**5. Evaluation approach and implementation**

We will present an evaluation of the base station planning algorithm according to the following evaluation criteria:

• Fault-tolerance: this shows the algorithm's ability to generate a network configuration that satisfies the fault-tolerance coverage requirements.

#### **Algorithm 2** Pseudo code of the graph consolidation step

	- (a) *v* → *v* �

16 Will-be-set-by-IN-TECH

parameters (*X*,*Y*, *Z*)*BS*. This is because the objective function contains the radio coverage model which includes the geometry of the model. Several algorithms exist for solving this type of problem (pattern search, genetic algorithm, simulated annealing). We have selected pattern search, because it has a proven convergence and supports any type of constraints [33].

For k-connectivity testing in a graph with *n* vertices, we use existing algorithms from the graph theory [9]. The complexity of this algorithm is *<sup>O</sup>*(*<sup>k</sup>* <sup>∗</sup> *<sup>n</sup>*3), under the condition that

In this step, the algorithm finds sub-graphs satisfying the connectivity requirements and transforms each subgraph into a single vertex. The formal specification of the graph consolidation step is described by pseudo code in algorithm 2 which is explained in the following list. Figure 7 shows an example of the operation of the graph consolidation step.

1. Given a graph *G*, identify all biconnected components *Gc* containing at least 3 vertices and store them in a set *BC*. For finding biconnected components, existing graph theory

2. Identify the *special articulation points* which are articulation points shared between the biconnected components in the set *BC*. An articulation point is a vertex whose removal disconnects a graph. On figure 7B) vertices 1, 2 and 3 are articulation points. Vertex 1 is a special articulation point, since it is shared between two biconnected components of size of at least 3. For identifying biconnected components and articulation points existing graph

3. Every vertex which is either a special articulation point or other vertex, not belonging to a biconnected component in BC, is directly transformed into a vertex in the consolidated

(a) If it contains special articulation points, then they are removed from the component. (b) All vertices from the component are transformed into a single vertex in the

(c) The consolidated vertex inherits all edges of the original vertices to other vertices in the graph. Other vertices are vertices not belonging to the same biconnected component.

We will present an evaluation of the base station planning algorithm according to the

• Fault-tolerance: this shows the algorithm's ability to generate a network configuration that

graph. The consolidated vertex inherits all edges of the original vertex.

(d) Duplicated edges in the consolidated graph are removed.

**4.5. Connectivity testing**

**4.6. Graph consolidation**

algorithms are used.

algorithms are used [9].

consolidated graph.

following evaluation criteria:

4. For every biconnected component in the set *BC*:

**5. Evaluation approach and implementation**

satisfies the fault-tolerance coverage requirements.

*<sup>k</sup>* <sup>&</sup>lt; <sup>√</sup>*<sup>n</sup>* which is true in our case.


$$\text{(a)}\quad G\_{\text{\textquotedblleft}c} = G\_{\text{\textquotedblleft}c} - V\_{\text{sup}}$$

�


**Figure 7.** Example of the graph consolidation step



**Table 1.** Evaluation parameters

We performed a model-based evaluation of the algorithm. We generated different inputs to the algorithm, then executed the algorithm and observed the evaluation criteria. As an input of the algorithm, we used a service area with various sizes; typical for a production environment (see table 1 for the parameter values). The service locations comprise of the entire floor. The candidate sites comprise of the entire ceiling. We also varied the attenuation of the propagation environment. For the radio connectivity model, we used the log-normal shadowing propagation model [36] which is used for radio coverage assessment. The path loss exponent has been fixed in these experiments. The shadowing factor *X<sup>σ</sup>* models the inhomogeneity of the propagation environment and it has been varied in these experiments. The other parameters of the propagation model are fixed. To determine the connectivity, we used our threshold-based link state model. The base station planning algorithm has been implemented in Matlab (about 600 lines of code). The algorithm has been tested on all the combinations of input parameters (area size and shadowing deviation) which make a total of 36 executions. At the end of each algorithm execution, we performed a requirements test. We tested whether the radio coverage and the connectivity were in normal (redundant) state.

<sup>0</sup> <sup>20</sup> <sup>40</sup> <sup>60</sup> <sup>80</sup> <sup>100</sup> <sup>120</sup> <sup>140</sup> <sup>160</sup> <sup>180</sup> <sup>200</sup> <sup>0</sup>

Achieving Fault-Tolerant Network Topology in Wireless Mesh Networks 221

Area size X [meters]

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>0</sup>

Number of iterations performed by the algorithm

90% of the base stations were selected at the first algorithm iteration. This means that 90% were selected according to the global optimization function and were optimally placed. The remaining 10% of the base stations were selected during the subsequent algorithm iterations in order to ensure the biconnectivity of the backbone. Figure 10 shows the result after the first iteration for area size 150/150m and shadowing deviation 7. In the middle of the graph (around coordinates 65/44), a base station exists, whose removal would disconnect the network. In the next iteration the algorithm corrected this by inserting one base station in

For the total 36 executions, the algorithm needed about 25 minutes to complete on a laptop with a dual core 2.5GHz processor and 3GB operating memory. This means that the average running time was 42 seconds. As a comparison, a related work algorithm in [39] needed 22

**Figure 9.** Algorithm termination: 80% of all algorithm executions terminated after 2 iterations. The

**Figure 8.** Example fault-tolerant (biconnected) topology produced by the algorithm

algorithm needed a maximum of 4 iterations to complete.

proximity of the first one (see figure 11).

Cumulative algorithm termination [%]

Area size Y [meters]

### **5.1. Results for fault-tolerance**

With all the inputs, the algorithm has generated a network topology in which the radio coverage and the connectivity were in the normal (redundant) state, as defined in section 3. An example graph of the network topology, generated by the algorithm for area size 200/200m and shadowing deviation 8 is shown on figure 8. The related work algorithms [2, 39] generated topologies which are not fault-tolerant. Their topologies optimized the network throughput, but the backbone network war not biconnected (see figure 3 in [2], and figure 4 in [39]). Figure 8 clearly shows the effect of the shadowing (inhomogeneous environment) on the base station planning. Because of the shadowing, some links are shorter than others and in some areas, more base stations are needed to provide coverage.

#### **5.2. Results for termination, minimality and running time**

Figure 9 shows the measured termination property of the algorithm within the performed evaluation. The figure shows the cumulative termination, i.e. the percentage of the algorithm executions that have terminated *up to* some number of iterations. 30% of the algorithm executions generated a correct fault-tolerant solution directly after the first iteration. This means that in these cases, the graph consolidation step was not performed at all. These were the cases when the area sizes were smaller (50/50m and 100/100m). 80% of the algorithm executions generated a correct fault-tolerant topology after the second iteration. This means that only two optimizations and one graph consolidation were needed. The algorithm needed a maximum four iterations to complete all the inputs.

**Figure 8.** Example fault-tolerant (biconnected) topology produced by the algorithm

18 Will-be-set-by-IN-TECH

Parameter Values

Area size (X/Y) [meters] (50/50),(100/100),...,(300/300)

Transmit power *Ptx* [dBm] 20 Required receive power *Pmin* [dBm] -78 Path loss exponent 3

Shadowing deviation *σ* [dB] 5,6,7,8,9,10

We performed a model-based evaluation of the algorithm. We generated different inputs to the algorithm, then executed the algorithm and observed the evaluation criteria. As an input of the algorithm, we used a service area with various sizes; typical for a production environment (see table 1 for the parameter values). The service locations comprise of the entire floor. The candidate sites comprise of the entire ceiling. We also varied the attenuation of the propagation environment. For the radio connectivity model, we used the log-normal shadowing propagation model [36] which is used for radio coverage assessment. The path loss exponent has been fixed in these experiments. The shadowing factor *X<sup>σ</sup>* models the inhomogeneity of the propagation environment and it has been varied in these experiments. The other parameters of the propagation model are fixed. To determine the connectivity, we used our threshold-based link state model. The base station planning algorithm has been implemented in Matlab (about 600 lines of code). The algorithm has been tested on all the combinations of input parameters (area size and shadowing deviation) which make a total of 36 executions. At the end of each algorithm execution, we performed a requirements test. We tested whether the radio coverage and the connectivity were in normal (redundant) state.

With all the inputs, the algorithm has generated a network topology in which the radio coverage and the connectivity were in the normal (redundant) state, as defined in section 3. An example graph of the network topology, generated by the algorithm for area size 200/200m and shadowing deviation 8 is shown on figure 8. The related work algorithms [2, 39] generated topologies which are not fault-tolerant. Their topologies optimized the network throughput, but the backbone network war not biconnected (see figure 3 in [2], and figure 4 in [39]). Figure 8 clearly shows the effect of the shadowing (inhomogeneous environment) on the base station planning. Because of the shadowing, some links are shorter

Figure 9 shows the measured termination property of the algorithm within the performed evaluation. The figure shows the cumulative termination, i.e. the percentage of the algorithm executions that have terminated *up to* some number of iterations. 30% of the algorithm executions generated a correct fault-tolerant solution directly after the first iteration. This means that in these cases, the graph consolidation step was not performed at all. These were the cases when the area sizes were smaller (50/50m and 100/100m). 80% of the algorithm executions generated a correct fault-tolerant topology after the second iteration. This means that only two optimizations and one graph consolidation were needed. The algorithm needed

than others and in some areas, more base stations are needed to provide coverage.

**5.2. Results for termination, minimality and running time**

a maximum four iterations to complete all the inputs.

**Table 1.** Evaluation parameters

**5.1. Results for fault-tolerance**

**Figure 9.** Algorithm termination: 80% of all algorithm executions terminated after 2 iterations. The algorithm needed a maximum of 4 iterations to complete.

90% of the base stations were selected at the first algorithm iteration. This means that 90% were selected according to the global optimization function and were optimally placed. The remaining 10% of the base stations were selected during the subsequent algorithm iterations in order to ensure the biconnectivity of the backbone. Figure 10 shows the result after the first iteration for area size 150/150m and shadowing deviation 7. In the middle of the graph (around coordinates 65/44), a base station exists, whose removal would disconnect the network. In the next iteration the algorithm corrected this by inserting one base station in proximity of the first one (see figure 11).

For the total 36 executions, the algorithm needed about 25 minutes to complete on a laptop with a dual core 2.5GHz processor and 3GB operating memory. This means that the average running time was 42 seconds. As a comparison, a related work algorithm in [39] needed 22

reconfigurable redundancy of the services. As the radio propagation environment changes,

Achieving Fault-Tolerant Network Topology in Wireless Mesh Networks 223

When the environmental dynamics is detected, the system recovery adds base stations to the network for restoring the redundancy of the services. But firstly, it has to be decided what the minimum number of base stations would be (and respectively their positions) which will restore the redundancy. For this purpose, we developed a new base station planning algorithm which takes the required decision and proposes reconfiguration instructions. Since the underlying optimization problem is NP complete, our algorithm is a trade-off between minimum base stations and minimum running time. The operating staff performs the

In future work the presented concept will be integrated in a system for dependable end-to-end communication in wireless mesh networks. This system will incorporate other ongoing research works within our working group [30, 31] developing concepts for end-to-end quality of service guarantees (throughput, packet loss, latency) in Wireless Mesh Networks. Another aspect of our future work is to integrate the developed concepts in components for industrial

This work has been partially funded by the European Commission within the EU-project

The project flexWARE (Flexible Wireless Automation in Real-Time Environments) develops a communication system for factory-wide wireless real-time control [12, 13, 38]. The methods, presented in this chapter, are used in flexWARE to achieve availability of the wireless medium

*Institut of Distributed Systems, Otto von Guericke University of Magdeburg, Universitätsplatz 2,*

[2] Amaldi, E., Capone, A., Cesana, M., Filippini, I. & Malucelli, F. [2008]. Optimization models and methods for planning wireless mesh networks, *Elsevier Journal on Computer*

[3] Avizienis, A., Laprie, J.-C., Randell, B. & Landwehr, C. [2004]. Basic Concepts and Taxonomy of Dependable and Secure Computing, *IEEE TRANSACTIONS ON*

[4] Avresky, D. & Natchev, N. [2005]. Dynamic reconfiguration in computer clusters with irregular topologies in the presence of multiple node and link failures, *IEEE Transactions*

network reconfiguration which restores the redundancy of the services.

wireless communication in cooperation with german product manufacturers.

by radio coverage monitoring and prediction and network engineering.

*rt-solutions.de GmbH, Oberländer Ufer 190a, D-50968 Cologne, Germany*

[1] *Ad-Hoc Wireless Distribution System* [n.d.]. http://awds.berlios.de/.

*DEPENDABLE AND SECURE COMPUTING* 1: 11–33.

our method changes the redundancy of services.

**Acknowledgement**

**Author details**

*39106 Magdeburg, Germany*

*Networks* 52(11): 2159–2171.

*on Computers* 54(5): 603–615.

Svilen Ivanov

Edgar Nett

**7. References**

flexWARE, grant number 224359.

**Figure 10.** Example network topology after the first algorithm iteration

**Figure 11.** Example network topology after the second algorithm iteration. Only one additional base station results in a biconnected topology.

hours for a 58-node scenario because of the intractability of the approach. This means that for the purpose of the system recovery, our algorithm has an acceptable running time.

#### **6. Conclusion**

In this chapter, we developed a new approach for guaranteeing the availability of the services radio coverage and connectivity of Wireless Mesh Networks in dynamic propagation environments. Our approach is to apply fault-tolerance for avoiding service failures in the presence of environmental dynamics. Differing from the existing methods, we use reconfigurable redundancy of the services. As the radio propagation environment changes, our method changes the redundancy of services.

When the environmental dynamics is detected, the system recovery adds base stations to the network for restoring the redundancy of the services. But firstly, it has to be decided what the minimum number of base stations would be (and respectively their positions) which will restore the redundancy. For this purpose, we developed a new base station planning algorithm which takes the required decision and proposes reconfiguration instructions. Since the underlying optimization problem is NP complete, our algorithm is a trade-off between minimum base stations and minimum running time. The operating staff performs the network reconfiguration which restores the redundancy of the services.

In future work the presented concept will be integrated in a system for dependable end-to-end communication in wireless mesh networks. This system will incorporate other ongoing research works within our working group [30, 31] developing concepts for end-to-end quality of service guarantees (throughput, packet loss, latency) in Wireless Mesh Networks. Another aspect of our future work is to integrate the developed concepts in components for industrial wireless communication in cooperation with german product manufacturers.
