Consistent Reliable Topology Control Computer Science Essay

Published Date: 02 Nov 2017

CHAPTER 4

4.1 Overview

In stationary ad hoc networks, owing to the limitation of network resources (i.e., bandwidth, sensor energy, and so forth), topology control has been considered as a state-of-the art approach to provision broadcasting with moderate energy costs, low interference, and short end-to-end delay. Moreover, localized versions of topology control algorithms, which avoid the use of central node supervision, have been employed in constructing network topologies with reduced cost, and have thus been tailored for Mobile Ad hoc Networks (MANETs).

The primary latency of mobile networks is attributed to unpredictable topology changes owing to mobility. As a result, topology control algorithms that can only guarantee 1- edge connectivity, such as Local Minimum Spanning Tree (LMST), Relative Neighborhood Graph (RNG), and Local Shortest Path Tree (LSPT), may no longer be applicable in MANETs because the network might be disconnected even when only a single link is broken. Accordingly, more reliable topology control algorithms such as Fault-tolerant Local

Spanning Subgraph (FLSS) and Local Tree-based Reliable Topology (LTRT) are considered for MANETs. They can preserve k-edge connectivity, i.e., network connectivity cannot be lost if the number of broken links are smaller than k, and are referred to as k-edge connected algorithms. The drawback of these algorithms is that the value of k, referred to as the level of redundancy, and is uniformly set for all local graphs regardless of the different moving speeds of nodes. Thus, in order to guarantee network connectivity, they need to use a high value of k to mitigate the case where some nodes move too fast. This might lead to a redundant topology, because some areas in the network may have slow moving nodes and do not need a high value of k.

Hiroki Nishiyama et al [1] introduced dynamic method for k-edge connected algorithms that determines the value of k for each local graph based on local movements while maintaining the required connectivity. Each node periodically broadcasts a �hello� message within its maximum transmission range, which contains information about its position and current moving speed. The �hello� message sending interval is referred to as the topology update interval. Afterward, each node collects information about positions and speeds of its neighboring nodes and builds its own local graph. The node uses a kedge connected algorithm with k-value decided based on the moving speeds of itself and its neighbors.

After applying a topology control algorithm, each node finds its logical neighbors and calculates a new transmission range to cover them. It should be noted that main focus is in topology control, i.e., how to determine the transmission range of each node in order to maintain network connectivity. Although flow control algorithms (which mitigate radio interference), routing techniques (which establish multiple paths), and security technologies have an important role in improving the reliability of mobile ad hoc networks.

In order to find an appropriate value of k corresponding to nodes� moving speeds, the relationship between network connectivity and the value of k is analyzed.

In MANETs, it is important to select an appropriate transmission power for each node, called topology control, to reduce energy consumption and signal interference while still maintaining network connectivity. Most existing topology control protocols use the localized approach. Each node collects 1-hop information through periodic, asynchronous �Hello� messages, which forms its local view. Each node selects a few logical neighbors from its 1-hop neighbors based on its local view.

The collection of logical links (i.e., links between logical neighbors) forms the logical topology. The logical topology is connected as long as the original network is connected under a (long) normal transmission range, and all nodes use consistent local views. Each node then sets its (short) actual transmission range to be the distance to the farthest logical neighbor. The majority of existing localized topology control protocols assumes a static network without mobility. Our recent study on mobility-sensitive topology control showed that these protocols cannot maintain connectivity in MANETs, either because insufficient actual transmission ranges are computed based on outdated location information, or because insufficient logical neighbors are selected due to inconsistent local views.

The problem of outdated location information was solved by slightly increasing the actual transmission range. The problem of view inconsistency is more challenging. Consistent local views are nforced using (loosely) synchronized �Hello� messages. The basic idea is to force all local views to use the same version of �Hello� messages from each node. The major drawback of this (strong) consistency mechanism is the extra overhead. In order to orchestrate �Hello� messages to construct consistent local views, a certain degree of global synchronization is required, which becomes costly in large scale networks.

To erase the above difficulty, in this work, we propose a new mechanism, called weak consistency, to preserve connectivity. In weakly consistent local views, several most-recent �Hello� messages from each node are maintained, and no inter-nodal synchronization is required. The original topology control protocols are enhanced to make the correct decisions based on this (possibly conflicting) history information. This method maintains connectivity via slightly increasing the number at logical neighbors.

In this chapter, we review several popular localized topology control schemes using a general framework, formally define the notion of view consistency, and prove topology connectivity guaranteed by consistent views. We divide localized topology control schemes into two categories: those using only link cost in their decision making (called cost based schemes), and those using node location information and properties of 2-D geometric graphs (called location-based schemes). For each category, we give a formal definition of weak consistency and enhanced topology control schemes that guarantee connectivity. A simple method has been introduced to construct weakly consistent views using multiple �Hello� messages from each node. We prove that two or three recent �Hello� messages are sufficient under normal circumstances.

4.2 Localized Topology Control in MANETs

In a localized topology control protocol, each node advertises its id and location in periodic �Hello� messages. We assume a fixed �Hello� interval; that is, the period between two �Hello� messages from the same node is a constant c. However, due to the inaccuracy of local clocks in individual nodes, �Hello� messages from different nodes are asynchronous. At a given time t, a bidirectional link (u, v) E implies that both nodes u and v have received a �Hello� message from each other during time period . We define the original topology as a dynamic graph G = (V, E), where V is the set of nodes, and E is the set of bidirectional links detected via �Hello� exchanges. We assume the network is sufficiently dense, such that the original topology is always connected.

Each node constructs its local view of its 1-hop neighbors in the original topology, and runs the topology control algorithm to determine its logical neighbor set. Given an original topology G, all topology control algorithms can be viewed as a process of removing links from E to produce a logical topology , where is the set of logical links after link removal. A link (u, v) can be removed only by its end nodes u and v, when a certain link removal condition is satisfied; otherwise, nodes u and v are logical neighbors.

Cost-based link removal

In cost-based link removal conditions, each link is given a cost, which is a function of the geographical distance between nodes u and v.

Fig. 4.1 Cost-based link removal (RNG)

Fig.4.2 Cost-based link removal (LMST)

As shown in fig. 4.1, the relative neighborhood graph (RNG) condition has been used in several topology control protocols. In the local minimal spanning tree (LMST) protocol (fig. 4.2), each node builds an LMST and removes all non-MST links.

Location-based link removal

Location-based conditions use both distance information and direction of each neighbor. As geometrical properties are used to prove the correctness of these protocols, the distance and direction information must be consistent with a node placement scheme in order to preserve connectivity. Fig.4.3 Location-based link removal conditions

Fig. 4.3 Location-based link removal conditions

4.2.1 STRONG VIEW CONSISTENCY

Inconsistent views and network partition

At each moment t, �Hello� messages sent and received during time period forms the local view. In Figure 4.4, three nodes sample their local views at different times (represented by black dots). Note that local times at different nodes (t0, t1, t2 �) are asynchronous.

Fig. 4.4 w�s position at t1 and t2

All nodes use latest �Hello� messages (represented by white dots) to construct their local views. The corresponding local view of node u and v are shown in Figures 4.5 and 4.6.

Fig. 4.5 U�s local view before t2

Fig. 4.6 V�s local view before t2

Fig. 4.7 logical topology at t�

Fig.4.8 using consistent views

Our objective is to maintain connectivity for a given observation period, if an observer collects adjacent logical links of all nodes at different times (with a maximal time difference of d), those logical links form a connected topology. In a routing process, the observer is a data packet and d is the maximal end-to-end delay. During an observation period, local views used by all nodes form a global state of a distributed computation. Due to the lack of globally synchronous clocks, local views in the same cut are sampled at different times. We define the maximal cut width as the maximal difference between sampling times of two local views in the same cut.

In a MANET, any non-zero may cause inconsistent local views. We use RNG condition to illustrate the partition problem caused by inconsistent views. Suppose node w in Figure 4.5 moves upward, and advertises its location twice at time t1 and t2 (local times of w), respectively. When node u applies RNG condition before t2, link is removed because in u�s local view. After t2, node v removes link because in its local view. The corresponding logical topology is disconnected.

Strong view consistency

For a given local view of node u, a sub graph of the original topology can be constructed, where Vu contains u and its 1-hop neighbors under the normal transmission range r, and Eu consisting of links for all v;w 2 Vu with dv;w � r. We define strong view consistency as follows.

Local views in a cut are (strongly) consistent, if for each node u, the same location of u is observed in local views of all u�s neighbors. When local views in a cut are strongly consistent, the corresponding logical topology is connected. As shown in Figure 4.8, when both u and v get w�s location from the older �Hello� message sent at t1 (marked by the dashed circle), only link will be removed and the logical topology is connected. The proof of the following theorem is omitted due to lack of space.

Fig.4.9. Time-space view of the example in Figure 4.5. Short vertical bars mark transmission times of �Hello� messages at each node. Dashed arrows illustrate the first round of �Hello� exchanges among neighbors.

Applying a link removal condition based consistent local views preserves connectivity. In Figure 4.9, local views of u and v are inconsistent because the cut �crosses� one of w�s �Hello� messages. Local views sampled before this �Hello� message contain the former location of w, while local views sampled after this message contain the latter location of w.

4.3 Consistent Reliable Topology Control (CRTC) For Mobility Impact in MANET

WEAK VIEW CONSISTENCY

Several methods were discussed, which avoid a cut crossing a �Hello� message, to maintain strong view consistency. However, all these methods require a certain degree of global synchronization, which may cause performance penalty in large scale networks. We propose to maintain weak consistency for making conservative decisions based on totally asynchronous local views. In this section, we give a systematic scheme for making �conservative� decisions in topology control, i.e., slightly increasing the number of logical neighbors, and prove that this method preserves logical topology connectivity.

Weak consistency in cost-based algorithms

When enforcing weak consistency among local views, each local view contains k recent �Hello� messages of each neighbor. The value of k depends on the �Hello� interval and maximal cut width.

Fig. 4.10 constructing weakly consistent local views

Figure 4.10 shows an example where the local view of each node contains 2 recent �Hello� messages sent by itself and each 1-hop neighbor. We propose enhanced link removal conditions that exploit this history information to preserve connectivity. For clarity, this subsection discusses only cost-based conditions. Location-based conditions will be discussed in the next subsection.

When applying cost-based conditions, the cost of each link is computed from locations of nodes u and v. With multiple locations of each node stored in different �Hello� messages, several costs will be computed for each link. Let Ce be the set of costs of link e in the local view of a given node. We use cMax e to denote the maximal cost and cMin e the minimal cost in Ce. Then we enhance the original link removal conditions as follows.

Consider the case when the enhanced RNG is applied to the MANET in Figure 4.5. Each node builds its local view based on two recent �Hello� messages of each node, as shown in Figure 4.10. The final logical topology consisting of link (u, v) and (u, w) is connected. Let cMinMax e be the minimal cMax e and cMaxMin e be the maximal cMin e in local views of all nodes, the following definition gives a sufficient condition for preserving logical topology connectivity in the above enhanced cost-based link removal conditions.

Local views of the original topology G = (V, E) are weakly consistent with respect to enhanced cost based link removal conditions.

Note that strongly consistent local views are always weakly consistent. Applying enhanced cost-based link removal conditions based on weakly consistent local views preserves connectivity.

Let ER be the set of removed links and the logical topology is disconnected. Since all previously removed links have larger maximal minimal costs than cMaxMin u;v , no link of P has been removed yet. Therefore, nodes u and v are still connected via path P, which contradicts the assumption that removing (u, v) causes partition.

If the difference between sampling times of any two local views is bounded, and all nodes use a fixed �Hello� interval, then the number of �Hello� messages from each node that is needed to build weakly consistent local views with respect to cost-based link removal conditions is k.

Let t be the starting time of a cut; that is, the first local view is sampled at time t. For any link (u, v), cMinMax u,v � cMaxMin u,v is guaranteed if a common cu;v exists in all local views containing this link, which, in turn, is guaranteed if a common location of u and a common location of v appears in all these local views. When all nodes collect k recent versions of �Hello� messages, all �Hello� messages issued within time period will be used to build local views of neighboring nodes. If the length of this time period is no less than cut, every node will have at least one �Hello� message received by all neighboring nodes, which carries the common location to build weakly consistent local views.

Fig. 4.11 Consistent Reliable Topology Control (CRTC) For Mobility Impact In MANET

Fig. 4.11 shows Consistent Reliable Topology Control (CRTC) For Mobility Impact in MANET. We consider two view updating strategies. When using the instantaneous updating strategy, each node updates its local view (and hence recomputes its set of logical neighbors) whenever it receives a new �Hello� message. In this case, the maximal cut width. When using the periodical updating strategy, each node updates its local view once per �Hello� interval. The following corollary holds, assuming reliable �Hello� message delivery. In practical networks, �Hello� messages may be lost due to collision and mobility. In this case, storing more �Hello� messages from each sender can enhance the probability of building weakly consistent local views.

The weak consistency definition for cost-based conditions is not sufficient for location-based scheme, because both link distance and relative node direction are involved in selecting logical neighbors. As each node may have multiple locations in each local view, multiple distances may be computed for each link, and multiple directions for each neighbor in each local view. Again, in each local view, we define the maximal (minimal) distance between nodes u and v, and the maximal (minimal) relative direction of a neighbor u. Using these notations, we enhance location-based link removal conditions to preserve connectivity, and provide the corresponding definition of weak consistency.

Local views of the original topology G = (V;E) are weakly consistent with respect to enhanced location-based link removal conditions if for each u 2 V , at least one common location of u appears in local views of all u�s neighbors. Compared with the cost-based definition, the above location-based definition of weak consistency requires exact locations of neighboring nodes. This is because location-based link removal conditions depend on properties of geometric graphs in a 2-D plane, especially those regarding to angles and edge lengths in a triangle. The previously used maximal/ minimal concepts are insufficient to ensure connectivity in these conditions. The following theorem uses a stronger definition of connected original topology: if we construct a virtual network by arbitrarily selecting a location for each node, which is one of the multiple locations advertised within a cut period, the resultant network is always connected. This is a reasonable assumption in a dense network with a relatively small. The proof is omitted due to the lack of space.

Applying enhanced location-based link removal conditions based on weakly consistent local views preserves connectivity. Obviously, it also applies to location-based topology control schemes. That is, weak consistency is guaranteed when two or three recent �Hello� messages in local view construction.

4.4 Performance Evaluation of Consistent View Reliable Topology Control (CRTC) for Mobility Impact MANET

In this section, we evaluate the performance of our proposed Consistent View Reliable Topology Control (CRTC) for Mobility Impact MANET. In order to compare the performance of CRTC and we take existing topology control methods such as DLTRT [1] and FLSS [2]. The performance evaluation is conducted by using Network Simulator 2 (NS-2).

4.4.1 Simulation setup

100 to 1000 nodes are randomly placed in an 1100 m � 1000 m area. The normal transmission range is 210m, which yields an average node degree of 17 without topology control. The mobility pattern is generated based on the random waypoint model with zero pause time and the average moving speed varying from 1 to 75 m/s. Note that the typical moving speed in a MANET ranges from 5m/s (walking) to 35m/s (driving). This study uses a much wider speed range to emulate the situation in dense networks that use a much short transmission ranges. For example, when the transmission range is 50m, the impact of a speed of 15m/s is equivalent to that of 75m/s in a MANET with a transmission range of 210m/s. In order to isolate the effects of mobility from other factors, all simulations use an ideal MAC layer without collision and contention. Each simulation lasts 90s and is repeated 10 times. All data are sampled 5 times per second and 500 times per simulation.

In our implementations of baseline protocols, each node advertises its location via asynchronous �Hello� messages. Although MAC layer collision is not simulated, the �Hello� interval of each node is randomly selected to avoid the collision in the real world. �Hello� messages are transmitted with the normal transmission power. Each node selects its logical neighbors based on the complete 1-hop information. In all protocols, each node updates its logical neighbor set whenever it sends a �Hello� message, and adjusts its transmission power to the minimal power that reaches the farthest logical neighbor. The logical neighbor set is attached in the header of every outgoing packet. The receiver will drop the packet if it is not in the sender�s logical neighbor set. Unidirectional links are neither removed nor converted into bidirectional edges.

Two connectivity models can be defined in MANETs: strict connectivity and weak connectivity. A MANET is strictly connected if its snapshot (i.e., the effective topology at a particular time) taken at every moment is connected. However, in a MANET with mobile nodes, it is difficult to capture network topology under a snapshot (although we can do so in simulations via assuming an omniscient �god�). Weak connectivity, which is application dependant, is more appropriate. In this model, the connectivity is defined in terms of capability of completing a connectivity-related task, such as global flooding, measured in terms of the percentage of nodes that receive the message. Note that a weakly connected network may not be strictly connected under a particular snapshot (or even any snapshot). However, the network is not connected under any snapshot. Note that weak connectivity is exploited only in special routing schemes such as Infostation variations and epidemic routing, where end-to-end delay is traded for eventual delivery. In a flooding that completes in a small (< 0.01s) time period, weak connectivity is a rather accurate approximation of the strict connectivity.

The baseline protocols and different enhancements are compared in terms of the following metrics.

4.2 Results and discussions

Table 4.1 Weak Consistent links

Node Density Weak Consistent links

Proposed CRTC DLTRT FLSS

100 8 21 25

200 14 33 36

300 17 36 49

400 21 43 58

500 23 46 63

600 25 56 67

700 26 61 74

The above table describes the weak consistent links obtained when node density increases in the MANET environment. The outcome of the proposed CRTC in MANET is compared with an existing Fault-tolerant Local Spanning Subgraph (FLSS) [2] and Dynamic Local Tree-based Reliable Topology (DLTRT) [1].

Fig. 4.12 Weak Consistent links

Fig. 4.12 describes the number of weak consistent neighbor links occurred when node density increases in the Mobile Ad-hoc network. Number of weak consistent links in the proposed CRTC method is low since we use consistent reliable topology model. If node density becomes high, then the weak consistent links also becomes high. Compared to an existing Fault-tolerant Local Spanning Subgraph (FLSS) [2] and Dynamic Local Tree-based Reliable Topology (DLTRT) [1] for weak consistent neighbor links, the proposed CRTC method outperforms approximately 31-42% well in MANET.

Information Location Latency

Information Location Latency is a measure of time taken to arrive the location information in the precise definition of which depends on the system and the time being measured. It is measured in terms of milliseconds (ms).

Table 4.2: No. of nodes vs. Location Information latency

Node Mobility (m/s) Location Information Latency (ms)

Proposed CRTC DLTRT FLSS

5 32 45 53

10 46 58 78

15 51 63 92

20 58 72 112

25 61 81 125

30 63 86 131

35 65 94 148

The above table 4.2 describes the location information latency needed for selection of a correct set of logical neighbors in local views. The location information latency by the proposed CRTC in MANET is compared with the previous works DLTRT and FLSS.

Fig. 4.13 No. of nodes vs. Location Information latency

Fig. 4.13 describes the location information latency needed for selection of a correct set of logical neighbors in local views in MANET. The mobility rate of nodes varies from 5 to 35. Compared to the previous works DLTRT and FLSS, the proposed CRTC method consumes approximately 40 -45 % less time taken to locate the information.

Average Node degree

One common goal of topology control protocols is to reduce the network density, which can be represented by the average node degree. Here we consider only the number of logical neighbors, except in the third enhancement, where physical neighbors also count.

Table 4.3: Average Node degree

Node Mobility (m/s) Average node degree

Proposed CRTC DLTRT FLSS

5 1 2 2

10 2 3 4

15 3 5 5

20 4 6 8

25 5 8 8

30 6 10 11

35 7 12 14

The above table 4.3 describes the average node degree obtained when node mobility increases in the MANET environment. The outcome of the proposed CRTC in MANET is compared with an existing Fault-tolerant Local Spanning Subgraph (FLSS) [2] and Dynamic Local Tree-based Reliable Topology (DLTRT) [1].

Fig. 4.14 Average Node degree

Node degree is another important metric to evaluate the performance of topology control algorithms. The higher the node degree is, the higher the collision will be. Node degree also reflects the redundancy of topologies. Therefore, all topology control algorithms attempt to achieve a small average node degree. The result of our proposal in terms of node degree is shown in Fig. 4.14. The figure demonstrates that the proposed CRTC method is as good as the result of the existing DLTRT and FLSS in terms of the average node degree. It is even more preferable because unlike the result, the average node degree gradually increases when the node mobility increases. When the node mobility increases, from 15m/s to 35m/s, the node degree of our proposal CRTC is slightly lower than the result of DLTRT and FLSS. The trade-off here is shown clearly because we also achieve a lower connectivity ratio when the node mobility is high in this range.

Connectivity ratio

The ratio of connected node pairs to the total number of node pairs. We compute the connectivity ratio as the average delivery ratio of broadcast packets originated from random sources.

Table 4.4 Connectivity ratio

Node Mobility (m/s) Connectivity Ratio (%)

Proposed CRTC DLTRT FLSS

5 98.2 94.19 91.05

10 97.65 93.94 87.96

15 96.78 92.3 84.46

20 96.12 86.93 82.24

25 95.45 89.04 82.56

30 95.06 87.74 79.82

35 94.91 82.96 70.74

Fig. 4.15 Connectivity ratio

Fig. 4.15 illustrates the performance of the proposed method in terms of the connectivity ratio. It satisfies the requirement of maintaining the connectivity ratio of at least 82%. When the node mobility is smaller than 20m/s, the connectivity ratio of CRTC is almost the same as that of the DLTRT which uses the same value of k for all local graphs. This is because when the average moving speed is small, the difference between nodes in terms of moving speeds is not large, and thus, the chosen value of k in every local graph in the proposed method may be the same. However, when the moving speed is higher, the connectivity ratios of the expected results obtained by the DLTRT, FLSS and the proposed method CRTC are different. When the average moving speed is varied from 20m/s to 25m/s, they can be considered comparable in the whole range. When the moving speed is higher, from 25m/s to 35m/s, the connectivity ratio of our proposal is slightly lower than the expected result, but is still higher than 85%.

4.5 Summary

This work introduces a new mechanism called weak consistency that preserves connectivity in localized topology control protocols, where each node makes independent decisions based on its local view to select a small set of logical neighbors and adjust its transmission range accordingly. Compared to previous view consistency mechanisms in [1], constructing weakly consistent local views require no global synchronization and has very low overhead. We also show that a wide range of existing topology control protocols can be enhanced to make conservative decisions based on asynchronous �Hello� messages, and prove that, using the information carried by two or three recent �Hello� messages from each node, these conservative decisions guarantee a connected logical topology in most scenarios.