that the conflict probability is increasing with increased q. It is increasing with increasing m when q ≤ 1. And it is mostly decreasing with increased m when q > 1. With q > 1, there are hidden terminals. The impact of hidden terminals is averaged over more nodes when m is larger, which may lead to a lower conflict probability. But with fixed m, the monotonicity is always holding with q. In Section 4.2, we select the bold number 0.2275 at q = 0.9 and m → + ∞ as the threshold to judge whether a channel is too busy or not.

Table 1. The maximum conflict probability with various nodes and channel usages.
q ∖ m2468 + ∞ 

The aforementioned analysis is the mathematical modeling of conflict probability from the transmission probability. In practice, we can estimate the transmission probability from the proportion of the transmission time of each node. By comparing all the conflict probabilities of the channels, we can select the channels with low conflict probabilities for the vehicles. We discuss the details of this dynamic channel selection algorithm in Section 4.2.

4.2 Dynamic channel assignment algorithm

The analysis in Section 4.1 is based on the transmission probability. In reality, the transmission probability can be estimated by the channel usage time. By recording the active transmission time ΔT on channel c in every T period by the node itself, it can estimate its current channel usage level. We still denote it using P(n,c) as

display math(3)

for node n on channel c in time period t. In algorithm, the exponentially weighted moving average of Pt is used to filter out the random fluctuations:

display math(4)

α is the exponentially weighted moving average parameter. The initial value of math formula is set to math formula. This channel usage level in Equations (3) and (4) is used to predict the transmission probability in a short period. They are exchanged by hello/beacon messages between nodes and substituted into Equation (1) to calculate the conflict probability.

With the estimated conflict probability on every channels, the node can select the channels with lower conflict probability to use in the next period. Considering that network interfaces have channel switch delays, too frequent switches waste the channel time. Moreover, too frequent switches will cause the thrashing problem. Also, if all the channel usages are low, channel switching is unnecessary. In order to minimize the channel switching cost and make full use of the channels, interfaces will switch their channels only when the conflict probabilities of the current channels are larger than a threshold. We denote it as Pthreshold and set Pthreshold = 0.2275. It can be seen in Table 1 that 0.2275 is the value of maximized Pconflict at q = 0.9 and m → + ∞ . According to the monotonic properties of the conflict probability we analyzed in Section 4.1, the threshold can keep the conflict within tolerance and the summed channel usage q below 1.0 as long as all the nodes use the channel fairly. If the channel usages are unbalanced, the conflict probability may be low even if the summed channel usage is above 1.0. For example, suppose two nodes with channel usages of 1.0 and 0.1. Their summed channel usage is 1.1, but their conflict probability is only 0.1. We do not trigger the channel switch in this condition, because the only factor that hurts the performance is the conflict probability, not the channel usage level. If the MAC protocol has the fairness property, this small conflict can give the chance for the MAC to balance the communication media usage between the nodes. The fairness problem of MAC protocols is out of the scope of this discussion.

The algorithm is fully distributed. The communication cost is the channel usage information and the active channel announcements of the nodes exchanged by the hello/beacon messages. Two bytes (16 bits) is enough to indicate the channels in use (1 bit for each channel). One byte (256 levels) is enough to indicate the usage level of each channel. Because the number of channels is small (for example, 12 for 802.11 a), the total message overheads in one hello message are within 14 bytes. Thus, the communication overhead is negligible.

The neighbor table is required to store the extra 1-byte channel usage level and a 4-byte updating timestamp of every channel for every neighbor. For a network with C channels and a node with M neighbors, the total storage cost is M × C × 5Bytes. For a dense VANET with 256 neighbors and the 802.11-a network with 12 channels, the extra storage cost on each node is 15 KB, which is a quite small memory requirement compared with the hardware resources of today's devices.

For a node with M neighbors, the number of multiplications/divisions it needs to calculate in Equation (1) is 2M + 1. For a network with C channels, the number of multiplications/divisions the node needs to do is C × (2M + 1). With C = 12 and M = 256, the calculation time is quite small compared with the second long refreshing period for the conflict probabilities.

From the aforementioned discussions, we can see that this channel usage-based dynamic multi-channel assignment method is a fully distributed, low overhead algorithm and can efficiently utilize the multi-channel resources. We will evaluate its performance with simulations in the next section.

5 Evaluations

We implemented this channel usage-based multi-channel assignment method for MIMC VANETs (MIMC-Chan-Usage) in NS2 [23]. The parameters used in Section 4 to describe the algorithm are listed in Table 2. We use AODV [24] to evaluate the network performance and compare MIMC-Chan-Usage with single interface single channel (SISC), Fix-Switch [5], and MIMC-Road [15]. In order to compare with Fix-Switch, the number of channels is set to a small number of 3, and the interface is 2. A channel switch delay of 10 ms is also implemented in the simulations. The communication range is set to 150 m. The channel segment size is set to about 300 m according to the rules in MIMC-Road.

Table 2. The parameters of the mutli-channel assignment algorithm.
TVaries randomly in 1.25–1.75 s
TswitchVaries randomly in 2.5–4.5 s

We simulate the network with 100, 200, 300, and 400 moving vehicles on a real road topology shown in Figure 3 (the black lines). They are the main roads extracted from a 2000 × 1700m2 area in south Beijing. The roads are simulated with several separated lanes. And the vehicles are moving according to the intelligent driver motion model [25].

Figure 3.

Road topology from the real map of south Beijing.

Figure 4 is the comparison of the number of all the packets delivered (total network throughput) during the simulations on different network sizes. It shows that the channel usage-based MIMC outperforms the others. With two interfaces, the channel usage-based MIMC can always keep the total delivered packets about double of the SISC's, while Fix-Switch and MIMC-Road cannot. This shows that the channel usage-based MIMC can better utilize the channel resources under different scenarios. The average delays of the packets in Figure 5show that the channel usage-based MIMC still performs the best in all the configurations.

Figure 4.

The total delivered packets on different network sizes.

Figure 5.

The average delays of the flows indifferent network sizes.

In theory, MIMC-Road and the channel usage-based MIMC are connectivity invariant, and they are resilient in the mobile and multi-channel scenarios. Table 3 compares their number of flows with non-zero traffics. Both MIMC-Road and the channel usage-based MIMC have the numbers of flows close to SISC. We inspect the source and destination nodes of the flows, and we find that most of them are the same. All the different flows are only those with very low throughputs. This means that the connectivity inconsistency only occurs with the flows that only have sporadic traffics. The random contention behavior of the MAC and the channel switching may kill some of them. Figure 6 is a close inspection on each flow for the network with 200 vehicles. Only MIMC-Road has traffic on flow 14, but the throughput is very small. The channel usage-based MIMC has the largest throughput in most of the flows. Some throughput improvements by MIMC-Chan-Usage are much greater than 2 (for example, flows 3 and 9). This is because MIMC-Chan-Usage uses the channels more flexible than Fix-Switch and MIMC-Road. It can make the full use of three channels and eliminate more conflicts.

Figure 6.

The throughput of every flow in 200-node network.

Table 3. The comparison of the number of flows with non-zero traffics.
Algorithm ∖ nodes100200300400
  1. a

    SISC, single interface single channel; MIMC, multi-interface multi-channel.


In summary, the channel usage-based MIMC uses the multi-channel resource efficiently and have the steady performance advantages over the other algorithms in various network configurations.

6 Conclusion

The channel usage-based dynamic multi-channel assignment method introduced in this paper has few impacts on the network connectivity, but it requires the network nodes to equip math formula for networks with C channels. However, this connectivity resilient property can preserve the layered network protocol architecture and ease the multi-channel assignment, which leads to a good network performance with low development and deployment costs. Considering the small number of channels and the obvious benefits of connectivity invariance, this hardware requirement is acceptable. By monitoring the active transmission time of the nodes on each channel, we can estimate the conflict probabilities of the channels. Then, the nodes can compare the conflict probabilities of the channels and select the channels with low conflicts. Because we do not need to worry about the connectivity, the dynamic channel selection is kept simple and efficient. Simulations show that this channel usage-based multi-channel assignment method has a better performance than Fix-Switch and MIMC-Road in various scenarios.

We only evaluated AODV protocol with this multi-channel assignment method in this work. Because the layered network protocol architecture is preserved, we can easily evaluate the performance with other routing and data disseminating protocols for VANETs in the future work. We can also design a data disseminating protocol to better utilize the multi-channels. Although our method improves the performance, we do not take the specific QoS requirements into consideration. This is also a topic for the future work.


This work is supported in part by National Natural Science Foundation of China (No. 61073155 and No. 61201245) and the State Key Laboratory of Virtual Reality Technology and Systems (No.BUAA-VR-13KF).