Simulation Results

Effects of Our Proposed Randomness Design

We first examine the effects of the randomness design used in TMEA-D on the control message scheduling of each TD. Suppose that the TD 1 of node 1 has data to send and the other TDs of node 1 do not have data to send. We show the the holdoff times used by the TDs of node 1 in Tab. 4.6. One can see that using TMEA-D TDs that have data to send on average can obtain smaller holdoff times to schedule its control message schedulings. In contrast, TDs that do not have data to send are forced to use larger holdoff times to schedule their control message schedulings. These results show that our proposed TMEA-D algorithm can make active TDs use smaller holdoff times to decrease the time for completing their THPs.

Effects of Holdoff Exponent Values

In this section, we studied the effects of nodes’ holdoff times on network performances.

For the STD scheme, a given holdoff time exponent value x means that all nodes use the 2^x TxOpps as their holdoff times in simulations, while for the MTD scheme a given holdoff time exponent value x means that the Sactive set used in the TMEA-D algorithm is {x, x+1, x+2, .., min(x+ Num of ActTDs -1, max exp)}, where x is from 0 to 4 in our simulations. In this series of simulations, the requested frame duration and the number of requested minislots per frame in a THP were set to 32 frames and 30 minislots, respectively.

Fig. 4.14 shows the ATOUN results of the STD and MTD schemes over different hold-off time exponent values. As one knows, increasing the holdhold-off time exponent value will increase the transmission intervals of nodes’ control messages. Thus, the TxOpp utiliza-tion of the network will decrease, when this value increases. One interesting phenomenon is that the TxOpp utilization of the STD scheme is higher than that of the MTD scheme, when the holdoff time exponent value is very small (i.e., below 2), but drops more rapidly than that of the MTD scheme, when this value increases. We explain this phenomenon from two aspects. First, when using the MTD scheme a node i uses multiple MEAIs to manage its transmission domains. Due to this design, from the perspective of node i’s neighboring nodes, on TxOpp T the set of TxOpps for which node i will not contend is denoted as S_{inact tx}ⁱ (T ) and given as follows:

S_{inact tx}ⁱ (T ) := ∩H_jⁱ(T ), 0 ≤ j ≤ Num of ActTDs - 1, (4.43) where H_jⁱ(T ) denotes the holdoff time interval of node i’s MEAI j known by node i’s neigh-boring nodes on TxOpp T . For node i, it is impossible that H_jⁱ(T ), ∀ existing MEAI j, exactly overlap. Thus, the size of S_{inact tx}ⁱ (T ) in the MTD scheme is much less than that in the STD scheme. This means that nodes in the MTD scheme more conservatively choose TxOpps to transmit control messages to avoid inter-node scheduling conflicts. As a result, when the flexibility of TxOpp scheduling is large (e.g. all nodes can use small holdoff time exponent values), the TxOpp utilization of the STD scheme can be better than that of the MTD scheme. Second, the reason why the TxOpp utilization of the MTD scheme decreases slower than that of the STD scheme, as the holdoff time expo-nent value increases, is explained here. The MTD scheme employs multiple MEAIs to

manage directional control message transmissions and all of these MEAIs need to find a conflict-free TxOpp to transmit their control messages in their respective TDs. Nodes using the MTD scheme therefore needs to consume more TxOpps than the STD scheme.

As a result, when nodes’ holdoff time intervals becomes large, nodes in the MTD scheme will use more TxOpps than those in the STD scheme, which makes the TxOpp utilization of the MTD scheme drops more slowly than that of the STD scheme.

However, as can be seen in Fig. 4.15, the time required for a node to establish a minislot allocation is insensitive to the holdoff time exponent value when it is below 3.

This is because the procedure to establish a minislot allocation is three-way based, which should finish a “requester-granter-requester” control message transmission sequence. Due to the randomness of the distributed TxOpp scheduling used in the 802.16(d) mesh CDS mode, the requesting and granting nodes may not always achieve the most efficient Tx-Opp scheduling to minimize the time for establishing a minislot allocation. In addition, although decreasing the holdoff time exponent value increases the TxOpp scheduling flex-ibility of nodes, it does not guarantee that a node that is performing a THP can always win a smaller TxOpp. (This is affected by how many MEAIs on this node and its neigh-boring nodes are performing THPs at the same time.) For these reasons, even when the holdoff time exponent value is set to very small (e.g. no more than 3), the average of the time required for establishing a minislot allocation remains the same.

As one also sees, a larger holdoff time exponent value (e.g., 4) can increase the time required for establishing a minislot allocation. These results confirm the findings presented in [2][3][4][21]. Another noticeable phenomenon is that the average minislot allocation establishment time of a node using the MTD scheme is greatly higher than that of a node using the STD scheme. Such a phenomenon results from two reasons. One is that, due to the directivity of a single-switched-beam antenna, a node using the MTD scheme cannot exchange control messages with a specific peer node on every TxOpp that it wins.

Instead, it is only allowed to communicate with a specific peer node on TxOpps won by its MEAI that manages the TD where this peer node resides. In contrast, nodes using the STD scheme can communicate with any of its neighboring nodes on every TxOpp that it wins. Due to this difference, nodes using the MTD scheme require more time to complete a THP and obtain a minislot allocation.

However, because the MTD scheme is capable of utilizing the spatial reuse advantage

0

Figure 4.14: ATOUN results over different holdoff time exponent values

Figure 4.15: ATHPT results over different holdoff time exponent values

of switched-beam antennas, it still can outperform the STD scheme on UDP and TCP flow throughputs. As shown in Figures 4.16 and 4.17, the MTD scheme can on average outperform the STD scheme on UDP flow throughputs by a factor of 2.71 and on TCP flow throughputs by a factor of 5.88, regardless of the used holdoff time exponent value.

The reason why TCP performs worse than UDP on average throughput is that TCP uses a complicated congestion control algorithm to prevent network bandwidth from being exhausted by a single flow, which usually regards packet losses as an indication of net-work congestion. Because the IEEE 802.16(d) mesh CDS mode schedules minislots in a distributed manner, the time for a node to obtain a minislot allocation may fluctuate and the number of minislots obtained in a minislot allocation may greatly vary. In this condi-tion, an outgoing network interface needs to temporarily store packets in its own packet queue. If the packet queue of an interface becomes full, packets sent from upper-layer applications will be dropped, which may make TCP unnecessarily reduce its congestion window size and under-utilize link bandwidth.

In this section, we showed that the holdoff time exponent value has great impacts on TxOpp utilization. However, because the IEEE 802.16(d) mesh CDS mode uses a distributed three-way handshake design to schedule minislot allocations on the data plane, as long as the used holdoff time exponent value is not too large (e.g. above 4), the average time for nodes to negotiate a minislot allocation is insensitive to the holdoff time exponent value. Thus, the average UDP and TCP flow throughput results of both the MTD and STD schemes are unchanged when the holdoff time exponent value is between 0 and 4.

0

Figure 4.16: ATUF results over different holdoff time exponent values

Figure 4.17: ATTF results over different holdoff time exponent values

Effects of Requested Frame Duration per THP

In this section, we studied whether the frame duration of a minislot allocation affects the network performances under the MTD and STD schemes. In this series of simulations, the holdoff time exponent value was set to 0 for both the MTD and STD schemes. The number of requested minislots per frame in a THP was set to 30 minislots. The requested frame duration for a minislot allocation was set to 2⁰, 2¹, 2², 2³, 2⁵, and 2⁷, respectively, which are all of the values allowed in the standard.

Fig. 4.18 and Fig. 4.19 show the average UDP flow throughput and average TCP flow throughput results over different requested frame duration in a THP, respectively. One intuitive result is that increasing the requested frame duration in a THP can increase the utilization of minislots, which results in increased UDP and TCP flow throughputs for both of the evaluated schemes.

A noticeable phenomenon is that, when the requested frame duration per THP is below 2³ frames, the UDP and TCP flow throughputs achieved by the MTD scheme is only the same as those achieved by the STD scheme. This is because, as discussed previously, using the MTD scheme nodes on average need 100 ms (i.e., 10 MAC-layer frames) to obtain a minislot allocation. To prevent a node from monopolizing link bandwidth, in our implementation a node A will be triggered to perform a THP with a neighboring node B, only when 1) it has data destined to node B and 2) node A does not possess any valid minislot allocation granted by node B. Due to this design and the long ATHPT property of the MTD scheme, if the requested frame duration in each THP does not exceed ⌈(ATHPT/Num of ActTDs)⌉ frames, nodes using the MTD scheme will not be able to schedule minislots as tight as those using the STD scheme. In contrast, when

0

Number of requested frames per THP (2^x) Legends

STD MTD

Figure 4.18: ATUF results over different re-quested frame durations in a THP

0

Number of requested frames per THP (2^x) Legends

STD MTD

Figure 4.19: ATTF results over different re-quested frame durations in a THP

0

Requested Frame Duration per THP (2^x) Legends STD MTD

Figure 4.20: ATHPT results over different frame durations under the UDP flow case

0

Requested Frame Duration per THP (2^x) Legends STD MTD

Figure 4.21: ATHPT results over different frame durations under the TCP flow case the requested frame duration greatly exceeds ⌈(ATHPT/Num of ActTDs)⌉ frames, due to the spatial reuse advantage, the MTD scheme can greatly outperform the STD scheme on UDP and TCP flow throughput performances.

We plotted the ATHPT results of the two evaluated schemes under the UDP and TCP traffic cases over different requested frame durations in Fig. 4.20 and Fig. 4.21. The results show that the time required for a node to complete a THP is less related to the requested frame durations.

Effects of Numbers of Requested Minislots per THP

In this section, we studied the effects of requested minislots in a THP (different MAC-layer traffic loads) under the MTD and STD schemes. In this series of simulations, the holdoff time exponent value was set to 0 and the requested frame duration in a THP was set to 2⁷ frames. The number of requested minislots per frame in a THP was set to 0, 10, ..., 70 minislots, respectively.

The average UDP flow throughput results over different numbers of requested minislots per THP is plotted in Fig. 4.22, which show that the achieved throughput of UDP flows

0

Number of requested minislots per THP Legends

STD MTD

Figure 4.22: ATUF results over different numbers of requested minislots in a THP

0

Number of requested minislots per THP Legends STD MTD

Figure 4.23: CV-ATUF results over different numbers of requested minislots in a THP under the MTD scheme significantly outperforms that of UDP flows under the STD scheme over most of the evaluated MAC-layer traffic loads. These results evidence that the MTD scheme can effectively exploits spatial-reuse advantages of single-switched-beam antennas to provide more network capacity for applications. One may notice that, when the number of requested minislots per THP is 10 only, the average UDP throughput results of the two evaluated schemes are close. This is because, when the generated traffic load is very light, the STD scheme can accommodate it without causing network congestion.

However, when the number of requested minislots in a THP increases (i.e., the generated MAC-layer traffic load increases), the STD scheme quickly reaches its saturation point and cannot keep up with the performance of the MTD scheme.

Fig. 4.23 shows the CV-ATUF results over different numbers of requested minislots in THPs, which indicate the fluctuation degree of the achieved throughputs of flows in a network over time and the fairness of network bandwidth allocation among them. One can see that the CV-ATUF values of the MTD scheme are much lower than those of the STD scheme, showing that network applications can achieve a more stable throughput over time under the MTD scheme than under the STD scheme. These results also indicate that network bandwidth sharing among these competing UDP flows is fairer under the MTD scheme.

Fig. 4.24 shows the ATTF results of the two evaluated schemes over different numbers of requested minislots per THP. There are several findings about this figure. First, the MTD scheme greatly outperforms the STD scheme over different traffic loads. Second, when the number of requested minislot is larger than 20 minislots, the average TCP flow throughputs achieved by the two evaluated schemes start to decrease. These results are explained here. When the number of requested minislots in each THP increases, the

0

Number of requested minislots per THP Legends STD MTD

Figure 4.24: ATTF results over different numbers of requested minislots in a THP

0

Number of requested minislots per THP Legends STD MTD

Figure 4.25: CV-ATTF results over different numbers of requested minislots in a THP number of minislots that each node can obtain in a THP will drastically fluctuate. As explained in Section 4.3.3, when outgoing packets cannot be sent immediately, they will be stored in the packet output queue of the interface card. However, TCP speculates about the amount of data that it can transmit mainly based on detected packet losses and therefore it does not take the number of minislots obtained by the MAC-layer in each THP into account. For this reason, TCP may inject an excessive number of packets down to the MAC-layer and thus may generate packet dropping at the MAC-layer. Such packet dropping will trigger TCP’s congestion control mechanism to reduce its transmission speed.

Although TCP is more sensitive to network congestion, as shown in Fig. 4.25, the MTD scheme still significantly outperforms the STD scheme on CV-ATTF, indicating that a TCP flow under the MTD scheme will achieve a more stable throughput over time than that under the STD scheme. These results also indicate that these competing TCP flows share the network bandwidth more fairly under the MTD scheme.

We finally studied the ATOUN and ATHPT results of the MTD and STD schemes under different numbers of minislots requested in THPs. The results are as expected.

The ATOUN metric measures the utilization of TxOpps, which are on the control plane.

However, varying the number of minislots requested in THPs only affects how minislots on the data plane will be allocated. Since TxOpps and minislots are not directly related, changing this variable has minor effects on the TxOpps utilization. In addition, varying the MAC-layer traffic load in each THP does not change the frequency that a node performs a THP. Varying this variable, therefore, has minor effects on the time required for finishing a THP.

0

Numbers of requested minislots per THP Legends STD MTD

Figure 4.26: ATOUN results over different numbers of requested minislots in a THP

0

Number of requested minislots per THP Legends STD MTD

Figure 4.27: ATHPT results over different numbers of requested minislots in a THP

Effects of Mixed Traffic

In this section, we studied the impacts of the MTD scheme on the network quality experienced by different traffic flow types. In this series of simulations, node 1 establishes traffic flows with different types to each of its neighboring nodes. The detailed setting is explained here: node 1 establishes 1) a TCP flow to node 9; 2) a UDP flow that transmits a 1400-byte packet per 0.1 second to node 13; 3) a UDP flow that transmits 800-byte packets using an exponential inter-arrival time distribution with the mean value 1.0 second, the minimum value 0.1 second, and the maximum value 2.0 second; and 4) a UDP flow that transmits 1400-byte packets with the inter-arrival time set to a normal distribution (the minimum value set to 0.1 second and the maximum value set to 2.0 second). The other nodes in the network runs greedy UDP flows with each of their neighboring nodes to generate background traffic.

The main effect of the MTD scheme on traffic flows is the increase of packet delays.

We show the average packet delay results of different flows on node 1 in Tab. 4.7. Each presented result is the average across the packet delays of all packets received by the flow.

One can find that, due to the time overheads of transmitting control messages, the MTD scheme greatly increase the packet delays of traffic flows. One first sees that the UDP flow with the constant inter-arrival time distribution experiences the shortest packet delays.

This is because nodes in the IEEE 802.16 mesh CDS-mode network transmits data in a reservation-based manner. Thus, when the packet inter-arrival time of a traffic flow is smaller, more packets can be transmitted over the same minislot allocation. As a result, the packet delays experienced by the traffic flow can be reduced.

In contrast, when the packet inter-arrival time is higher (e.g., the UDP flows with the

Table 4.7: Experienced packet delays of different flows

Flow Type Average Packet Delay (ms)

UDP flow with a constant inter-arrival time 73.92 UDP flow with an exponential inter-arrival time 218.20 UDP flow with a normal inter-arrival time 198.80

Table 4.8: Throughputs obtained by different flows

Flow Type Average Flow Throughput (KB/s)

TCP flow 0.003

UDP flow with a constant inter-arrival time 13.556 UDP flow with an exponential inter-arrival time 1.019

UDP flow with a normal inter-arrival time 1.27

exponential and uniform inter-arrival time distributions used in our simulations), their transmitted packets may not be transmitted over the same minislot allocation. In this condition, the packet delays experienced by traffic flows are increased. To reduce the packet delays experienced by applications, each node can in advance trigger its THPs as long as the output buffers of its connections have data to send. This design is an item of our future work and not included in our current implementation.

We also presented the average throughput obtained by each flow in Tab. 4.8. One can see that the throughputs of UDP flows greatly match those derived from their inter-arrival time distributions. The reason why the throughputs of the TCP flow are down to nearly zero are explained here. The ACK packets of the TCP flow should compete the slots of

We also presented the average throughput obtained by each flow in Tab. 4.8. One can see that the throughputs of UDP flows greatly match those derived from their inter-arrival time distributions. The reason why the throughputs of the TCP flow are down to nearly zero are explained here. The ACK packets of the TCP flow should compete the slots of