Performance Comparison between the minimum holdoff time Scheme and Our Proposed Schemetime Scheme and Our Proposed Scheme

One may think that using the minimum holdoff time (i.e., 1) is an alternative to achieve the optimal network performance. In this section, we compare the performance of such a naive scheme (denoted as the HT-1 scheme) and our proposed dynamic holdoff time scheme. Most of the simulation settings are the same as those used in previous sections, except that the simulated topology is changed to a 25-node grid network, where each is spaced with 450 meters. In the simulated topology, each node establishes a TCP

Table 4.3: MAC-layer performance of the evaluated schemes

MAC

ATOUN ATHPT (ms) NodeUI

Avg. Std. dev. Avg. Std. dev. Avg. Std. dev.

HT-1 0.742 0.0911 19.187 12.9448 0.051 0.0413 Dynamic 0.676 0.0932 18.917 12.9952 0.184 0.0900 HT-16 0.375 0.0787 29.865 11.9366 1.293 0.3121 HT-32 0.223 0.0529 51.028 13.9581 2.131 0.3657 HT-64 0.119 0.0300 97.320 19.2756 3.076 0.3827

connection to each of its one-hop neighboring nodes. The number of frames of each minislot allocation in this series of simulations is set to 128.

Tab. 4.3 shows the MAC-layer performance of the evaluated schemes. As can be seen, both the HT-1 and our proposed dynamic holdoff time scheme can generate the shortest time for completing THPs. However, as compared with the HT-1 scheme, the proposed dynamic holdoff time scheme can further reduce the used DSCH TxOpps. Thus, it is more bandwidth efficient than the HT-1 scheme.

Although both the HT-1 scheme and our proposed dynamic holdoff time scheme can achieve the best network performance among the evaluated schemes, they greatly differ in the required computation complexity. Tab. 4.11 shows 1) the contention time of a node, 2) the size of the contending node list for each TxOpp, and 3) the required computation complexity under the evaluated schemes. The contention time of a node and the average size of the contending node list under the fixed holdoff time schemes are derived based on the analytical model proposed by Cao et al. [2]. The required computation complexity can be estimated by multiplying these two values. Note that, to fairly analyze the contention time and the size of the contending node list, we assume that the next TxOpp information broadcast by each node is the accurate TxOpp number. This can be easily accomplished by adding an offset field into the MSH-NCFG and MSH-DSCH message formats.

As shown in Fig. 4.11, the behaviors of the proposed dynamic holdoff time scheme is more complicated than fixed holdoff time schemes and can be divided into two cases.

In the first case, our proposed dynamic holdoff time scheme calculates the most efficient next DSCH TxOpp when a node needs to send a Request IE. This calculation process may need to perform MEA at most three times and the maximum number of contending nodes per TxOpp during this calculation process is nbr2(x). In the second case, when a node need not transmit Request IEs, our proposed dynamic holdoff time scheme simply

Table 4.4: The computation cost of the HT-1 scheme and the proposed Dynamic holdoff time scheme

Contention Time Contending Node List Size Computation Complexity

HT-1 nbr2(x) nbr2(x) O((nbr2(x))²)

HT-16 ^2∗nbr2₁₇^{(x)+16 2∗nbr2}₁₇^(x)+16 O(^4∗(nbr₂₈₉^2(x))2) HT-32 ^2∗nbr2₃₃^{(x)+32 2∗nbr2}₃₃^(x)+32 O(^4∗(nbr₁₀₈₉^2(x))2) HT-64 ^2∗nbr2₆₅^{(x)+64 2∗nbr2}₆₅^(x)+64 O(^4∗(nbr₄₂₂₅^2(x))2) Dynamic (128 frames) 0.509 ∗ nbr2(x) 0.509 ∗ nbr2(x) O(0.302 ∗ (nbr2(x))²) Dynamic (32 frames) 0.536 ∗ nbr2(x) 0.536 ∗ nbr2(x) O(0.446 ∗ (nbr2(x))²) Dynamic (8 frames) 0.617 ∗ nbr2(x) 0.617 ∗ nbr2(x) O(0.895 ∗ (nbr2(x))²) Dynamic (4 frames) 0.690 ∗ nbr2(x) 0.690 ∗ nbr2(x) O(1.295 ∗ (nbr2(x))²) Dynamic (2 frames) 0.775 ∗ nbr2(x) 0.775 ∗ nbr2(x) O(1.764 ∗ (nbr2(x))²) Dynamic (1 frames) 0.855 ∗ nbr2(x) 0.855 ∗ nbr2(x) O(2.203 ∗ (nbr2(x))²)

Figure 4.11: The operation of the proposed dynamic holdoff time scheme

sets the node’s holdoff time to 2^{f loor(log2}(|nbr(i)|)). In this condition, the calculation process performs MEA once. We used simulations to estimate the number of contending nodes per TxOpp for all nodes and obtained such a value is roughly ^nbr₂^2(x).

On the other hand, in this network nodes usually use THPs to reserve a minislot allocation that lasts multiple frames (e.g., 8 frames to 128 frames). This means that the second case more frequently occurs than the first case. For example, suppose that the frame duration of each minislot allocation is 128 frames. In the second case, each node on average transmits its MSH-DSCH messages every 19.6 TxOpps in the 25-node grid network. Given that each scheduling control subframe contains 8 TxOpps, the number of the occurrences of the second cases within 128 frames is 53.895. This means that one occurrence of the first case follows 53.895 occurrences of the second case. Thus, the total computation complexity of the proposed dynamic holdoff time scheme can be amortized by the light-weight processing of the second case. We formalize the expected contention

time for node k (E[Ck]) as follows:

E[Ck] = 1 ∗ nbr2(x) + l ∗ u

1 + u , (4.29)

where l denotes the average contention time of node k in the second case (which is ^nbr₂^2(k) in the 25-node grid network) and u denotes the number of the occurrences of the second case (which is 53.895 when the frame duration is set to 128 frames). Based on Cao’s model [2], the expected value of the contending node number per TxOpp is E[Ck]. By multiplying these two values, we can obtain the computation complexity of the proposed dynamic holdoff time scheme under different frame durations, which are presented in Tab. 4.4. One sees that, as long as the reserved frame duration is large enough (e.g., larger than 8 frames), the computation complexity required by our proposed scheme is less than that required by the HT-1 scheme.

When the reserved frame duration is very small (e.g., 1 frame to 4 frames), the pro-posed dynamic holdoff time scheme has higher computation complexity than the HT-1 scheme. This fact inspired us that the proposed dynamic holdoff time scheme can simply set the holdoff time to 1, when the reserved frame duration is small. This is because in the conditions where Request IEs are very frequently transmitted and minislot allocations are very frequently reserved, using large computation cost to reduce the time for scheduling a minislot allocation is not cost-effective.

4.2.7 Summary

In an IEEE 802.16 mesh network, the holdoff time value setting design is very impor-tant for achieving good scheduling performances in the distributed coordinated scheduling mode. In this paper, we show that using a small value for this parameter can improve MAC-layer performances, quantified by three performance metrics — ATOUN, ATHPT, and NetUI. However, we show that doing so can easily cause a node’s network initializa-tion process to fail in a dense network. In this paper, we further explain why using a fixed holdoff time value for all nodes regardless of their node densities and dynamic bandwidth needs can result in suboptimal performances.

To address these problems, we propose a two-phase holdoff time setting scheme to (1) guarantee the success of network initialization and (2) improve MAC-layer scheduling performances. Both a static approach and a dynamic approach of this scheme are proposed

and their performances are studied and compared in this paper.

The overall simulation results show that the dynamic approach significantly outper-forms all fixed-value schemes. The ATOUN and ATHPT results show that it significantly increases the utilization of the control-plane bandwidth and decreases the time required for completing the three-way handshake procedure. The NetUI results show that it generates efficient and fair scheduling in the distributed coordinated scheduling mode. In addition, the throughput results show that it generates the highest TCP and UDP throughputs among all studied schemes. Finally, the round-trip time results show that the dynamic approach generates the shortest end-to-end round-trip packet delay among all studied schemes.

4.3 Numeric Evaluation for the Directional-antenna