Analysis of Multi-hop Assignment Function

In the merger study a successful merger in LHA is deemed to have been achieved when the broadcast message sent by a border node detects the merger, so the performance in the merger depends mainly on the successful delivery of this message to all nodes with, of course, low mer- ger latency and low message redundancy. Thus, the performance metrics here are the success rate of the merger, the merger latency and the redundancy measured by the number of messages sent by a node for successful merger.

What follows is a special scenario to serve the analysis of the multi-hop assigning function utilized by the LHA and Buddy protocols. Then follow the main ns2 simulation setup and sce- narios used to evaluate the LHA protocol with all selected protocols during the assignment func- tion. Finally comes a description of the evaluation scenarios for the merger function in the LHA protocol.

4.1 Analysis of Multi-hop Assignment Function

Because LHA and Buddy are the only ones of the evaluated protocols to utilize a search func- tion with the task of finding free addresses in other nodes located further than one hop away from the new node, it is important to compare the performance of the two mechanisms used by those protocols. As the search in two-hop neighbors is not sufficient as a performance metric for the protocols, a special scenario is defined in which a single node owns a number of free ad- dresses and other nodes obtain their addresses over different hops. This scenario is implemented in the way that there are 10 stable nodes as shown in Figure 4-1. In the scenario nodes 2, 3, 4, 5 and 6 will be activated one by one every 3 seconds and get their addresses from node 0 over hops 2, 3, 4, 5 and 6 respectively, while nodes 7, 8 and 9 are set with no available free addresses to show the signaling impact of such nodes on the middle and end of the assignment path. The transmission range shown in a dotted line is set to 230 m for each node. DSDV is used as a rout- ing protocol, while IEEE 802.11 is applied as a MAC protocol. Most results discussed here and in the following sections are shown as boxplots [85]. This type of depiction has been chosen be- cause boxplots are more robust than classical statistics based on normal distribution, in that box- plot does not disguise the presence of outliers in the results. The method is that for each data set, a box is drawn from the first quartile to the third quartile, and the median is marked with a thick line. Additional whiskers extend from the top and bottom edges of the box towards the minimum and maximum of the data set. Data points outside the range of the box and whiskers are consid- ered outliers and drawn separately. There is, additionally, a depiction of the mean value which is depicted in the form of a small filled square.

4.1 Analysis of Multi-hop Assignment Function

Figure 4-1: Address assignment of multi-hop Scenario

4.1.1 Assignment latency:

Figure 4-2 shows the boxplot of the latency resulting from multi-hop assignments when the number of hops varies from 2 to 6 hops; LHA and Buddy results are side by side. The scenario is repeated 10 times and each point in the figure represents the result of one of the10 trials.

Figure 4-2: Latency impact of multi-hop assignment scenario

As the plot shows, the time required to assign an address for a new node in both protocols in- creases as the number of hops increases. This is normal for multi-hop assignment. However, with LHA the time required by a new node is less than the time required by Buddy: the median as- signment latency employing LHA varies between 0.14 and 0.3 sec. while it varies between 0.45 and 1.86 sec. employing Buddy. The reason for this is that Buddy algorithm needs a predefined timeout (200ms as defined in the present work) to finish the search in each hop until it reaches

500 1000 1500 A ss ignm ent lat enc y ( m sec ) 2 3 4 5 6 2 3 4 5 6 LHA Buddy # of Hops

4.1 Analysis of Multi-hop Assignment Function

the last hop, which includes a node that may have a free address, it performs subsequent search processes which in turn increase the whole searching time dramatically. This is not the case in LHA because it searches for the hop which may provide a free address by means of one search process; therefore, it uses two kinds of timeouts, a big timeout (Tm-search) used by the requester like the one used in each attempt in Buddy, and a small one (Tm-ws timeout) used by every re- sponding node. To avoid unnecessary responses in LHA, Tm-ws is stopped upon receipt of reply messages. Because this is a special scenario with special definition (one node owns all addresses)

a node with no free addresses selects1 _{its timeout between 25 and 50 msec., while a node with}

free ones selects the timeout randomly between 0 and 25 msec. In the figure we can see that the assignment latency from hop 3 and 4 in LHA has some outliers (in some attempts, slightly lengthening the latency). This is because node 9 and 8 may try to forward the request massage if they have not overheard the reply messages sent by nodes 3 and 4 respectively.

4.1.2 Signaling Overhead:

Figure 4-3 shows the overhead resulting from multi-hop assignment when the number of hops varies between 2 and 6 hops; LHA and Buddy side by side.

Figure 4-3: Signaling overhead of multi-hop assignment scenario

In the figure the red box (i.e. the average number of messages) shows that the average number of messages sent by each node required to join a new node deploying LHA is very low, stable and independent of the number of hops in the network (between 2 to 2.5 messages per node). On the other side, the average number of messages sent per node when Buddy is used increases sig-

1 _{Random selection from the range considering the number of neighbors (high priorities for bigger number)}

2 3 4 5 6 7 8 M es sages per nod e 2 3 4 5 6 2 3 4 5 6 LHA Buddy # of Hops