Wireless Personal Communications

, Volume 100, Issue 4, pp 1393–1404 | Cite as

Shortest Path Evaluation in Wireless Network Using Fuzzy Logic

  • G. U. Mali
  • D. K. Gautam


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.


Fuzzy logic Shortest path Crisp values Inference engine Wireless network 

1 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 well-known 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.

The weighted function of the graph is w: E → R mapping edges to real valued weights. If e = (u, v), we write w (u, v) for w (e). The distance amongst u to v, is denoted by δ (u, v), it is a minimum length path if there is a path from u to v; and is ∞ otherwise.
  • 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 algorithm works overvaluing length of the path from the start vertex to all other vertices. Iteratively finds estimations by continuously finding smaller paths. This process guarantee finalized results are better (Fig. 1).
Fig. 1

Dijkstra’s Algorithm

In initial step weighted graph has been selected for processing. Then choose a starting vertex and assign path values to all vertices. Visit every edge and relax path distance if found accurate. Five times traversing is being done to find worst case and readjustments have been applying on network as shown in Fig. 2 and then finally negative path lengths are being checked. Complete procedure of Bellman–Ford is depicted using Figs. 3 and 4.
Fig. 2

Negative edges in network

Fig. 3

Select weighted graph

Fig. 4

Choosing a start vertex and assign infinity path

As the Bellman–Ford Algorithm is calculating the shortest path by analyzing all the edges in the network that include negative edges also, this eventually increase its time complexity than that of Dijkstra’s Algorithm (Fig. 5).
Fig. 5

Working Patten of fuzzy logic

The Fuzzy Logic concept was initially presented by Dr. Lotfi Zadeh in the 1960s. It is intended to manage of issues in an indistinguishable path from human do, by apperceiving real (truth) values of variables might be any real number between 0 and 1. In fuzzy logic the real (truth) values are the values in middle of true (1) and false (0) rather than binary logic. Software applications predicated on the perception of fuzzy logic permit computers to mimic human reasoning more proximately, so that decision can be made with incomplete or skeptical data (Fig. 6).
Fig. 6

Overview of the proposed model

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.

This paper explores the possibilities of using fuzzy logic to classify the shortest path for routing in wireless networks. Basically fuzzy logic contains mainly four parts.
  • Fuzzyfication Module

This step transforms the input of the system into fuzzy sets, which are obtained from the difference division of the lowest and the highest input values to yield 5 set members like VERY LOW, LOW, MEDIUM, HIGH and VERY HIGH.
  • Knowledge Base

This Step stored the protocols set by the expert system which are generally known as IF–THEN rules, which can be learned or decided by the designer.
  • Inference Engine

Here IF–THEN rules are evaluated based on the input provided to the system and creates classified fuzzy sets.
  • 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.

Cota-Ruiz and Rivas-Perea [6] proposed a recursive algorithm to evaluate the distance amongst sensors in multi-hop 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 sketch-based index structure that not only evaluates the distance between nodes, but also calculate the comparable shortest path. Implementation of the algorithm is done with RDF-3X 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 back-pressure 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 back-pressure 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 in-depth 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.

$$f\left( x \right) = \frac{{\left| {Max - Min} \right|}}{5}$$
where f(x) is fuzzyfication function, Which contains value like

  • LOW


  • HIGH


Step 3: Knowledge base Here in this step a knowledge base is stored provided by our system which decides the boundaries of the fuzzy crisp values. The boundaries are provided based on below mentioned Algorithm 1.
Step 4: Inference Engine Here based on the knowledge base and the IF-THEN rules an inference engine is created for the accumulated response delay, which eventually yields the intelligence to our system based on the below Algorithm 2.

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 i5-4200U 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

The proposed model of shortest path evaluation using fuzzy logic in a wireless network is tested for its performance based on the time for the given number of the nodes. And also the recorded results are columned with that of Dijkstra’s and Bellman–Ford Algorithm as mentioned in [13]. The obtained results are shown in Table 1.
Table 1

Comparative time in milliseconds

No of nodes



Fuzzy logic









































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 (27n2). Whereas time complexity of the Dijkstra Algorithm can be stated as O (2n2) [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 (n2).

So it can be clearly seen from Fig. 7 that our system of shortest path evaluation using fuzzy logic yields better results in terms of time complexity than that of a Bellman–Ford Algorithm and Dijkstra Algorithm.
Fig. 7

Comparative analysis graph

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 D-Links 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.

This characteristic of the system guarantees the data delivery in bad network phases irrespective of the location constraint within the range of the network. The system also measures the time based on the different locations of the nodes and compared this with many other methodologies as mentioned in [14]. The gathered information is tabled in Table 2.
Table 2

Network life time comparison Time

Node sink location










































The Fig. 8 shows that our methodology FS_TPC, that is “Fuzzy shortest path along with the two phase commit protocol” yields the maximum network lifetime. This is due to the physical implementation of the routing protocol using recursive multi-threaded environment.
Fig. 8

Comparison of network life time

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 multi-threading 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.



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electronics Engineering and TechnologyNorth Maharashtra UniversityJalgaonIndia

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