Simulation Environment

We created a 25-node grid network topology shown in Fig. 4.12 as our simulation topology. The main parameter settings used in the simulations are listed in Tab. 4.5.

Two different traffic types are used to generate network traffic. One is greedy TCP and the other is greedy UDP. The word “greedy” means that the source node of a flow will transmit data as many as it can. For example, for a greedy UDP traffic generator program using the standard socket APIs to transmit data, each time when being waken up by the operating system, it will continuously generate data and send them out via socket APIs,

until the socket APIs return error codes such as “full socket buffer.”

In a simulation case, each node sets up a greedy UDP flow to each of its 1-hop neigh-boring nodes. Because UDP is a transportation layer protocol that simply transmits data down to the MAC-layer, the throughputs obtained by all greedy UDP flows of a node are equivalent to the MAC-layer throughputs that can be obtained by the nodes minus the bandwidth overheads introduced by MAC-layer, network-layer, and transport-layer headers. Therefore, the throughput results obtained from our greedy UDP flow cases are useful to evaluate the capacity of a network. We use this property to evaluate the capacity gain of an 802.16(d) mesh CDS-mode network using single-switched-beam antennas.

In addition to evaluate the raw network capacity, we also use greedy TCP flows to conduct simulations in the same scenario. TCP is a complicated transportation-layer protocols that employs sophisticated error-control and congestion-control mechanisms to guarantee error-free in-order data delivery. It is widely used by many network applications, such as File Transfer Protocol (FTP) and HTTP web accesses. Thus, observing how TCP works over an 802.16(d) mesh CDS-mode network using single-switched-beam antennas is worthwhile and important to researches for the network transport layer and application development.

Each of our simulation case was run ten times, each time using a different random number seed. The simulated time of each run was set to 500 seconds. In a simulation, the traffic generator programs are activated at the 200-th second of the simulated time. This arrangement is to ensure that they transmit data packets after the simulated network has been stabilized¹. In each of the figures shown below, both the average and the standard deviation of the collected simulation results are presented.

In the simulated grid network, each node is spaced 450 meters away from its vertical and horizontal neighboring nodes and equipped with a single-switched-beam antenna.

The gain pattern of this antenna on the horizontal plane across 360 degrees is plotted in Fig. 4.13, which is derived from [20].

For wireless channel modeling, we conducted simulations with several channel models, such as the two-ray model, Ercegs model with terrain type B, and the ECC-33 model.

In our experiences, in absence of dynamic fading effects (e.g., the Rayleigh fading), by properly setting the transmit power of a node, the receive power sensitivity threshold of a

1We define a stabilized network as a network in which all of its nodes have joined the network.

Table 4.5: The parameter settings used in the simulations

Parameter Name Value

Number of TxOpps per Frame 8

Number of TxOpps per Frame Used by the CDS Mode 8

Number of Mini-slots per Frame 220

Number of OFDM Symbols per Mini-slot 3

Requested Mini-slot Size per THP 10, 20, 30, 40, 50, 60, 70 Requested Frame Length 2⁰, 2¹, 2², 2³, 2⁵, 2⁷

Modulation/Coding Scheme 64QAM-3/4

Channel Model ECC-33

Frame Duration 10 ms

Binary Increase

TCP Version Congestion Control

TCP (BIC-TCP)

Figure 4.12: The topology of the simulated network

Figure 4.13: The gain pattern of the used single-switched-beam antenna

node, and the distance between nodes, the link connectivity and signal quality experienced by nodes can be adjusted to the same level. Thus, to save space we only present the simulation results under the ECC-33 model in this section. The effects of the Rayleigh fading on network capacity and flow throughputs are studied in Section 4.3.3.

When the dynamic fading effect is absent in our simulations, with proper settings of transmit power and receive sensitivity, the effective transmission range and interference range used in our simulated grid network topology are set to 500 and 850 meters, re-spectively. In contrast, when the dynamic fading effect is present, there are no explicit values for the transmission range and the interference range of a node. In this condition, a proper receive power threshold is set for each simulation case to maximize flow through-puts. Because the antenna gain patterns of the used single-switched-beam antenna and the omnidirectional antenna greatly differ, the transmit powers of the radios used in the MTD and STD schemes were set to different values to maximize their respective network performances. The transmit power of the radio using the single-switched-beam antenna was set to 22 dBm while that of the radio using an omnidirectional antenna was set to 50 dBm.

The ECC-33 model was originally proposed for modeling the path loss effect over 3.5 GHz omnidirectional radios. For this reason, when single-switched-beam antennas are used in simulations, the transmit antenna gain and the receive antenna gain used in this model will be recomputed using the gain pattern shown in Fig. 4.13 and the relative angle between the orientations of the antennas of the transmitting and receiving nodes.

4.3.2 Performance Metrics

Two performance metrics are used to study the average throughput performances of the application flows in simulations: 1) the Average Throughput of a UDP Flow in a network (ATUF) and 2) the Average Throughput of a TCP Flow in a network (ATTF). In addition, the coefficients of variation (CVs) of the ATUF and ATTF values of all flows in a network are presented to study the fluctuation degree of application throughputs under the evaluated schemes. In addition to these application-layer metrics, we use two MAC-layer performance metrics to evaluate the performance gain of the proposed scheme. One is the Average TxOpp Utilization of Nodes (ATOUN) and the other is the Average Three-way Handshake Procedure Time (ATHPT). In the following, we explain the definitions of

these performance metrics in detail.

ATUF and ATTF

The ATUF metric is used to estimate the average throughput that a greedy UDP flow can achieve whereas the ATTF metric is used to estimate the throughput that a greedy TCP flow can achieve. The ATUF metric is defined as the average throughput of a UDP flow across all network nodes, which is defined as follows:

ATUF = TTAF

TNST, (4.30)

where TTAF (total throughputs of all flows) denotes the sum of all nodes’ average UDP-flow throughput samples across the different runs of a case, which is defined by the following equation: where nc denotes the number of runs that a simulation case was performed and nn denotes the number of nodes in the simulated network. The ts time denotes when a UDP-flow sender program starts transmitting data packets in seconds and the te time denotes when a UDP-flow sender program stops transmitting data packets in seconds. In our simulations, ts time and te time are set to 200 and 499 seconds, respectively. The udp thijm(n) denotes the average throughput of a UDP flow from node i to node j during the nth second in the mth run. The definition of nbr1(i) has been given in Eq. 2.2.

TNST (total number of sampled throughput ²) denotes the total number of sampled UDP-flow throughputs across all flows and all runs of a case and is defined as follows:

TNST =

The definition of ATTF is similar to that of ATUF, except that ATTF uses the fol-lowing formula to calculate its TTAF:

TTAF = where tcp thijm(n) denotes the average throughput of a TCP flow from node i to node j during the nth second in the mth run.

2In our simulations, a flow is sampled every one second to record its average throughput in the past one second.

CV-ATUF and CV-ATTF

The coefficients of variation (CV) of ATUF and ATTF values (denoted as CV-ATUF and CV-ATTF) are used to estimate the fluctuation degree of a traffic flow’s through-put during simulation. The zero value of CV-ATUF (or CV-ATTF) indicates that the throughput of a greedy UDP (or TCP) flow in a network is stabilized at any given time.

In contrast, a large CV-ATUF (CV-ATTF) value means that the throughput of a greedy UDP (TCP) flow in a network fluctuates greatly over time. The definition of CV-ATUF is defined as follows:

CV-ATUF = StdDev ATUF

ATUF , (4.34)

where StdDev ATUF denotes the standard deviation of all UDP-flow throughput samples in a case, which is defined by the following equation:

StdDev ATUF = The definition of CV-ATTF is similar to that of CV-ATUF and is shown as follows:

CV-ATTF = StdDev ATTF

ATTF , (4.36)

where StdDev ATTF denotes the standard deviation of all TCP-flow throughput samples in a case, which is defined as follows:

StdDev ATTF =

The ATOUN metric is used to evaluate whether a network efficiently utilizes the control-plane bandwidth. As explained in Section 2.2, MEA guarantees that on each Tx-Opp, from the perspective of a node, only one node can transmit an MSH-DSCH message within its two-hop neighborhood. That is, nodes within the same two-hop neighborhood cannot transmit MSH-DSCH messages on the same TxOpp. Therefore, the average Tx-Opp utilization viewed from a node j using a single-switched-beam antenna can be defined as follows:

AvgTxOppUtil(j) = (PN umT D−1 k=0

P

i∈(nbr(jk)−{j})txnum(i)) + txnum(j)

total(j) , (4.38)

where txnum(i) denotes the number of TxOpps won by a node i; total(j) denotes the number of total TxOpps that have elapsed since node j joins the network; NumTD denotes the number of TDs that node j has; and the definition of nbr(jk) has been given in Eq. 3.6. On the other hand, the average TxOpp utilization viewed from a node j using an omnidirectional antenna can be defined as:

AvgTxOppUtil(j) = P

i∈nbr(j)txnum(i)

total(j) . (4.39)

The AvgTxOppUtil(j) can be used to indicate how well the nodes in node j’s two-hop neighborhood together utilize the TxOpps of the network. Ideally, the average TxOpp utilization viewed from each node should be 100%, indicating that, from the perspective of each node, no TxOpps are left unused in its two-hop neighborhood. Recall that on each TxOpp, only one node can transmit its MSH-DSCH message; thus each node has to choose a distinct TxOpp to transmit its MSH-DSCH message on the time axis. We note that due to the conservative eligibility determination rule used in the standard, the maximum value of this metric will not exceed 100%. The ATOUN metric is defined as the average of the AvgTxOppUtil values across all nodes in a case. The definition of ATOUN is shown as follows:

ATOUN = Pm

j=1AvgTxOppUtil(j)

m , (4.40)

where m is the number of nodes in a simulation case. Each ATOUN result presented in Section 4.3.3 is the average ATOUN value of a case across ten runs. The ATOUN metric reflects the TxOpp utilization of a network. A higher value of ATOUN indicates that a network case has a higher utilization of TxOpps while a lower value of this metric indicates that a network case has a lower utilization of TxOpps.

ATHPT

The ATHPT metric is defined as the average time required to complete a THP (which establishes a minislot allocation) across all nodes in a case. A node is allowed to transmit data packets to another node only after it has scheduled a minislot allocation with that

Table 4.6: The used holdoff times of node 1’s TDs

TD Average Used Holdoff Time Standard Deviation

0 5.464 0.9623

1 2.162 2.6064

2 5.465 0.9274

3 5.430 0.9466

node. For this reason, ATHPT significantly influences the packet delay time experienced by upper-layer application programs. The definition of this metric is explained here. For a case, we first average the times required to establish minislot allocations for a node i (denoted as THPT(i)) using the following equation:

THPT(i) = Pn

j=1tij

n , (4.41)

where tij denotes the time required to establish the jth minislot allocation of node i with one of its neighboring nodes and n denotes the number of minislot allocations that node i establishes during simulation. We then compute the ATHPT value of a case as follows:

ATHPT = Pm

i=1THPT(i)

m , (4.42)

where m is the number of nodes in a simulation case. Similar to ATOUN, each ATHPT result presented in Section 4.3.3 is the average ATHPT value of a case across ten runs.