esa-sceva/satcom-chunk-collection huggingface dataset:
## 3. Results and Discussion
### Volume-Free Near-Equal Optimal Bale Dimensions Design  
Let us consider the following problem of the optimal choice of bale dimensions.  
**Problem 1**.: _Given film parameters \(b_{f}\), \(v_{f}\), \(\epsilon_{lf}\), upper layers overlap ratio \(k_{f}\), Equation (20), number of global film layers \(p_{l}\), and the order of near-equilibrium \(\epsilon_{0}\). Find film layers decomposition \((p_{b},p_{u})\) and the bottom layers overlaps_  
\[\delta_{min}\leq\delta\leq\delta_{max}, \tag{22}\]  
_where \(\delta_{min}\) and \(\delta_{max}\) are the smallest and largest admissible overlap \(\delta\), and_  
\[k_{fb,min}\leq k_{fb}\leq k_{fb,max}<\frac{1}{2}, \tag{23}\]  
_where \(k_{fb,min}\) and \(k_{fb,max}\) are the smallest and largest admissible \(k_{fb}\), such that the applicability condition, Equation (21), holds and for any bale volume \(V_{b0}\) the optimal bale dimensions \(D_{b}^{*}\), \(H_{b}^{*}\) are near-equal with given order \(\epsilon_{0}\)._  
In view of Proposition 1, case (ii), the solution to the above problem exists if and only if there exist integer \(p_{b}\), \(p_{u}\) and continuous parameters \(k_{fb}\), \(\delta\) satisfying Equations (8) and (9), inequalities expressed by Equations (22) and (23), and the applicability condition, Equation (21). This set of equations and inequalities is solved in the Appendix B, this solution is summarized in the next result.  
**Proposition 4**.: _If inequality_  
\[b_{fr}(2+2\epsilon_{0})>2\delta_{max}(1+2\epsilon_{0}) \tag{24}\]  
_holds, then the solution to the Problem 1 exists if and only if there exists an integer \(p_{b}\) such that inequalities:_  
\[p_{l}\frac{\Big{(}1-k_{fb,max}\Big{)}(1+2\epsilon_{0})}{(2+2\epsilon_{0})-k_{ fb,max}(1+2\epsilon_{0})}\leq p_{b}\leq p_{l}\frac{\Big{(}1-k_{fb,min}\Big{)}(1 +2\epsilon_{0})}{(2+2\epsilon_{0})-k_{fb,min}(1+2\epsilon_{0})}, \tag{25}\]  
\[p_{l}\frac{\Big{(}b_{fr}-2\delta_{max}\Big{)}(1+2\epsilon_{0})}{b_{fr}(2+2 \epsilon_{0})-2\delta_{max}(1+2\epsilon_{0})}\leq p_{b}\leq p_{l}\frac{\Big{(} b_{fr}-2\delta_{min}\Big{)}(1+2\epsilon_{0})}{b_{fr}(2+2\epsilon_{0})-2\delta_{ min}(1+2\epsilon_{0})} \tag{26}\]  
_are satisfied together with the applicability condition, Equation (21). For any \(p_{b}\) solving Problem 1 the overlap radio \(k_{fb}\) is given by equation_  
\[k_{fb}=\frac{p_{l}(1+2\epsilon_{0})-p_{b}(2+2\epsilon_{0})}{(p_{l}-p_{b})(1+2 \epsilon_{0})}, \tag{27}\]  
_while by Equation (9) the overlap \(\delta=\frac{1}{2}b_{fr}k_{fb}\). For the assumed bale volume optimal bale dimensions \(D_{b}^{*}\) and \(H_{b}^{*}\) are given by Equations (5) and (6), respectively._  
Problem 1 is a mixed decision problem with integer variable \(p_{b}\) and continuous variables \(\delta\), \(k_{fb}\). From Proposition 4 the following algorithm follows.
# A New Method to Determine the Steel Fibre Content of Existing Structures--Evaluation and Validation
## 3 Results and Discussion
### Tests on Concrete Cubes as Additional Specimens
#### 3.1.2 Estimation of the Fibre Content and Orientation
In contrast to this, the concrete with a higher fibre content of 80 kg/m\({}^{3}\) shows lower variations even in the horizontal direction, which is based on the higher fibre content where fibres are expected to be oriented more uniformly (see Figure 9). This hypothesis can be verified by comparing to the vertically oriented fibres in both concretes, where in the SFRC, with a higher fibre content, more fibres are oriented in a vertical direction. Overall, a more 3-dimensional orientation of the fibres is detected. One explanation can be the size of the fibre orientation coefficient in the horizontal direction, which is based on the higher fibre content. Figure 8: Calculated fibre orientation of the cubic specimens with a fibre content of 40 kg/m\({}^{3}\), based on the electrical resistivity measurements on specimens with different concrete ages at a frequency of the alternating current of 1 kHz. Figure 7: Calculated fibre content of the cubic specimens at varying frequencies of the alternating current of the samples with a fibre content of 80 kg/m\({}^{3}\) (dotted lines represent the fitted trend lines according to the equations given in the corresponding graph). specimens. Due to the ratio of fibre length to smallest specimen dimension, in smaller specimens, a free distribution and orientation of the fibres with ongoing compaction process can be hindered by the formwork, and edge effects are the main influencing parameter for small specimens. In contrast to this, inside the cubes, there seems to be a volume in the middle, where the fibres are able to freely orientate themselves and only interact with the large grains, but no interaction with the edges of the formwork occurs.
# Application-Aware SDN-Based Iterative Reconfigurable Routing Protocol for Internet of Things (IoT)
## 5 Proposal of SADFIR  
In this section, we propose the SDN-Based Application-aware Distributed adaptive Iterative Flow Reconfiguring (SADFIR) routing protocol to configure the DSDN-IRIoT network model periodically. The principal purpose of this periodic routing reconfiguration of the proposed SADFIR protocol is to manage heterogeneity-awareness and application-sensitivity of sensed information. Consistency of periodic reconfigurations sometime results in more computational overhead and reduces the duration of actual data transmissions. In order to avoid the computational cost, the proposed SADFIR model optimizes the reconfigurations by delaying the periodic execution up to 10 th round, if the heterogeneity index of IoT devices remains stable. Distributed SDN controllers follow the unique computational threshold to enable reconfiguration methodology for the current period;  
\[RM_{q}=\left\{\begin{array}{ll}\frac{D_{p}}{(1-D_{p}\times(qmod \frac{1}{D_{p}})},&\text{if }rE>0\\ 0,&\text{otherwise}\end{array}\right. \tag{1}\]  
where, \(RM_{q}\) is threshold settings for reconfiguration methodology for current round \(q\), while \(D_{p}\) is desired percentage, \(D_{p}=0.1\) represents the initial default settings of desired percentage, \(rE>0\) indicates that computational criteria is implementable on alive nodes. This threshold methodology provides additional heterogeneity-level network optimization to establish a smart reconfiguration strategy.  
Figure 2: Hybrid architecture of heterogeneous SDN-IRWSNs.  
The execution of SADFIR routing protocol generates the clustering formulation, which is shown in Figures 3 and 4. In particular, the Figures 3 and 4 provide slightly different data transmission as SADFIR is flexible to report critical information directly. The above described DSDN-IRIoT network model consists of IoT enabled sensors that provide sensing ability of multiple applications such as; temperature, humidity, and pressure. Figure 5 shows the communication of different sensors transmitting data of the various applications. Similarly, Figure 6 indicates the SADFIR ability to communicate the critical data directly once appeared in the sensing of IoT network environment.  
The complete implementation of the proposed SADFIR is divided into three phases of interrelating processes called; Network Topology Management Phase (NTMP), Network Settling Phase (NSP), and Network Forwarding Phase (NFP). The technical details of these phases are given in the next three subsections.
# A General Statistical Physics Framework for Assignment Problems
## 2 A General Formulation of the Assignment Problem
### Optimizing the Effective Free Energy
For a given value of the parameter \(\beta\), \(\overline{n}_{1\beta}(i)\) and \(\overline{n}_{2\beta}(j)\) are the numbers of elements of \(S_{2}\) and the number of elements in \(S_{1}\) that are in correspondence with \(i\) and \(j\), respectively, and \(\overline{G}_{\beta}\) forms a transportation plan between \(S_{1}\) and \(S_{2}\) that is optimal with respect to the free energy defined in Equation (8). Note that these values are mean values and fractional. The matrix \(\overline{G}_{\beta}\) belongs to a polytope, which we define as \(\mathcal{U}^{k}(p_{min}^{max},Q_{min}^{max})\) (see Appendix A for a full characterization of this polytope). We can link the mean field assignment matrix \(\overline{G}_{\beta}\) to an optimal free energy \(F_{\beta}^{MF}\) and to an optimal internal energy \(U_{\beta}^{\text{MF}}=\sum_{i,j}\overline{G}_{\beta}(i,j)C(i,j)\). These values serve as mean field approximations of the exact free energy and internal energy of the system, respectively. Here are the key properties of \(U_{\beta}^{MF}\) and \(F_{\beta}^{\text{MF}}\):  
**Proposition 2**. : \(F_{\beta}^{\text{MF}}\) _and \(U_{\beta}^{\text{MF}}\) are monotonic increasing and monotonic decreasing functions, respectively, of the parameter \(\beta\)._  
Proof. : See Appendix C for \(F_{\beta}^{\text{MF}}\) and Appendix D for \(U_{\beta}^{\text{MF}}\). Theorem 1 and Proposition 2 outlined above underscore several advantages of the proposed framework, which reframes the multi-assignment problem as a temperature-dependent process. Firstly, at each temperature, the multi-assignment problem with a generic cost matrix is transformed into a concave problem with a unique solution. This problem exhibits linear complexity in the number of variables, contrasting with the quadratic complexity of the original problem. The concavity facilitates the utilization of straightforward algorithms for identifying a minimum of the effective free energy function (Equation (8)). Additionally, Equation (12) offers robust numerical stability for computing the transportation plan and the functions \(n_{1}\) and \(n_{2}\), owing to the characteristics of the functions \(h(x)\) and \(g(x)\). Lastly, the convergence with respect to temperature is monotonic.
# Prediction of Vibration-Mode-Induced Noise of Structure-Acoustic Coupled Systems
## 2 Induction Characteristics of Acoustic Modes
### Prediction of Vibration-Mode-Induced Noise in the Acoustic Domain
 \tag{15}\]  
where \(N=2\omega_{s}\omega_{a}(\xi_{s}\omega_{a}+\xi_{a}\omega_{s})D=4\xi_{s}\xi_{a} \omega_{s}\omega_{a}\big{[}\big{(}\omega_{a}^{2}-\omega_{s}^{2}\big{)}^{2}+4 \omega_{s}\omega_{a}(\omega_{s}\omega_{a}\big{(}\xi_{s}^{2}+\xi_{a}^{2}\big{)} +\xi_{s}\xi_{a}(\omega_{s}^{2}+\omega_{a}^{2})\big{)}\big{]}\)  
The dispersion ratio (R) of the acoustic mode against the vibration mode dispersion is  
\[R(\xi_{s},\xi_{a},\omega_{s},\omega_{a},g_{a})=\rho_{a}^{2}g_{a}^{2}\frac{\xi _{s}}{\omega_{s}}\frac{N}{D} \tag{16}\]  
Figure 1 shows the normalized dispersion ratio, expressed as the ratio of the natural frequency of the acoustic mode to that of the vibration mode (\(\omega_{a}/\omega_{s}\)), as indicated in Equation (16). The ratio decreases as the difference in the frequencies of the acoustic and vibration modes increases, and the value is 40% of the maximum dispersion ratio when the frequency ratio varies by 5%. If the vibration and acoustic modes are close, with \(\omega_{a}=\omega_{s}\), the maximum dispersion ratio can be expressed as  
\[R(\xi_{s},\xi_{a},\omega_{s}=\omega_{a},g_{a})=\frac{\rho_{a}^{2}g_{a}^{2}}{4 \omega_{s}^{4}\xi_{a}(\xi_{s}+\xi_{a})} \tag{17}\]  
In this manner, the acoustic mode dispersion can be predicted from the vibration mode dispersion as follows:  
\[E[q(s)q(\widehat{s})]=RE\big{[}\ddot{\eta}(s)\ddot{\eta}(\widehat{s})\big{]} \tag{18}\]  
As mentioned previously, \(R\) depends on the natural frequency and damping ratio of the vibration and acoustic modes and coupling coefficient \(g_{a}\). The influence of the damping ratio of the acoustic mode on the ratio is significant. Therefore, in an acoustic domain with minor damping, such as a reverberation chamber, a greater sound pressure can be expected to be induced for the same vibration.
## 4 Connector Behavior Specification
### Enhanced Connector Profile  
Using a profile is one of the methods for extending UML. Figure 9 shows the UML profile developed for representing the enhanced connector concepts. Defining stereotypes for enhanced connectors enables the model transformations to differentiate between the standard UML model elements and the model elements used for the enhanced connectors.  
We apply the _ConnectorBehavior_ stereotype to OpaqueBehaviors that we use to specify connector behaviors. In UML, since Behaviors are _Classifiers_, they are allowed to have _Properties_. We denote the reply and request buffers using specific properties of OpaqueBehaviors. _ReplyBuffer_ and _RequestBuffer_ stereotypes generalize the abstract _Buffer_ stereotype, which extends the metaclass Property. The stereotype Buffer has a _type_ property, whose type is _BufferType_ enumeration. BufferType defines two enumeration literals that denote FIFO and single-copy buffers.  
We distinguish the enhanced UML connectors from the standard UML connectors by setting their contract role to an OpaqueBehavior. We also apply the _EnhancedConnector_ stereotype to enhanced connectors to avoid ambiguity in case the contract role is used for another purpose.  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**Term** & **Description** \\ \hline OutPort[1..*] & Ordered array of references to the providers. An operation declared in the port contract can be called using this reference. \\ \hline ReplyBuffer[1..*] & Reply buffer for storing replies from the providers. \\ \hline InPort[1..*]RequestBuffer & Ordered array of references to the request buffers for each requester. \\ \hline PRV\_CNT & Placeholder for the number of providers. \\ \hline REQ\_CNT & Placeholder for the number of requesters. \\ \hline arg & Name of the argument of the operation which is declared by the interface provided/requested by the port. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Special terms used in connector behavior specifications.  
Most of the current UML tools do not support creating n-ary connectors. Therefore, we represent n-ary enhanced connectors using an _n-1_ number of binary connectors. We designate one of the binary connectors as _the primary enhanced connector_ by setting its contract role to an OpaqueBehavior. Then, we designate the remaining _n-2_ binary connectors that are part of the n-ary enhanced connector as the _secondary enhanced connectors_. We create dependencies from the primary enhanced connector to the secondary enhanced connectors to form a group of connectors that constitute the n-ary connector. Figure 8a shows one such dependency among the connectors using a dashed line. The contract role of the secondary enhanced connectors is empty.
## 4 ADMM Formulation and Solution
### Termination Criteria of the Algorithm  
Let the primal residuals at iteration \(m+1\) be defined as  
\[d_{pr1}^{m+1}=\mathbf{A}_{r}^{T}\mathbf{r}_{r}^{m+1}+\mathbf{A}_{r}^{T} \mathbf{s}_{r}^{m+1}-2\mathbf{x}_{r} \tag{32a}\] \[d_{pr2}^{m+1}=\mathbf{T}\Big{(}\mathbf{r}_{r}^{m+1}\Big{)}\mathbf{s}_{r}^{m+1} -\mathbf{1}\] (32b) \[d_{pr3}^{m+1}=\mathbf{r}_{r}^{m+1}-\mathbf{s}_{r}^{m+1} \tag{32c}\]  
and the dual residuals be defined as  
\[d_{rs1}^{m+1}=\mathbf{r}_{r}^{m+1}-\mathbf{r}_{r}^{m} \tag{33a}\] \[d_{rs2}^{m+1}=\mathbf{s}_{r}^{m+1}-\mathbf{s}_{r}^{m}. \tag{33b}\]  
Then, as suggested by [54], reasonable termination criteria are  
\[\parallel d_{pr1}^{m+1}\parallel_{2}^{2}\ \leq\ \ e_{1}^{pri}, \tag{34a}\] \[\parallel d_{pr2}^{m+1}\parallel_{2}^{2}\ \leq\ \ e_{2}^{pri},\] (34b) \[\parallel d_{pr3}^{m+1}\parallel_{2}^{2}\ \leq\ \ e_{3}^{pri},\] (34c) \[\parallel d_{dr1}^{m+1}\parallel_{2}^{2}\ \leq\ \ e^{dual},\] (34d) \[\parallel d_{dr2}^{m+1}\parallel_{2}^{2}\ \leq\ \ e^{dual}. \tag{34e}\]  
where \(e_{1}^{pri},e_{2}^{pri},e_{3}^{pri}\) are the tolerances for the primal residual and \(e_{1}^{dual}\) is the tolerance for dual residuals. These tolerances, in accordance with [54], are defined as  
\[e_{1}^{pri}=\sqrt{4N}\epsilon^{abs}+\epsilon^{rel}\text{max}\Big{\{}\parallel \mathbf{A}_{r}^{T}\mathbf{r}_{r}^{m+1}\parallel_{2},\parallel\mathbf{A}_{r} ^{T}\mathbf{s}_{r}^{m+1}\parallel_{2},\parallel\mathbf{2}\mathbf{x}_{r} \parallel_{2}\Big{\}} \tag{35a}\] \[\epsilon_{2}^{pri}=\sqrt{MN}\epsilon^{abs}+\epsilon^{rel}\text{max}\Big{\{} \parallel\mathbf{T}\Big{(}\mathbf{r}_{r}^{m+1}\Big{)}\mathbf{s}_{r}^{m+1} \parallel_{2},\parallel\mathbf{1}\parallel_{2}\Big{\}}\] (35b) \[\epsilon_{3}^{pri}=\sqrt{2 MN}\epsilon^{abs}+\epsilon^{rel}\text{max}\Big{\{} \parallel\mathbf{r}_{r}^{m+1}\parallel_{2},\parallel\mathbf{s}_{r}^{m+1} \parallel_{2}\Big{\}}\] (35c) \[\epsilon^{dual}=\sqrt{2 MN}\epsilon^{abs}+\epsilon^{rel}\parallel\rho_{1} \mathbf{w}\parallel_{2} \tag{35d}\]  
Algorithm 1 summarizes the steps of the algorithm.
# Telepresence Social Robotics towards Co-Presence: A Review
## 2 Co-Presence Taxonomy
### Immersive Qualities
#### 2.1.5 Depth Cues (Stereoscopy and Motion Parallax)  
Considering an interaction between two persons through a teleoperated robot, the depth cues become more important for the remote user, since the local user is with the robot, and has natural depth cues. On the other side, if the remote user can perceive the local user in a 3D space, it improves the scene's realism and the co-presence. The use of 3D displays or head-mounted displays (HMDs) by the remote user are common approaches to delivery depth cues. However, this requires 3D sensors in the robot's side (e.g., stereo cameras and RGBD sensors). Additionally, with the inclusion of an autostereoscopic or 3D display in the robot to present the remote user to the local user, it is possible to enhance the closeness [75; 76; 77].
## 2 Fisher-Snedecor \(\mathcal{F}\) Composite Fading Model
### Moment Generating Function (\(\mathcal{M}_{\text{MGF}}\))  
The \(\mathcal{M}_{\text{MGF}}\) of the end-to-end SNR for the considered FSO RIS-ACs system can be derived as ([24], Equation (28)):  
\[\mathcal{M}_{\text{MGF}}(s)=s\int_{0}^{\gamma}e^{-s\gamma}F_{\gamma}(\gamma)d\gamma \tag{24}\]  
The C-F \(\mathcal{M}_{\text{MGF}}(s)\) was derived in terms of the Meijer G function ([41], Equation (07.34.02.0001.01)), using ([41], Equation (07.23.26.0007.01)) and ([41], Equation (07.34.21.0088.01)), respectively, and obtained as:\[\mathcal{M}_{\text{MGF}}(s)=\frac{(b_{1}-1)^{b_{1}}a_{2}{}^{a_{2}}(b_{2}-1)^{b_{ 2}}\tilde{\gamma}^{(b_{1}+b_{2})/2}}{\beta(a_{1},b_{1})\beta(a_{2},b_{2})}\sum_{k= 0}^{a_{1}-1}\binom{a_{1}-1}{k}(-1)^{k}\frac{((b_{1}-1)\tilde{\gamma}^{1/2})^{k }}{b_{1}+k}\]  
\[\times\left(\frac{(\frac{(b_{2}-1)\tilde{\gamma}^{1/2}}{a_{2}})^{a_{2}}\beta(a _{2},b_{2})}{((b_{1}-1)\tilde{\gamma}^{1/2})^{b_{1}+k}((b_{2}-1)\tilde{\gamma} ^{1/2})^{a_{2}+b_{2}}}-\frac{(\frac{a_{1}}{(b_{1}-1)\tilde{\gamma}^{1/2}})^{a_{ 2}+b_{1}+k}\beta(a_{2}+b_{1}+k,b_{2})s}{(a_{1})^{b_{1}+k}(b_{2}-1)\tilde{\gamma }^{1/2})^{a_{2}+b_{2}}}\]  
\[\times\frac{\Gamma(b_{1}+a_{2}+b_{2}+k)}{\Gamma(a_{2}+b_{2})\Gamma(b_{1}+a_{2} +k)\Gamma(b_{1}+k)\Gamma(b_{2})}\frac{2^{a_{2}+2b_{2}+k-1}}{(2\pi)^{2}s^{(1/2 )a_{2}+1}}\]  
\[\times\left.G_{5,4}^{4,5}\Bigg{(}\frac{(a_{1}a_{2})^{2}}{(s(b_{1}-1)(b_{2}-1) \tilde{\gamma})^{2}}\right|\begin{array}{c}-\frac{1}{2}a_{2},\frac{1-a_{2}- b_{2}}{2},\frac{2-a_{2}-b_{2}}{2},\frac{1-a_{2}-b_{2}-k}{2},\frac{2-a_{2}-b_{2}-k}{2} \\ 0,\frac{1}{2},-\frac{a_{2}}{2},\frac{1-a_{2}}{2}\end{array}\right)\Bigg{)} \tag{25}\]  
**Remark 1**: _To date, the statistical distribution functions of the FSO communications based on RIS subject to turbulence effects have been derived. In the context of 5G and 6G, FSO communications coexist with other radiofrequency (RF) systems, e.g., a point-to-point system transmitting in the mmWave frequency domain. Thus, it is possible to combine both frequency domains in order to generate a hybrid FSO and RF system. Although the evaluation of this hybrid system is out of the scope of this paper, it would improve the performance of any system operating independently and its evaluation will be considered in further works._
## 2 Numerical Model and Simulations
### Numerical Algorithm  
The numerical algorithm to solve the governing equations is shown in Figure 2. The geometry parameters are given at the beginning. The boundary conditions and initial data are set to start the calculation. An iteration at a given time step involves calculating the velocity, pressure and temperature of all gas parcels as well as the temperature of all solid elements. After each iteration, the gas velocity of each parcel is compared with the value in the previous iteration, thus obtaining the maximum absolute difference in all gas parcels. This value is then compared with the convergence criteria. If the convergence condition is not satisfied, iterations in the same time step are continued with the updated velocity, pressure and temperature. When the convergence criteria are achieved, the iteration in this time step is completed and the boundary conditions are updated. The calculation in the next time step starts with the updated values of gas velocities, pressures, temperatures, and the new temperature field of solid matrix.
## 6 Simulations and Testbed Experiments
### Simulation Results
#### 6.2.3 Queue Length  
Figure 12 shows the queue length of these three approaches. Each point in Figures 12a,b is the mean value of 20 simulation experiments in each group, and each point in Figure 12(c) is the value from the first experiment in each group. Figure 12(a) reflects the relation between the maximum queue length and the nodes' hop. From Figure 12(a), we can obtain that the maximum queue length falls when the nodes' hops increase. The maximum queue length of the O-CDSA is the biggest value among the three schemes when nodes are located close to the sink node. But it falls down quickly approaching close to that of non-scheduling when the hop is bigger enough. The maximum queue length of the T-CDSA always comes close to that of the non-scheduling scheme. Figure 12(b) reflects the relationship between the maximum queue length and the number of descendants of nodes. From this figure, we can find that the maximum queue length rises up when he number of nodes' descendants increases. In addition, the performance metric of the O-CDSA rises up more quickly than that of the other two schemes. While the maximum queue length of the T-CDSA comes always close to that of non-scheduling approach. Furthermore, Figure 12(c) reflects the average queue length at each round. From Figure 12(c), we can conclude that the average queue length of O-CDSA increases quickly at the initial stage, but keeps below a specific value after several stages. While the average queue length of T-CDSA is below that of non-scheduling in most cases.  
Figure 12: Queue length of the three schemes: (a) Maximum queue length versus the nodes’ hop. (b) Maximum queue length versus the number of descendants. (c) Average queue length at each round.