Duplication of Identities

A 0

B A

a-bit b-bit

B A

0 ≠ 0

a – b

2^a– 1 +

(2^a– 1) ∙2^b ID space (2^a-b – 1) ∙2^b 2^a– 2^b

Duplication of ID a > b,A≠0 Leak of ID: 1

2^nd 1^st

Figure 4-4 Identities duplication of backward assignment on two segments.

However, if the length of the first segment is longer than any other’s, the identities du-plication will occurs, which is not allowed. An example of identities dudu-plication for two segments is shown as Figure 4-4. Similar to the example of Figure 4-3, there are two types of identities, (0. A) and (A. B). Since the length of the first segment is longer then the second one’s, the identities with the first a-bit zero code and next (b-a)-bit non-zero code will be generated twice. But such duplication would not be permitted for the most network environment, so the first segment’s length must not exceed the others’.

In order to avoid duplication of identities, we would configure the length of the first segment shortest while executing the backward assignment. Furthermore, we ob-serve that the backward assignment indeed decreases the effect of identities leaking sig-nificantly while the number of partitioned segments increases from the mathematical derivation and simulation results.

4.2.3 Quantitative Analysis

Figure 4-5 Identities leaking of backward assignment.

The following equation calculates the number of leaking identities when there are k par-titions, where n_i represents the length of segment i.

(

)

Figure 4-5 shows the effect of identities leaking on the different number of seg-ments for a 16-bit long identity. This figure indicates the worst, average and best cases of identity leaking among the entire HPID formats and assumes the length of each ment is at least 2-bit long. We observe that in the best cases for each number of seg-ments there will be some HPID formats that make the number of leaking identities pretty low. In other aspect, the worst case happens when there are two segments and the number of leaking identities is 16381 which is 30% of the identity space. Comparing to 80% to the forward assignment, the backward assignment really reduces the effect of the problem about leak of identity.

4.3 Summary

If there are just two partitioned segments of the HPID format, the forward assignment is

a perfect solution. If the number of segments is three, the performance of both forward and backward assignment is about the same. But if the number of partitioned segments is more than three, the backward assignment would perform better than the other one generally.

However, in the most situations the slight leak of identity is acceptable since the number of identity space usually exceeds the number needed. This is also the reason why we adopt the backward assignment for the simulation and analysis latter. Besides, we still have to notice the problem of identities duplication from the backward assign-ment and completely avoid the duplication happening.

Chapter 5

Simulation and Analysis

Figure 5-1 An example of network topology for simulation.

The HPID mechanism integrates the different PID mechanisms and combines the fea-tures of them. Next, we would give an example for the simulation environment and de-scribe the process of our mechanism. We generate 100 nodes randomly in a 100×100 (square unit) area. The signal range of each node is 20 (unit), thus the node would have 10 neighbors in average. The network topology is shown as Figure 5-1 and the root node is marked as a square.

Figure 5-2 The tree structure via the HPID mechanism.

According to the above network topology, we would use 8-bit long identities to identity all the nodes. The HPID format is configured like that the first 4 bits are pro-duced via the Prime DHCP scheme while the last 4 bits are via the ZigBee mechanism (nwkMaxRouters = 2, nwkMaxChildren = 2, nwkMaxDepth = 9). The tree structure of the network is shown as Figure 5-2 after allocating all the identities of nodes via the backward HPID assignment mechanism with modification. All the nodes could get an identity eventually and the average failure probability to obtain an identity of each node is 0% which is better than the other two mechanisms. Furthermore, the failure probability also effects the identities utilization of the network directly.

100 nodes

Figure 5-3 The failure probability on different identity lengths.

However, if the failure probability is high on certain length of identity, we may try to increase the length to improve the failure probability. In order to analysis the im-provement of the different mechanisms, we simulate the Prime DHCP scheme and the ZigBee mechanism to compare with ours the failure probability of 100 nodes on differ-ent iddiffer-entity lengths. In this simulation, the network environmdiffer-ent is the same as the above one except the root node which is set in the center of the network area. As the Figure 5-3 shows, the failure probability of each node goes down while the length of identity increasing. When the length is 8-bit long, our mechanism could make all the nodes have their unique identities and the failure probability is almost 0%.

On the contrary, the Prime DHCP scheme does the job awfully and the failure

probability is still high while the length is up to 12-bit long. While the ZigBee mecha-nism needs to increase the length to 11-bit long to make the failure probability drop to 0%. From the results we could observe that for the other two mechanisms the increasing of the length cannot reduce the failure probability efficiently. It also means that these two mechanisms cannot use the identity space efficiently even though raising the iden-tity length. Unfortunately, the increasing of the length is not desirable in some environ-ments and the sensor network is just a critical example. Because to increase the length not only adds the data size but also make the overhead higher while computing the iden-tities to find the routing path. The problems induced by the increased length also con-sume more power to the sensor devices.

By the way, when the length is 7-bit long, our mechanism is a little worse than the ZigBee mechanism. This is because the length of the partitioned segment is too short and the problem of leak of identities will appear more significant corresponsively.

Next, we will compare our mechanism with the other two related mechanisms to analysis the failure probability to the number of nodes and identity length. The simula-tion environment is as follows. In a 100×100 (square unit) area, we will generate differ-ent number of nodes randomly and set the signal range dynamically to make each node have 10 neighbors in average. The root node is also set in the center of the network area and the length of the identity is configured different number of bits.

ID-length = 9 bits

Figure 5-4 Failure probability on various number of nodes (ID length = 9 bits)

ID-length = 10 bits

Figure 5-5 Failure probability on various number of nodes (ID length = 10 bits)

ID-length = 16 bits

Figure 5-6 Failure probability on various number of nodes (ID length = 16 bits)

Figure 5-4 , Figure 5-5 and Figure 5-6 illustrate the failure probability on the in-creasing number of nodes in 9-bit , 10-bit and 16-bit long identities respectively. In

Figure 5-4 we observe that the failure probability of the Prime DHCP scheme rises badly, and this curve is induced by the skew tree structure which is not applicable in the most network topologies. Although the curve of ZigBee mechanism seems better than the Prime DHCP scheme, it still increases obviously since the low flexibility of topol-ogy induced by the network restrictions. While our mechanism combines the benefits of different mechanisms and does the best job. In a saturated condition where the number of nodes is up to 500, we can also bound the failure probability under 40%. The simula-tion in Figure 5-5 also tells us the similar results mensimula-tioned above. In Figure 5-6, when there are 1000 nodes acquiring for identities among the 65536 identities, the other two mechanisms perform poorly, while our mechanism could still use the identity space ef-ficiently and the failure probability is less than 6%. From the above results, our mecha-nism indeed decreases the failure probability of each node and also improves the identi-ties utilization.

The HPID mechanism 0

0.1 0.2 0.3 0.4 0.5 0.6

50 150 250 350 450

550 650 750 850 950

Number of nodes

Failure Prob.

10-bit 11-bit 12-bit 16-bit

Figure 5-7 Failure probability on various identity lengths for HPID mechanism.

The Prime DHCP saheme

Figure 5-8 Failure probability on various identity lengths for Prime scheme.

The ZigBee mechanism

Figure 5-9 Failure probability on various identity lengths for ZigBee mechanism.

Performance of HPID mechanism on the different lengths is shown as Figure 5-7.

As the length of identity increasing, the failure probability is improved significantly. But Prime DHCP scheme and ZigBee mechanism could only enhance the failure probability lightly as shown in Figure 5-8 and Figure 5-9. Besides, the performance of out mecha-nism is also outstanding and these simulation results prove again that out mechamecha-nism could use the identity space more efficiently.

Chapter 6

Conclusions and Future Works

We have proposed a hybrid path-aware identity assignment mechanism to integrate the different path-aware identity assignment mechanisms. Our mechanism not only com-bines the benefits of the others but also improve the identities utilization significantly.

Besides, we also propose a hybrid routing mechanism to perform the routing procedure with the HPIDs. Therefore, the routing path could be figured out by computing to the HPIDs directly and no extensive routing table is needed anymore. Our mechanism could not only enhance the performance of routing but also omit the additional messages for table maintenance. Although our hybrid mechanism may increase some computations of devices, the messages omitted could save more power, however. Nowadays the power saving is a very important issue to many network environments. Furthermore, the simu-lation results also reveal that our mechanism could decrease the failure probability for a node to obtain a unique HPID, which will improve the identities utilization directly.

Therefore, we could shorten the length of identities due to the high utilization and the data and computing overhead are both decreased which are also helpful for power sav-ing.

However, there are several types of identities produced by our mechanism accord-ing to the number of partitions of the HPID format. We have provided the forward and backward assignment mechanisms and also discussed their features. Besides, the policy to assign the different types’ identities can be arranged for the network requirements and features. For example, if a network is composed of the backbone nodes and non-backbone nodes, we can select two PID mechanisms for the HPID format base on the features of the two kinds of nodes respectively. Then the nodes of each kind obtain

their identities of the different types. In other words, the HPID assignment policy could be adjusted dynamically through the different requirements. Therefore, each network can have its personalized and applicable HPID assignment mechanism and the identities utilization can be enhanced even more.

There are still many research issues of the proposed mechanism. For example, we would try to figure out the relationships between the HPID format and network features.

Provide a method for the selection of PID mechanisms to achieve optimal identities utilization. Besides, we would also try to make our mechanism more robust for fault tolerance and mobility support. If some nodes are broken, the tree structure can heal by itself. If some nodes move, the routing procedure can be operated as usual.

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