Chapter 2: Related Works
2.4 DIS_RAD Algorithm
An efficient broadcast scheme was developed in this study. A scheme named
“DIS_RAD” which introduces the distinct range of RAD into the counter-based broadcast scheme in MANETs, was proposed. The nodes with higher EAC are given a shorter RAD, meaning that they expire earlier to first determine whether to rebroadcast the packets. Conversely, nodes with lower EAC are given a longer RAD, which makes these nodes more likely to be blocked because the rebroadcast packets of short RAD nodes may increase the counters of long RAD nodes.
Tseng et al [2] indicated that border nodes have higher EAC than interior nodes.
Therefore, we introduce a distance threshold (Dth) which is less than or equal to communication radius (R) in the counter-based scheme, to separate the border nodes from the interior nodes. As shown in Fig. 3, node A denotes the source node, and R denotes the transmission range (all nodes in the network are assumed to have the same
transmission range). The nodes lying within node S’s transmission range but outside the range of Dth are called border nodes (e.g. node B and C). The nodes lying within Dth are called interior nodes (e.g. node D and E).
The proposed algorithm runs as follows. First, the source node initiates a broadcast request. All of its neighbor nodes increase their counters as soon as they receiving the broadcast message. The border nodes initiate an SRAD, and interior nodes initiate an LRAD, where the LRAD is always longer than the SRAD. The remaining procedure is the same as counter-based scheme. Nodes increase their counters by 1 when hearing a duplicated message during RAD. When the RAD expires, if the nodes’ counters exceed the counter threshold (Cth), then the rebroadcast is blocked. Otherwise, the broadcast packets are sent out.
The following serves as an example. In Fig. 3, suppose that Cth is set to 3, and that each node initializes its counter value to 0. The notation CB represents the counter of node B. When source node A initiates a broadcast request, all of its neighbors increase their counter to 1 (i.e. CB = CB BC = CD = CE = 1). Nodes B and C have SRADs since they are located at the border, and their RADs expire before the RADs of nodes D and E, which are LRADs. Since counters CBB and CC are less than 3, node B and C rebroadcasts the message. Counters CD and CE are increased to 3; thus nodes D and E are suspended from rebroadcasting when their RADs expire. If the RAD timer of nodes D and E expire first, which is possible in the counter-based scheme, then nodes B and C are blocked. As shown in Fig. 3, the EAC of nodes D and E are much smaller than the EAC of nodes B and C.
The value of Dth also affects the performance of DIS_RAD. Taking extreme cases the highest and lowest values of Dth (Dth = R and Dth = 0) degenerate the DIS_RAD scheme to a counter-base scheme. A large Dth should perform better than a small Dth, since border nodes always have large EAC values. Special cases often
emerge from the networks with sparse node densities. Thus, the correct Dth value must be found for all network densities. Section Ⅴpresents the effect of Dth on overall performance through simulation results.
Figure 3. An example of DIS_RAD
.5 DISCOUNT-RS
We must now return to the example in section 2.3. Suppose that ICth is set to 2 at the b
2
eginning which means that the rebroadcast of a node will be suppressed when its counter grows equal to or greater than 2. Let us resume the process of the example. Currently, node S and A have done their transmission and CC=0, CB=1 and CD=CE=2. Under the circumstance, the rebroadcast of node D and E are blocked by DISCOUNT scheme. The counters of node B and C, however, both are not yet exceeded. It is obviously that the coverage area of node B overlaps seriously with nodes A and C. In other words, it is unnecessary for node B to rebroadcast the message. Unfortunately, the probability that RAD of node B expires first and starts
the rebroadcast is 1/2. This is because node B and C choose their RAD randomly at the same time when they receive the request from source node. In order to avoid the situation, the DISCOUNT scheme should be improved if rebroadcast number is concerned as a more important issue than reachability.
The main purpose of DISCOUNT-RS is to reduce the unnecessary rebroadcast of bord
At that time, we c
ent algorithm of DISCOUNT scheme. It takes the a
er nodes. We don’t try to reduce the rebroadcast probability of interior nodes because they already hold an extremely low rebroadcast probability. We introduce a condition to help a border node decide whether to rebroadcast or not in order to save more rebroadcast. The condition is described as follows. Similar to DISCOUNT scheme, each node determines whether it is a border or interior node as soon as it receives a new broadcast request. On one hand, if it is an interior node, it simply applies to the original DISCOUNT scheme. On the other hand, when it is a border node, it decides whether to rebroadcast or not according to received duplicated rebroadcast requests before its RAD timer expires. If the duplicated rebroadcast request comes from the interior area of the listening node, the rebroadcast of the node will simply be suppressed; otherwise, if the duplicated rebroadcast request comes from interior area, the node just keeps operating as DISCOUNT scheme.
We must now return to the example postponed in the last paragraph.
annot choose rebroadcast between node B and node C cleverly. For the moment, rebroadcast of node B will simply be suppressed and node C will set out the rebroadcast after RAD timer expires. This is because node B is destined as a border node related to source node and then node B receives a duplicated packet from node A which is an interior node of node B.
DISCOUNT-RS is an enhancem
dvantages from reducing unnecessary rebroadcast of border nodes. The main purpose of the algorithm is to save more rebroadcast. On the contrary, the algorithm
may cause some degradation to the performance of reachability. We will show the influences of DISCOUNT-RS on overall performance through simulation results in next section.
2.6 Analytical Model
formal analysis of broadcast probability for the DIS_
RAD algorithm. In [7], Tracy et al. proposed a predictive probability model of the counter-based scheme. Since the proposed scheme adds the concept of distance concept to the counter-based scheme, the analysis becomes more complicated. Two rebroadcast probabilities for the border and interior nodes need to be deduced.
Because the RAD of the border nodes is shorter than that of the interior nodes, the rebroadcast probability of border nodes should be higher than that of interior nodes
As in [7], several assumptions were made to simplify the analysis process. Fir ize of an area can represent the number of nodes located in that area. Second, each node in the network is independent, and moves unaffected by any other nodes.
That is, the topology is regarded as uniformly distributed at any time. Third, the broadcast requests are generated randomly from all nodes in the network. The DIS_RAD analysis is likely to be workable in a network with these properties.
As mentioned earlier the broadcast probability is divided into two comp
dcast probability of interior nodes (Pi) and of border nodes (Pb). The probability of an individual node cannot be precisely predicted. However, this analysis gives a general trend of the rebroadcast probability under DIS_RAD.
In a DIS_RAD scheme, each node initiates a RAD as so
dcast packet. The length of a node’s RAD is determined by its relative distance from the source node. When the RAD expires, each node rebroadcasts the packet only if its counter is less than the counter threshold. The counter of each node is increased
by 1 for each duplicated rebroadcast packet received before its RAD expires.
Therefore, the probability that a node increases its counter must be deduced. The analysis starts as follows [7].
When node v receives a duplicated packet from node u, three conditions must apply
Node u must be a neighbor of node v.
than v.
can be neglected, nodes u and v are assum
hat these three events are independent, the probability Q that node v’s coun
: A.
B. Node u must transmit the packet.
C. Node u must have a shorter RAD
Since the broadcast signal propagation delay
ed to have received the original broadcast request from the source node simultaneously.
Supposing t
ter increases by 1 can be obtained as follows:
)
The parameters P(A), P(B) and P(C ately as the followings. Parameter P(A) deno
) separ
tes the probability that node u locates within node v’s transmission range, and is calculated as:
ase I: Given a distance threshold Dth, node v is located at the border annulus if its notes the transmission radius and Anet den s the entire network r area. In DIS_RAD, the distance concept divides the rebroadcast probability into Pi and Pb. When node v receives a packet from an imaginary source, its position is determined according to two cases.
C
distance from the source is greater than Dth. Therefore the broadcast probability of v is given by Pb. When node v receives a duplicate packet from node u, in counter-based
rebroadcast model proposed by Tracy et al., the location of node u is insignificant as long as it falls into node v’s transmission radius. In the proposed algorithm, however, the position of node u affects the probability of increment of the v counter. Therefore, two situations are considered:
S1: Node u is located at interior circle of source node, as shown in Fig. 4(a). The
probability S1 is given as:
2
Since the border nodes are assumed to have the same rebroadcast probability equal to
(2)
Under S1, node is est d ca a e rde
Pb, and the interior nodes have the same rebroadcast probability equal to Pi, the rebroadcast probability of node u is given by:
i
S P
B
P( 1)=
v d ine an SRAD since it is lo ted t th bo r annulus, while node u is destined an LRAD since it is located at the interior circle. Since node v’s RAD expires earlier than that of node u, node v does not receive a duplicated packet from node u before its RAD expires. Therefore, P(C) under S1 (referred as P(CS1)) equals zero. probability S2 is given as:
)
Since node u is now located at the bo t probability of node
(4)
destined SRADs. Since the two nodes have the same range of RAD (SRAD), the
probability that node u‘s RAD expires first is 1/2, because RADs are chosen randomly, and nodes v and u are assumed to receive the same broadcast request simultaneously (the signal propagation delay is negligible). Thus, P(CS2) is given as:
2
With (1)、(2) 、(3)、(4) and (5), the probab e v’s counter increases by
2
1 when node v is located at the border annulus, is computed by summing S1 and S2:
)
Equation (6) describes the probability that the counter of node v is increased by 1 by any other node in the network. Therefore, Pb can be computed by summing all possible scenarios when 0 to Cth−1 duplicated packets are received before node v’s RAD expires. Since the imaginary source definitely increases the counter value of node v from 0 to 1, only 0 to Cth −2 cases need to be considered. This is leading to:
ase II: Given a distance threshold Dth, node v is located at the interior circle if its
circle of the source node, as shown in Fig. 5(a).
C
distance from the source is less than Dth. Likewise, two situations are discussed according to the position of node u:
S3: Node u is located at the interior The probability of S3 is given as:
2
The rebroadcast probability of node u is given by:
i
S P
B
P( 3)= (8) Under S3, both nodes v and u are located at the interior circle, and share the same RAD range (LRAD). As with S2, the probability that node u‘s RAD expires first is given by 1/2. Thus, P(CS3) is represented as:
2
S4: Node u is located at the border annulus of the source node, as shown in Fig. 5(b).
The probability of S4 is given by:
)
The rebroadcast probability of node u is given by:
(10)
Under S4, node u D, while
S Pb
B
P( 4)=
is located at the border annulus and is attached with SRA
node v is attached with LRAD according to the DIS_RAD scheme. Therefore the node u’s RAD expires prior than node v. Thus the probability that node u causes node v’s counter to be increased is 1.
) that node v’s counter increases by 1 when node v is located at the interior circle is given by:
From (12), Pi can be calculated by summing all possible Qi values as the same method when calculating Pb. Therefore,
i
From the analysis above, Pb and Pi can be compared with the broadcast probability in the counter-based scheme analyzed in [3], given by Pc by observing the curve of the analytical results. Figures 6, 7, 8 and 9 show various L×L maps analyzed using MATLAB, where L denotes a multiplier of the length of the communication radius R, which was set to 250 meters. Hence, the area of a network Anet equals 250×250×L×L m2. The number of nodes N was set to 100, and counter threshold Cth was set to 3.
The X-axis denotes the value of Dth, and the Y-axis denotes the probabilities calculated by the analytical models. Clearly, Pb approximates Pc when Dth approaches 0, while Pi approximates Pc when Dth is set to 250 (equals R). In both cases, DIS_RAD is degenerated into the counter-based scheme.
Figure 4. The cases where node v locates at the border annulus.
Figure 5. The cases where node v locates at the interior circle.
Figure 6. Pb, Pi and Pc vs. Dth with Cth=3 in 3×3 map
Figure 7. Pb, Pi and Pc vs. Dth with Cth=3 in 5×5 map
Figure 8. Pb, Pi and Pc vs. Dth with Cth=3 in 7×7 map
Figure 9. Pb, Pi and Pc vs. Dth with Cth=3 in 9×9 map
Chapter 3: Simulation Results
3.1 Simulation Environment
DIS_RAD was implemented using an NS-2 simulator. To ensure that the simulation results were comparable to others, the simulation environment was modeled on that in [1]. The simulation network contained 100 nodes placed randomly in a map of L×L units, where a unit is the length of communication radius set to 250 meters. The random waypoint model for mobility patterns was adopted. The topologies were generated randomly by the “setdest” program supported by NS-2.
The moving speed was randomly distributed from 0 to 20 (m/s), and the pause time was set to 0. Each node in the network made a broadcast request exactly once during the 200 seconds of the simulation period. The MAC layer was constructed using the IEEE 802.11 standard, which is implemented in NS-2. The simulation results were averaged by the results of 15 simulation runs. The following two performance metrics were considered:
．RE – the percentage of nodes which can be REached as compared with blind flooding.
．SRB – the percentage of Saved ReBroadcasts as compared with blind flooding.
3.2 results of DISCOUNT and DISCOUNT-RS schemes
Figure 10 shows the performance of RE and SRB when the counter threshold ICth equals 2. We can observe that the performance of RE can only be satisfied (larger than 90%) in dense networks such as 3x3 and 5x5 maps. This is because a small number of rebroadcasts from border nodes are enough to cover the most part of the network area.
When the network density becomes low, the nodes which are critical in maintaining a good RE are easily suppressed if the counter threshold is not big enough. Thus, we
can observe that the RE performance is unacceptable under 7x7 and 9x9 maps.
However, when the counter threshold ICth is increased to 3 and 4, as shown in Figure 11 and 12, it is obvious that the overall performance of RE is relatively satisfactory.
Even when the networks are sparse, we also have about 90% of RE when ICth is 3.
When the ICth increases to 4, the RE is almost perfect in most cases; however, we can observe the performance degradation of SRB is about 10% when the ICth increases from 3 to 4. It is straightforward that the smaller the ICth is, the better the SRB will be.
However, it is important to keep both RE and SRB in acceptable values. To keep good balance between RE and SRB, we recommend that Dth should be set around 200 (80%
of transmission radius) and the ICth should be set to 3, where the optimal balance of RE and SRB performance can be observed. We can also observe that if Dth is set to a small value, RE decreases sharply. It is reasonable that if Dth is set too low (say smaller than 72 meters), the EAC of the border node may not be large enough to cause our algorithm to work almost the same as Counter-Based scheme. It’s obvious that the DISCOUNT will be degenerated into a Counter-Based scheme when Dth is set to 250. From Figures 10, 11 and 12, we can find that DISCOUNT provides much better performance in RE in comparison with Counter-Based scheme. The detail comparison between Counter-Based scheme and DISCOUNT will be described later.
From the figures above, we can observe that when the networks are dense, it is easy to keep the RE high. When the networks are sparse, we cannot keep a good RE in all situations. Therefore, it is necessary to give a more detailed analysis under a sparse network. As shown in Figure 13, we compare the Counter-Based scheme with DISCOUNT scheme under 7x7 and 9x9 maps. The Dth is set to 225. SRB7x7C denotes the SRB under 7x7 map of Counter-Based scheme, and SRB7x7DC denotes the SRB under 7x7 map of DISCOUNT scheme. In an attempt to get the RE higher than 90%, Counter-Based scheme should adjust Cth to 4 or 5 for 7x7 map and 5 or 6
Figure 10.The performance of DISCOUNT scheme with Cth = 2
Figure 11.The performance of DISCOUNT scheme with Cth = 3
Figure 12.The performance of DISCOUNT scheme with Cth = 4
for 9x9 map respectively. However, when Cth increases to 5, the SRB of Counter-Based scheme is only about 11%. When Cth is 6, the SRB of Counter-Based scheme remains even less than 5%. On the contrary, DISCOUNT scheme can keep at least 90% of RE in both network topologies with Cth equals to 3. It also provides a much better SRB when compared with Counter-Based scheme. The SRB is 30% and 21% when Cth is 3 under 7x7 and 9x9 maps respectively. It is very clear that DISCOUNT outperforms Counter-Based scheme. We can also observe that DISCOUNT is not sensitive to the value of Cth. In Counter-Based scheme, one way to keep a good balance between RE and SRB for different network densities is to adjust
th
C dynamically [4]; however, it is not practical since the network topology is not predictable. DISCOUNT maintains stable performance of RE under fix C .
As shown in Figure 14, we compare the Distance-Based scheme with DISCOUNT scheme under 7x7 and 9x9 maps. The C of DISCOUNT scheme is set to 3.
SRB7x7D denotes the SRB under 7x7 map of Distance-Based scheme, and SRB7x7DC denotes the SRB under 7x7 map of DISCOUNT scheme. In an attempt to get the RE higher than 90%, Distance-Based scheme should adjust D to less than 72 meters for 7x7 map. While under 9x9 map, the RE cannot reach the 90% in all conditions. However, when D is set to less than 72 meters, the SRB of Distance-Based scheme is only about 17%. On the contrary, DISCOUNT scheme can keep at least 90% of RE in both network topologies with D about 225 meters. It also provides about 30% SRB under 7x7 map. It is obvious that DISCOUNT outperforms Distance-Based scheme. Figure 15 declares the reason why DISCOUNT scheme performs better than Distance-Based Scheme. PD denotes the rebroadcasts that caused by pure Distance-Based scheme and PC denotes the rebroadcasts that transmitted by
SRB7x7D denotes the SRB under 7x7 map of Distance-Based scheme, and SRB7x7DC denotes the SRB under 7x7 map of DISCOUNT scheme. In an attempt to get the RE higher than 90%, Distance-Based scheme should adjust D to less than 72 meters for 7x7 map. While under 9x9 map, the RE cannot reach the 90% in all conditions. However, when D is set to less than 72 meters, the SRB of Distance-Based scheme is only about 17%. On the contrary, DISCOUNT scheme can keep at least 90% of RE in both network topologies with D about 225 meters. It also provides about 30% SRB under 7x7 map. It is obvious that DISCOUNT outperforms Distance-Based scheme. Figure 15 declares the reason why DISCOUNT scheme performs better than Distance-Based Scheme. PD denotes the rebroadcasts that caused by pure Distance-Based scheme and PC denotes the rebroadcasts that transmitted by