This paper involved the computation of quickest paths with the help of servicelevel agreement (SLA) and energy constraints. The consideration of these constraints helps to propose a novel system model which computes the path to strengthen the continuity and criticality of the data transmission. The proposed riskenergy aware SLA provisioning (RESP) system model incorporates the research gaps of the existing risk assessment models in the literature without any increase in time complexity. The formulation of RESP shows the usefulness in the critical applications. The results show that the computation of riskprovisioned path gives the SLA satisfied paths and has a great impact of variations in the data traffic. The performance of the proposed algorithm has been indicated in terms of different performance parameters such as mean
Due to the advancements in the technology of the computer networks, the applications associated with network have been provided by the service providers. These applications have a great impact on the life of human beings [
With evolution of network services, quickest path problem (QPP) was proposed by the authors in [
The network is associated with certain uncertainties which may lead to service failure, and to deal with these failures, reliability theory has been used in [
Recently, QoS routing has been provided by considering the amount of energy used for the data transmission services by considering parameters like reliability, risk, and availability. [
Here, in this paper, the authors have made an attempt to provision the riskfree path computation model with consideration of SLA and energy constraints. The main contributions of this paper are presented as follows: (i) A novel system model has been presented with the riskprovisioned mechanism which is the upgraded version of the existing REQPP risk assessment system model in the existing literature. (ii) The contribution can also be seen with the reference to SLA violation factor. The proposed system model gives the full SLA satisfaction as compared to the existing REQPP system model.
The rest of the paper is organized into sections. Section
To explain the QPP model, let us consider the directed loopless graph
Let us assume that
To transmit
Hence, the minimum transmission time is given as
The quickest path problem (QPP) is formulated as
In the beginning, when QPP was conceptualized [
To deal with energy, various authors tried to incorporate them in QPP. Let us assume that each link is allied with energy rate
To compete with successful data transmission, the following has to be proved:
For data transmission without any disruption, find minimum link capacity used for transmission of
In the given network, each link follows the following equation for the path capacity path
The residual energy of path
Hence, constrained QPP has been formulated by using above equations as
The abovediscussed model has been proposed by several authors [
The availability of sufficient amount of energy is not only the factor for the continuity in data transmission. The link reliabilities are also helpful for the continuity of data transmission [
Recently, the authors in [
The proposed system model for the RESP required some assumptions for better understanding and they are given as follows:
There are no parallel and duplicate links in the network graph [
Capacities of links are generated randomly with the uniform distribution and are statistically independent [
Bifurcation of data is not allowed, and also, flow of conservation is followed by data transmission [
Let us take the performance reliability which constitutes the link reliability
Let us assume that link reliability is ideal, i.e.,
The link performance factor constitutes the servicelevel agreements (SLAs) and link delays; therefore, along a path, the performance factor is calculated as
Equation (10) is known as the performance reliability due to delay
In equation (
Here, in this paper, the authors have tried to incorporate the research gaps of the existing risk assessment REQPP model proposed in [
A path
The minimum SLA aware link capacity is shown as follows:
To incorporate both parameters (energy and SLA) for sorting, the minimum link capacity has been given as follows:
The remaining value of performance reliability is termed as residualrequested performance reliability.
The SLAenergy awareness allows us to combine the characteristics of the both models (energy and SLA) and formulate the constraint model of the riskenergy aware SLA provisioning (RESP) given as follows:
By following this, Algorithm
(i)
(ii)
For
Set
Solve
If No
go to STEP 3
else
Let
end
end
For
go to STEP 4
else
set
end
Find index
}
The time complexity of the proposed RESP algorithm is
The complexity of RESP is explained using the time complexity of
The experiment for the performance evaluation of the proposed RESP algorithm has been performed over the personal computer having the configuration of Intel(R) Core^{TM}i5–7400, CPU@ 3.00 GHz, 8 GB RAM, and Windows 10 operating system. All simulations have been performed in MATLAB R2010a environment platform. The simulations show that the proposed RESP algorithm is solvable in polynomial time using Dijkstra’s algorithm which used binary heap data structure. The illustrations of results have been explained with the help of standard network topologies as shown in Figure
(a) 24node USdirected mesh network with
The associated values of link parameters like delay and capacities are taken from the uniform distribution range [1, 1000]. As discussed in the previous sections, the amount of fixed powers at each node and amount of energy rate at each link is given by
The quantitative performance analysis of the proposed algorithm has been shown in Tables
Number of
Sr. no.  Traffic  


Hop counts of shortest 
Capacity of shortest 
Energy efficiency of shortest 












 
1  13  10  4  7  8  8  12  20  12  1.0933 MJ  0.2727  0.1968 
2  8  9  6  8  10  8  7  25  29  0.2539 MJ  0.2846  0.2339 
3  9  10  11  7  6  6  25  38  69  0.3633 MJ  0.4422  0.3351 
4  5  8  5  7  7  6  12  16  29  0.1174  0.2571  0.4326 
5  5  12  10  7  8  7  7  11  48  0.1455  0.1021  0.3536 
6  10  9  4  7  7  6  12  38  27  0.2531  0.7795  0.5594 
7  11  7  6  7  7  7  3  12  19  0.00375  0.4081  0.1346 
8  13  8  10  7  7  7  2  33  45  0.0557  0.4670  0.5593 
9  7  6  10  7  7  7  29  15  35  0.5187  0.1670  0.8984 
10  9  9  8  7  8  8  4  49  30  0.0915  0.4998  0.6006 
Mean  9  8.8  7.4  7.1  7.5  7  11.3  25.7  34.3  0.289615  0.36801  0.43043 
Number of
Sr. no.  Traffic  


Hop counts of shortest 
Capacity of shortest 
Energy efficiency of shortest 












 
1  6  6  4  3  4  4  9  37  47  0.1264  0.9527  1.1781 
2  7  3  2  3  3  4  15  22  16  0.3360  2.6999  0.3110 
3  3  7  3  4  4  4  19  35  22  1.3800  2.1949  0.5721 
4  5  3  5  4  3  4  24  23  39  0.3952  0.2289  0.4877 
5  3  5  5  5  4  3  7  19  24  0.2209  0.6922  0.4690 
6  6  6  6  4  3  4  16  27  27  0.3795  0.3887  0.9240 
7  2  6  3  3  3  4  7  14  34  0.1651  0.7255  0.8131 
8  5  3  2  5  3  4  10  15  18  0.7991  0.2552  0.8775 
9  6  3  4  4  5  4  14  19  27  1.1382  0.9686  0.3725 
10  9  6  2  4  4  3  53  33  28  0.9906  0.2891  0.5150 
Mean  5.2  4.8  3.6  3.9  3.6  3.8  17.4  24.4  28.2  0.5931  0.93957  0.652 
The results for the standard topology as shown in Figure
The trend in the adopted capacity of path is increased as the data traffic increases as shown in the eighth, ninth, and tenth columns of Table
The experiment conducted for the Figure
The variation of data traffic has high impact on the energy efficiency (
The illustrative results show that the proposed RESP algorithm is outperforming over the REQPP algorithm [
This paper has proposed the concept of riskenergy aware SLA provisioning (RESP) for the planning of critical routing where continuity of data transmission is given utmost priority. Continuity of transmission in this paper has been quantified in terms of performance of the link in a data transmission path considered as energy required for the link connectivity. The link delay has also been considered for the risk provisioning. The result shows an improvement in energy efficiency and capacity of path. The proposed RESP algorithm is able to compute the paths without any risk in terms of SLA. Present work is considering only energy of the link in path computation. In future work, the proposed algorithm can be extended with incorporating the security paradigms which enable the computation of paths in presence of any malicious activities.
No data have been used separately for the presentation of the work. Each and every detail of the results has been included already in the Results section.
The authors declare that they have no conflicts of interest.
The authors are thankful for the financial grant for this paper from the research project titled “Reliability Modeling and Optimized Planning of RiskBased Resilient Networks” sponsored by IndoPolish Program under grant DST/INT/POL/P04/2014.