Shortest Path Evaluation in Wireless Network Using Fuzzy Logic
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Abstract
Evaluation of the shortest path in a wireless network is to ensure the fast and guaranteed delivery of the data over the established wireless network. Most of the wireless protocols are using a shortest path evaluation technique which is based on the random weights assigned to the network nodes. This alone may not be sufficient to get the accurate shortest path for routing process. Most of the shortest path evaluation algorithms perform the blind search to find the shortest routes for routing, this eventually increase the complexity of the whole process itself. This article puts some light on facts of using real time estimated routing delay from source node to other nodes by broadcasting a “knock” message. And this delay is being used to evaluate the shortest path for routing using fuzzy logic. This process is enhanced with its improved inference engine model and furnished fuzzy crisp patterns to deploy the shortest routing path in real time wireless nodes.
Keywords
Fuzzy logic Shortest path Crisp values Inference engine Wireless network1 Introduction
In today’s world the communication is a significant component of each individual’s life. The wireless communication is a faster medium of transmission of instructions or data between two devices, which are not plugged with any electrical conductor, wires or cables without any delay and loss rates.
To generate feasible and fastest route between two nodes in wireless networks shortest paths are playing a vital role. Many shortest path evaluation algorithms are existed like Dijkstra’s Algorithm, Genetic Algorithm, Bellman–Ford Algorithm and Floyd–Warshall Algorithm.
Dijkstra’s Algorithm
In 1956, Edsger W. Dijkstra’s formulate an algorithm to determine the shortest paths amongst nodes in a weighted graph. By his name this algorithm is called as Dijkstra’s Algorithm and there are many variants of this algorithm is existed. The most wellknown variants make a tree like structure of the shortest path from the origin or starting vertex to all other points in the weighted graph. This algorithm is applicable for directed and undirected graph.
There are some rules for applying this algorithm to determine the shortest path like graph should be connected and all edges must have nonnegative weights. This algorithm is also used to acquire the shortest path between single node and single destination node and algorithm terminates on determination of the destination node.
In the above figure let be a weighted graph G = (V, E), where V is vertices set and W is the set of edges.

Value: δ (1, 6) = 6

Path: {1, 2, 5, 6}
The original Dijkstra’s Algorithm is modified to obtain the solutions of different real time problem like the telephone network, geographical map, networking etc.
The major limitation of Dijkstra’s Algorithm is that this performs the blind search over the given graph, so this increases its complexity. And is incapable of handling the negative edges in the graph so most often it cannot yield desired shortest path.
Bellman–Ford Algorithm
Bellman–Ford [1] is classical shortest path algorithm focusing on the single source path problem. Algorithmic complexity can be evaluated as O (n*m) with n as the number of nodes and m as available paths. And it is strongly polynomial in comparative to Dijkstra’s negative weights are being acknowledged [2]. As such graph in Bellman–Ford might contain cycles of negative weights from start to destination. Algorithm consists of several iterations where in every phase edge values are being minimized. Total n − 1 phases are being required to find the shortest path.
Negative edges do occur in real time modeling, which is the demerit of Dijkstra’s Algorithm Bellman–Ford Algorithm overcomes this problem. Negative edges in the graph are oftenly useless, but depict network data flow and implement the correct network design. These negative edges create negative weight cycles, reducing the distance and commonly start point of the network becomes a cyclic point.
The fuzzy logic is extremely useful in the field of artificial intelligence and expert system. It is utilized in the field of an advance trading system that is outlined to respond to evolving markets. It investigates a huge number of securities in real time and to exhibit the vendor the best available opportunity. Fuzzy logic is utilized to depict how information is handled inside human brains. Extra advantages of fuzzy logic incorporate its simplicity and its adaptability.

Fuzzyfication Module

Knowledge Base

Inference Engine

Defuzzification module
Here it converts the fuzzy sets obtained from the inference engine model into crisp classified values.
Bhuiyan and Wang [3] introduce RSP in WSN to preserve reliable shortest path to overcome loss of data and number of retransmission attempts. The research considers that link disconnections in WSN are stochastic and free. Introduces an algorithm named LRPR (local routing path reliability) to ease link failures over shortest path. LRPR algorithm finds the routing path between sensors to prevent shortest path reliable. This technique is much better than traditional H2H and E2E recovery techniques. It shows that this method is more energy effective and the success rate is maintained over 90% in comparison with traditional techniques.
Khan et al. [4] presents a modified version of Floyd–Warshall’s Algorithm to find the shortest path routing in WSN. Research use Turbo C to run Floyd–Warshall’s Algorithm and modified version of Floyd–Warshall’s Algorithm to compare the output matrix of both the algorithm. Modifications done in Floyd–Marshall’s Algorithm by showing the differences in path lengths in between nodes. Modified algorithm is based on handshaking mode and it is helpful in finding all shortest path available amongst node at a time.
Magzhan and Jani [5], presents an evaluation of Genetic Algorithm, Floyd–Warshall Algorithm, Dijkstra’s Algorithm and Bellman–Ford Algorithm to resolve shortest path problem. The evaluation and explanations of the algorithms in graphical form and a final review is accomplished for each algorithm.
CotaRuiz and RivasPerea [6] proposed a recursive algorithm to evaluate the distance amongst sensors in multihop WSN. The proposed algorithm usage the recursive functions and distance matrix to evaluate and find all possible routes between sensors with least count of hops. Author also compares their proposed algorithm with alternative classical approaches and results reveal that their algorithm is much better than other algorithms in finding distance estimates. There proposed technique is easily implemented in different fields like web mapping, Least Squares (LS), artificial intelligence, transportation etc.
Gubichev et al. [7] presents algorithms which are fast and precise for shortest paths approximation by introducing a scalable sketchbased index structure that not only evaluates the distance between nodes, but also calculate the comparable shortest path. Implementation of the algorithm is done with RDF3X graph database system. And conducted many experiments on several data sets to evaluate performance and the quality of their approaches and prove that their algorithm speed up query response time by maintaining the estimation error between 0 and 1%.
Johnson [8] presents an algorithm which takes no extra time than Dijkstra, Ford to recognize the negative cycle to solve shortest path problems. They introduce an “arc set partition” algorithms for mono source criteria on non negative networks.
Jiang et al. [9] introduced an enhanced form of Dijkstra’s Algorithm. Proposed approach had taken both node and edge weights to derive a graph from SDN. The system uses pyretic for implementing an enhanced form of Dijkstra’s Algorithm and perform comparisons on both original and extended Dijkstra’s Algorithm. The comparison results display that the extended Dijkstra’s Algorithm performed better than original one.
Gla et al. [10] present a comparison of 12 shortest path solving algorithm and their performance evaluation. The paper also indicates the importance of appropriate choice of method to solve the shortest path problem that would be the most efficient for a type of the graph structure to be used.
Ying et al. [11] proposed a new scheduling/routing algorithm that combines shortest path routing and backpressure algorithm. The system uses simulations to show the improved performance using the new algorithm. The results indicate that the proposed algorithm’s end to end routing delay become effective as the routes were selected according to traffic load on the network and thus long route is selected only when required in comparison to backpressure algorithms.
Mali and Gautam [12] narrate a technique of enhanced two phase commit protocol, which is the best solution for loosely coupled network protocols. Author performs indepth analysis of AODV and DSR protocols for end to end delay and deploys the two phase commit protocols to achieve best results. This will explore the new possibilities of the deploying the shortest path in two phase commit protocol to have over performed results of the routing process in the future.
The rest of the paper is organized as follows. Section 2 presents the design of our approach. The details of the results and some discussions we have conducted on this approach are presented in Sect. 3 as Results and Discussions. Section 4 provide hints of some extension of our approach as future scope and its conclusion.
2 Proposed Model
Proposed methodology of shortest path evaluation using fuzzy logic can be elaborated with the below mentioned steps.
Step 1: This is the initial step of our system where source node “S” contacts the pool manager for all the remaining receivers. As intact to this pool manager revert back with all the remaining node details to the source Node “S”. After having a list of receivers source node “S” selects one of the receiver as destination node “D” and asks the pool manager to provide the shortest path.
Now pool manager sends “knock” message to all the nodes except the destination node “D “. And then waits for their reply, as the pool manager receives the reply it keep recording the time delay of all the nodes for the evaluation process of shortest path to send it back to Source node “S”.
Step 2: Fuzzyfication This is the step where all the receiver’s response time is taken to convert into crisp values. And often these crisp values are called as Fuzzy Crisp values. Here in this process a distance is evaluated in between the minimum and maximum response time. And then this distance is divided into 5 signals as denoted in the following equation.

VERY LOW

LOW

MEDIUM

HIGH

VERY HIGH
Step 5: Defuzzification Here in this step our system transforms the values of the reasoning clusters into the shortest path. Here evaluation of the shortest path is based on the number of the set hops in the wireless scenario.
For this process system starts were estimated the shortest path from the very lowest range of the fuzzy crisp value and moving towards the very highest peak to get the shortest path nodes for the mentioned hops.
3 Results and Discussions
3.1 Experimental Setup
Proposed model conducted experiments on a computer running Windows 7 operating system with an Intel i54200U 1.6 GHz CPU and 6 GB RAM with the stable working state. The proposed system is developed with Java technology using Netbeans 6.9.1 as IDE and MySQL server 5.5 as database.
3.2 Complexity Performance Evaluation
Comparative time in milliseconds
No of nodes  Dijkstra  Bellman–Ford  Fuzzy logic 

10  2  5  4 
20  2  10  6 
30  6  35  7 
40  8  48  12 
50  8  52  14 
60  15  75  14 
70  21  110  19 
80  24  150  21 
90  28  200  22 
100  31  280  24 
On plotting the graph for the data of Table 1, some facts are revealed based on the time complexity of the system. According to the [13] Bellman–Ford’s time complexity can be stated as O (27n^{2}). Whereas time complexity of the Dijkstra Algorithm can be stated as O (2n^{2}) [13].
And finally proposed model uses only two iterations, one for the fuzzy inference engine and another for IF then Rules of fuzzy logic. By using these iterations only systems achieve proper shortest path for the given hop count. So the time complexity of our model can be stated as O (n^{2}).
3.3 Network Life Time of Nodes Based on Sink Location
To complete this task of measuring network’s lifetime of a node in different sink node locations we measure the time when the first node finishes its performance. As we earlier stated that our system is being implemented in the real time physical scenario. So it has higher tendency to live in the network than that of the system which are incorporated into the simulation environment.
For this purpose our proposed methodology is merged with improved two phase commit protocol of our past edition mentioned in [12]. Two phase commit protocols are well known for their recursive knocking and checking the availability of the destined node along with the network superior links.
For this experiment our system uses the physical nodes, which are actually computers of 20 numbers. Each of them has a minimum configuration of Core i3 Intel processor with 4 GB of RAM. And system uses DLinks double antenna, Wireless router.
On initiating the process of data routing our system keep the nodes alive for a longer time due to Recursiveness of the two phase commit protocol. The system is also powered with the network socket handling threads which are engaging the specific ports till the job is accomplished.
Network life time comparison Time
Node sink location  NonCs  HybridCs  MSTP  WCDA  CWCDA  FS_TPC 

0  25  400  450  500  2300  3142 
5  35  400  480  550  2500  3500 
10  50  400  500  600  2700  3500 
15  50  400  600  650  2800  3654 
20  50  400  650  700  2900  3659 
4 Conclusion and Future Scope
In this paper a novel idea to evaluate the shortest path in wireless networks based on the real time reply delay to the pool manager is introduced efficiently. The most important factor of the system is that proposed model identifies the shortest path based on the user defined hop count that actually provides the control of the routing in the hands of the user or we can say to the source node “S”.
Here the system is also indicated its better performance over the Bellman–Ford Algorithm and exceeds the result of Dijkstra’s Algorithm. This indicates the system is having high potential in real time, shortest path evaluation scenario.
Along with this system also measure the performance of the node for network life time after the first node sends the data on initiation of the process. Due to real time deployment with the recursive multithreading socket programming system yields more life time than that of [14].
This type of system efficiently can be incorporated in the energy constraint wireless network to take the proper decision of routing. This can be achieved on the basis of available energy levels of the other nodes of the network to save the energy.
Notes
References
 1.Goldberg, A. V., & Radzik, T. (1993). A heuristic improvement of the Bellman–Ford algorithm. Applied Mathematics Letters, 6(3), 3–6.MathSciNetCrossRefzbMATHGoogle Scholar
 2.Magzhan, K., & Jani, H. M. (2013). A review and evaluations of shortest path algorithms. International Journal of Scientific & Technology Research, 2(6), 99–104.Google Scholar
 3.Bhuiyan, M. D. Z. A., & Wang, G. (2014). Reliable shortest paths in wireless sensor networks: Refocusing on link failure scenarios from applications. In IEEE. https://doi.org/10.1109/prdc.2014.
 4.Khan, P., Konar, G., & Chakraborty, N. (2014). Modification of Floyd–Warshall’s algorithm for shortest path routing in wireless sensor networks. In Annual India, IEEE conference. ISBN 9781479953646/14.Google Scholar
 5.Magzhan, K., & Jani, H. M. (2013). A review and evaluations of shortest path algorithms. International Journal of Scientific and Technology Research. ISSN 22778616.Google Scholar
 6.CotaRuiz, J., & RivasPerea, P. (2016). A recursive shortest path routing algorithm with application for wireless sensor network localization. IEEE Sensors Journal, 16, 4631–4637.CrossRefGoogle Scholar
 7.Gubichev, A., Bedathur, S., & Seufert, S., & Weikum, G. (2010). Fast and accurate estimation of shortest paths in large graphs. ACM 9781450300995/10/10.Google Scholar
 8.Johnson, D. B. (1977). Efficient algorithms for shortest path in sparse networks. Journal of the Association for Computer Machinery, 24(1), 1–13.MathSciNetCrossRefzbMATHGoogle Scholar
 9.Jiang, J.R., Huang, H.W., Liao, J.H., & Chen, S.Y. (2014). Extending Dijikstra’s shortest path algorithm for software defined networking. APNOMS.Google Scholar
 10.Gla, M., Musznicki, M., Nowak, P., & Zwierzykowski, P. (2013). Efficiency evaluation of shortest path algorithms. ISBN 9781612082790, IARIA.Google Scholar
 11.Ying, L., Shakkottai, S., Reddy, A., & Liu, S. (2010). On combining shortestpath and backpressure routing over multihop wireless networks. IEEE/ACM TRANSACTIONS ON NETWORKING, 10636692.Google Scholar
 12.Mali, G. U., & Gautam, D. K. (2017). A model application of two phase commit protocol in wireless DTN. International Journal of Computer Applications, 162(5), 23–28.CrossRefGoogle Scholar
 13.Thippeswamy, K., Hanumanthappa, J., & Manjaiah, D. H. (2010). A study on contrast and comparison between Bellman–Ford algorithm and Dijkstra’s Algorithms. Research gate, publication/209423960Google Scholar
 14.AbbasiDaresari, S., & Abouei, J. (2015). Toward clusterbased weighted compressive data aggregation in wireless sensor networks. Ad Hoc Networks, Elsevier B. V.Google Scholar