Service level agreement and energy cooperative cyber physical system for quickest healthcare services

Abstract

In this paper, typical application of Cyber Physical System (CPS) has been highlighted for the critical-healthcare data transmission services. Sensors of CPS are providing patient’s health information via a communication network to a medical practitioner at some distant place. Needs of development of dependable routing protocol for such type of applications in healthcare are increased day-by-day. This paper proposes a quickest, critical and energy efficient routing for the CPS based healthcare system. Simulations performed to convey the appropriateness of the quality of data transmission system according to the well-defined Service Level Agreement (SLA) formulation. Proposed energy and SLA cooperation in data transmission is beneficial for the tele-operated medical service. A medical practitioner is able to monitor a patient in real-time with the help of proposed dependable and energy efficient data transmission. The results shows that CPS with consideration of different constraints such as energy and SLAs have a severe effect on its performance parameters such as mean number of QSS s-t paths, average hop counts and average energy efficiency. In addition to this comparison with existing algorithms shows the improvement in consideration with all performance components.

Keywords

Quickest services critical-healthcare services green energy service level agreement cyber physical system

1 Introduction

In recent years, cyber physical system (CPS) has revolutionized the E-healthcare technology to the new heights of advancement [1]. Presently, the E-healthcare technology is competent to fulfill the user’s expectations in the tele-operated mode of healthcare services [3]. All this has happened with the evolution of cyber physical system (CPS) where physical entities are controlled, commanded and managed by a cyber-based intelligent element [1]. Now a day, due to versatility of CPS, it is being used in several critical service applications [4] like E-healthcare, E-business, E-shopping, E-banking etc. Shown as in Fig. 1, all these applications are relying over both physical architecture as well as cyber architecture. Both the architectures are equally important for the design and development of CPS. The physical architecture is more vulnerable toward the failure of CPS because physical architecture deals with the uncertainties happened in the world. Simultaneously, these uncertainties in the physical system draw an impact on the performance of cyber system also. Therefore, the consideration of these uncertainties has a important role for the working and the high performance of CPS [5]. In CPS, the numerous applications got integrated into the healthcare services; therefore, awareness in the implementation of CPS in healthcare technologies has received attention by the several researchers. There are a lot of medical sensors used for monitoring the healthcare which are supervised by the intelligent cyber system [1, 2]. The medical sensors placed on the patient body and corresponding health data managed by the intelligent computational component of CPS. Use of the CPS provides a prescription along with the monitoring of a patient’s health at a remote location by the experts which are far apart from patient [3]. The block diagram of the healthcare CPS presents the general idea of the working of existing model. An E-healthcare CPS is generally a combination of a cyber system of network and physical system of sensors, medical equipment that provides the monitoring data to the doctor.

Fig.1

General E-healthcare cyber physical system.

The diagram of E-healthcare cyber physical system shows that doctor monitors the health of a patient over the cyber space. Here, the health data from the equipment is transmitted through the cyber space to the experts at a remote location. The cyber space consist a network and intelligent computational components [4]. The success of whole working of CPS relies mostly on the intelligent component because every intelligent decision and computations are performed on it. Lots of researchers are associated to strengthen the traditional approaches with the help of CPS based computations [5]. Recently, it has been found that consumption of energy is a major issue for the computational components in the CPS and it is highly recommended to design the highly energy efficient cyber system [6]. In addition, the consideration of energy has been emphasized due to the bar of environmentalist on the energy resources, it is highly recommended to consume the energy resources wisely. Therefore, research in the CPS leads to the green computations [7, 8].

However, sometime the working of CPS is found for the critical services, while we are considering the case of critical healthcare where it can be the matter of loss of life. At this time, the critical healthcare services are required to be provided to the patient with in the requested service time. The requested service time is the time for which a patient can survive. Moreover, the requested service time to the patient also relies on the mean time to failure (MTTF) of the services. Here, the services are used to transmit the health data between two ends i.e. doctor or patient [7 , 10]. The parameters discussed in the above paragraph needs to be firm and this firmness has been provided with the agreement between service providers and users known as service level agreements (SLAs). Here, in the case of critical healthcare cyber physical system, the SLAs drawn in between doctor and patient in terms of requested service time and mean time to failure of service. These SLAs are the promise toward the satisfaction of services and provide the quality of experience (QoE) [11]. For the best explanation, a huge literature is available to support the proposed system model and concepts.

CPS was introduced for the very first time in 2006 by [12] in the NSF workshop where it has been studied that how the physical process with computations are integrated together. The authors show its potential toward the numerous applications such as high confidence medical services, medical devices, telemedicine, smart infrastructure, smart driving etc. However, due to the developing phase of CPS, design challenges have been discussed by the authors in [13] as this technology requires the system safety and reliability qualitatively which was different from the general purpose computing architecture. This paper shows the level of abstractions to rebuild the key components of the CPS. Over the years, the authors in [14] have shown that the researchers from both eminence research fields pioneered the powerful methods and tools to deal with CPS. In physical certain developments have been made CPS more enrich using advances in state space analysis, time and frequency domain analysis, tracking, optimization, filtering etc. Also, in parallel the researchers have been also involved in the development of the technology in computational components such as design of new programming, biomedical sensors, computer system reliability, fault tolerance, cyber security etc.

The functioning of CPS lies on three basic components; sensing, computing/processing and networking [15]. The continuous advances in wireless sensor networks (WSNs), medical sensors and reliable networks made the involvement of CPS throughout in the field of E-healthcare and home-to-hospital (HTH) care or vice versa [16]. These applications get involved in the body area sensor networks and medical sensors which is the hot topic of research [17]. Various researchers added their efforts to made the service easy and compatible using these sensors. However, it is difficult to manage wired sensor networks, therefore, the advancement of these sensors boats on the wireless sensor networks (WSNs) which gives the more comfort to the doctor and patient. Further, sometimes these healthcare services provided at the remote locations using networking facilities. This health data transmission requested to takes place as quickest with minimum delay. Numbers of authors [18 –23] have been associated with the quickest path problem (QPP). As this point, health data of patient is helpful to provide necessary diagnostic /treatment/prescription services to patients [24]. This confidential health data of patient requested from concerned authorized medical personnel and therefore, chances of security threats are there [25]. Thanks to the researchers for providing better solutions to deal with these type of compromising situation [26]. In addition to this, health data transmitted over wireless, wired or mixed sensor network is severely affected by the certain constraints [15] like energy, storage capacity, service level agreements, intelligent computing and processing etc.

Numbers of authors have been associated with the different sections of the CPS [15, 27]. However, extensive research has been in progress in the field of networking to support the critical and continue health data transmission in CPS [28]. Networking abstractions to made the compatible CPS for healthcare are on the peak [28] and lots of researchers are dealing with this part [29 –31]. Sometimes, the healthcare services requests for reliable and promising health data services [32 –34]. Recently, it is observed that critical healthcare services rely more over the cyber component such as networking intelligent computing etc. Moreover, the health data is critical and request for the reliable connection of networks [35 –37]. A second delay in services can leads to the loss of life, therefore the need of designing health data transmission system without any violation in service level agreement is necessary [38, 39]. For these types of services, SLAs plays an important role for the support of CPS. The research in CPS shows the constraints of energy also; therefore consideration of energy consumption can hold the computation of health data transmission [40]. The ignorance to energy constraint may give the interrupted services due to the lack of sufficient amount of energy for health data transmission [41, 42]. Also, the deteriorating conditions of environment and bar of environmentalist on consumption of energy resources forced to consider these constraints on the data transmission [43]. In the above literature, the discussed issues are highly sensitive toward the working of a CPS. Therefore, the main consideration of this paper lies on cyber system with the energy constraint and SLA constraints collectively toward the proper functioning of CPS. Also, here we are assuming that our physical system is perfect and in the functioning order. Specific contribution of this paper are (i) SLAs for the criticality constraint with service assurance to CPS (ii) energy constraint for the continuity of service in the critical healthcare services (iii) variation of SLA and energy plays an important role in the selection of critical healthcare CPS. The remainder of this paper is organized with the help of different sections and subsections. The preliminaries for the proposed system model are presented in the Section 2. Section 3 constitutes the proposed system model with its performance analysis. The illustration of the theoretical results is given with the help of an example in the Section 4. An algorithm of the proposed approach with its time complexity analysis is also presented in Section 4. The experiment setup, results and discussion are presented in Section 5. In the last section, conclusion is drawn.

2 Preliminaries

In E-healthcare CPS, the health data is transmitted from one end to other end over a computer communication network (CCN). To understand the working of CCN, a CCN can be modeled as a directed loopless graph G = (N, E) where N and E are a set of nodes and links, respectively. Health data is being transmitted over a link (u, v) connected between two nodes u to node v and s-t nodes are the doctor and patient nodes, vice versa. A E-healthcare data transmission path has been considered as a series sequence (without loop) of links between any two specified nodes.

To consider the CCN for CPS, let c (u, v) >0 and d (u, v) >0 are the endowed capacity and delay time respectively for a given link (u, v). The capacity defined as the traffic that can be sent over link (u, v) per unit time and delay time represents the amount of delay (like propagation, queuing delay etc.) that is faced during transmission of traffic for a link (u, v).

Let σ healthcare data units have to be transmitted via a s-t path then minimum delay at link (u, v) is given by [20]: $T_{σ} (u, v) = d (u, v) + [\frac{σ}{c (u, v)}]$ (1)

For the minimum delay, capacity c(u, v) has to be minimum and consider the assumption that data units are transmitted in seamless flow through link (u, v) and the output set of efficient paths is non-empty for a given network graph G (N, E) i.e. there should be a single path for a given network.

Let path P = (s = u₁, u₂, u₃ …… , u_k = t) where u_i ∈ N, i = 1, …… , k, u_i ≠ u_j if i ≠ j, and (u_i, u_i+1) ∈ E, i = 1, …, k - 1 be the loopless path from source (s) to destination (t). Thus, minimum transmission delay for the σ unit’s healthcare data from s-t path is given by [18]: $T_{σ} (P) = d (P) + [\frac{σ}{c (P)}]$ (2) where d (P) is the delay of path and given as $d (P) = \sum_{i = 1}^{i = k - 1} d (u_{i}, u_{i + 1})$ and c (P) is the minimum capacity for the s-t path given as [18, 20]: ${min}_{i = 1}^{k - 1} c (u_{i}, u_{i + 1})$ (3)

Therefore, the minimum transmission delay expanded as [18 , 41]: $T_{σ} (P) = \sum_{i = 1}^{i = k - 1} d (u_{i}, u_{i + 1}) + [\frac{σ}{{min}_{i = 1}^{k - 1} c (u_{i}, u_{i + 1})}]$ (4)

The quickest path problem for CCN enabled CPS can be formulated for finding efficient s-t path (P) is [18 , 41]:

$\begin{matrix} min T_{σ} (P) \\ s . t . P is an s - t path in network G (N, E) \end{matrix}$ (5)

The quickest path for healthcare data transmission in CCN for CPS has a strong impact on the optimality of a s-t path. According to (4), when data is of large amount, path delay is depending on the path with maximum capacity. When healthcare data is in small amount the transmission time is controlled by the link delays. Hence, link delays lay down a criterion to support for the solution of QPP by computing an optimum sequence of links.

3 Proposed system model

As we have discussed cyber physical system (CPS) is the combination of different sub parts of systems, a computer communication network (CCN) is the major part of the CPS. Here, the proposed system involved into strengthens the CCN for optimum working of CPS and in the rest of paper the focus is given to CCN only. In CCN, for the continuity and criticality, all the link performance components are requested to be evaluated together in a single link parameter as service performance factor (SPF) [44] to find the quality service set (QSS). Following assumptions have been considered:

There are no parallel links or loop in the network to utilize the network resources efficiently.

Although nodes have been considered as perfect with respect to physical failure, however, these are subjected to the performance failure such as delay, traffic, requested SPF and bandwidth etc.

All flows in the network obey conservation law.

3.1 SLA mapping and service performance factor

In CCN for critical-healthcare applications, the SLA cooperation has a great role in the completion of the service to prevent the wastage of resource which are considered in number of different terms [45]. During the problem formulation, these SLAs have been mapped in terms of requested service time and service mean time to failure (MTTF_s) denoted as t_s and MTTF_s, respectively. These SLAs may be in terms of seconds, hours, months or years. In CCN, data transmission services occurred and completed in fraction of seconds therefore the units for the considered SLAs are considered into seconds (secs). Using theory of reliability [46], the requested service performance factor (RSPF) at nodes denoted as (r_u) is defined as the probability of failure-free service performance for a requested service time (t_s) which is an important performance metric for getting the service and given as: $r_{u} = e^{- \frac{t_{s}}{{MTTF}_{s}}}$ (6)

The completion of service or data transmission has been affected not only by the link reliability but also with the delay, capacity and the amount of data to be transmitted through with it. Therefore, the integrity of all the link parameters is requested to make comparable to link reliability. Its importance can be seen in a wide sense as it depends on the two basic factors (i) total transmission time and (ii) MTTF of a link. As link delay, capacity, MTTF and data plays a prominent role in the completion of data transmission [44, 47]; therefore, mapping of SLAs have been incorporated in terms of service performance factor of the link (SPF) denoted as r_s (u, v) given as: $r_{s} (u, v) = e^{- [\frac{d (u, v) + \frac{σ}{c (u, v)}}{MTTF (u, v)}]}$ (7)

Service performance factor of the path (P) is computed and expanded putting equation (2) in to equation (7) as: $\begin{matrix} R_{s} (P) = e^{- [\frac{[\sum_{i = 1}^{i = k - 1} d (u_{i}, u_{i + 1}) + [\frac{σ}{{min}_{i = 1}^{k - 1} [c (u_{i}, u_{i + 1})]}]]}{\prod_{i = 1}^{i = k - 1} MTTF (u_{i}, u_{i + 1})}]} \\ \Rightarrow R_{s} (P) = e^{- [\frac{d (P) + \frac{σ}{c (u, v)}}{MTTF (P)}]} = e^{- [\frac{T_{σ} (P)}{MTTF (P)}]} \end{matrix}$ (8)

3.2 SLA Cooperation

In CCN, there are number of links and nodes where each node can be a user, a service provider, a router or a computer. A path P is formed either combination of several links or a single link. Therefore, it is more realistic to satisfy the SLA piecewise or between two consecutive links other than satisfying the SLA after completion of data transmission service among the path. The SLAs are considered for mission-critical applications; therefore, each node is endowed with the RSPF (r_u) and defined as the probability of failure-free service for a particular service time (t_s). Hence to satisfy criticality constraint across the link (u,v), SPF has to be more than that of RSPF given as: $e^{\frac{- [d (u, v) + \frac{σ}{c (u, v)}]}{MTTF (u, v)}} \geq r_{u}, \forall (u, v) \in E$ (9)

The remaining value of SPF is termed as residual requested service performance factor (RRSPF) along a path denoted as r_u (σ, P). RRSPF is defined as the remaining endowed RSPF from the SPF at the nodes after complete data transmission along a path. The role of RRSPF has been used to find the SLA cooperative nodes, which take part in the data transmission. In this paper, we use SLA cooperation and extensive reliability theory framework to enhance the service performance. The RRSPF r_u (σ, P) along the path gives feasibility of path P i.e. r_u (σ, P) ≥0, ∀u ∈ P as:

$r_{u} (σ, P) = {\begin{matrix} - ln (r_{u}) - {- ln [e^{\frac{- [d (u_{i}, u_{i + 1}) + \frac{σ}{c (P)}]}{MTTF (u_{i}, u_{i + 1})}}]}, & if u = u_{i}, i = 1, 2, ., k - 1 \\ - ln (r_{u}) & otherwise \end{matrix}$ (10)

The s-t path (P) will be feasible only if the condition shown in the above equation i.e. r_u (σ, P) ≥0, ∀u ∈ P. The explanation for this feasibility condition is for the measurement of satisfaction of SLAs at nodes to transmit the healthcare data between two ends with the rate of c (P). Hence, the SLA cooperative quickest healthcare data transmission service is modeled as below: $\begin{matrix} min_{P} T_{σ} (P) \\ s . t . r_{u} (σ, P) \geq 0, u \in P \\ P is an s - t path in network G \end{matrix}$ (11)

3.3 Energy cooperation

In CCN, the requested energy at node u to transmit σ unit data over a link (u, v) is known as the energy rate ω(u, v) and calculated as $ω (u, v) \frac{σ}{c (u, v)}$ . Since, a network consists of number of nodes and links therefore; each node u ∈ N has been associated with the limited energy supply (P_u) provided with batteries [42]. To satisfy the continuity, σ data transmission through link (u, v) has to be more than associated energy supply with requested energy (RE) given as: $P_{u} \geq ω (u, v) \frac{σ}{c (u, v)}, \forall (u, v) \in E$ (12a) The remaining value is termed as residual energy supply (RES) along a path P_u (σ, P). RES is defined as the remaining endowed energy supply from the requested energy at the nodes after complete data transmission along a path. The role of RES has been used to find the energy cooperative nodes which take part in the data transmission [41]. The RES P_u (σ, P) along the path P gives the feasibility of path P i.e. P_u (σ, P) ≥0, ∀u ∈ P as: $P_{u} (σ, P) = {\begin{matrix} P_{u} - ω (u_{i}, u_{i + 1}) \frac{σ}{c (P)}, & if u = u_{i}, i = 1, \dots, k - 1 \\ P_{u} & otherwise \end{matrix}$ (12b) The s-t path (P) will be feasible if and only if the condition shown in the above equation i.e. P_u (σ, P) ≥0, ∀u ∈ P followed. The explanation for this feasibility condition is given by the measurement of availability of energy as noted at each node to transmit healthcare data having path capacity c (P). Hence, the energy cooperative quickest healthcare data transmission is modeled as below: $\begin{matrix} min_{P} T_{σ} (P) \\ s . t . P_{u} (σ, P) \geq 0, \forall u \in P \\ P is an s - t path in network G \end{matrix}$ (13) From equations (11) and (13), the SLA-Energy cooperation allows us to combine the characteristics of the both models and formulate the constraint model of the SLA-Energy cooperative quickest healthcare data transmission (SEQHDT) given as below: $\begin{matrix} min_{P} T_{σ} (P) \\ s . t . r_{u} (σ, P) \geq 0, u \in P \\ P_{u} (σ, P) \geq 0, u \in P \\ P is an s - t path in network G \end{matrix}$ (14)

4 Main theoretical results

Generally, there are r different capacities c₁ < c₂ < ⋯ < c_r present in any CCN of a CPS. The minimum SLA and energy cooperative link capacity is given below in equations (15) & (16), and corresponding to this the minimum SLA-energy cooperative link capacity is also shown as in equation (18): $c_{min SLA} (u, v) = min_{i = 1, . ., r} {c_{i} : e^{\frac{- [d (u, v) + \frac{σ}{c_{i}}]}{MTTF (u, v)}} - r_{u} \geq 0}$ (15)

Using above equation, the procedure for SLA cooperation has been given for sorting the links to support the critical applications. $c_{minE} (u, v) = min_{i = 1, . ., r} {c_{i} : P_{u} - ω (u, v) \frac{σ}{c_{i}} \geq 0}$ (16)

The equation (16), helps to corporate the efficient use of energy for continues data transmission. Further from (15) and (16), we have the following expression

$\begin{matrix} c_{min} (u, v) & = & min {[c_{min E} (u, v) \\ \geq & c_{a} \geq c (u, v)] \cap [c_{min SLA} (u, v) \\ \geq & c_{b} \geq c (u, v) \geq c (u, v)]} \end{matrix}$ (17)

Where c_a and c_b are the capacities lies in the minimum cooperative energy and SLA capacities, respectively and link capacity The above equation (17) provides the label of minimum link capacity to support the continuity and criticality in data transmission if c_minSLA (u, v) and c_minE (u, v) >0. A s-t path P is feasible if c (P) ≥ c_min (u, v).

The above equations sort the minimum capacity which incorporates the both critical and continues data transmission by considering the AND rule. The AND rule is mentioned here as for a specific link both parameters SLA and energy needs to be satisfied. Let us assume that when a link supports any parameter then the logic has been given it as “1” otherwise “0”. Now using property of AND gate, the link will support the minimum capacity c_min (u, v) only when both parameter gives logic “1”. Therefore, c_min (u, v) has to follow the AND rule for SLA-energy cooperative reliable and quickest data transmission problem for mission critical applications.

From equation (18), r number of sub-networks has been sorted and each link has to follow the given inequality for the path capacity c (P). $c (u, v) \geq c_{j} \geq c_{min} (u, v); where j = 1, 2, \dots, r$ (18)

Lemma 1: Let a path P = u₁, u₂ … , u_k-1, u_k has been known as the s-t path in a sub-network then that path has been called as SLA-energy cooperative quickest healthcare data transmission (SEQHDT).

Proof: Path P is s-t path in the sub-network, the capacity of path c (P) has to follow c (P) ≥ c_j ≥ c_min (u_i, u_i+1), where i = 1, …, k - 1. Hence:

For the nodes, which have not been accounted in the path, the endowed parameters remain same. $\begin{matrix} P_{u} (σ, P) & = & P_{u} - ω (u_{i}, u_{i + 1}) \frac{σ}{c (P)} \\ \geq & P_{u} - ω (u_{i}, u_{i + 1}) \frac{σ}{c_{min} (u_{i}, u_{i + 1})} \geq 0 \\ r_{u} (σ, P) & = & e^{\frac{- [d (u_{i}, u_{i + 1}) + \frac{σ}{c (P)}]}{MTTF (u_{i}, u_{i + 1})}} - r_{u} \\ \geq & e^{\frac{- [d (u_{i}, u_{i + 1}) + \frac{σ}{c_{min} (u_{i}, u_{i + 1})}]}{MTTF (u_{i}, u_{i + 1})}} - r_{u} \geq 0 \end{matrix}$

Therefore, surplus service performance factor and residual energy follows this for a path.□

Lemma 2: Let a s-t path P is said to be a feasible path with path capacity c (P) = c_j, then P is said to be a path in G_j.

Proof: From Lemma 1, let P is feasible. $\begin{matrix} P_{u} (σ, P) & = & P_{u} - ω (u_{i}, u_{i + 1}) \frac{σ}{c (P)} \\ \geq & 0, i = 1, 2, \dots, k - 1 \\ r_{u} (σ, P) & = & e^{\frac{- [d (u_{i}, u_{i + 1}) + \frac{σ}{c (P)}]}{MTTF (u_{i}, u_{i + 1})}} - r_{u} \\ \geq & 0, i = 1, 2, \dots, k - 1 \end{matrix}$

Hence, c_min (u_i, u_i+1) ≤ c (P) = c_j ≤ c (u_i, u_i+1), where i = 1, …, k - 1, and (u_i, u_i+1) are in the path with sorted links of G_j, hence, P is an s-t path.

In this paper, for any given network topology, the major concern of the routing is to find the SEQHDT path P and the relaibility of path depends on the computation of shortest path problem (SPP). The solution of SPP is found using Dijkstra’s algorithm using link cost function of SPF r_s (u, v) in the sub-network graph G_j. However, algorithm considers the minimum cost values; therefore proposed problem is the delay minimization problem: $\begin{matrix} SP P_{j} : min_{P} d (P) \\ s . t . P is a s - t path in the network G_{j} \end{matrix}$ (19) □

Lemma 3: Let P be an optimal path solution of SPP_j and c (P) = c_h > c_j. Then, there is no other optimal solution for the SEQHDT with capacity c_j.

Proof: Let Q be a s-t feasible path for the SEQHDT path with capacity c_j then Q is a path in G_i. $T_{σ} (P) = d (P) + \frac{σ}{c_{h}} < d (Q) + \frac{σ}{c_{j}} = T_{σ} (Q)$

Therefore, Q cannot be an optimal solution.□

Algorithm SEQHDT

Algorithm: SEQHDT Algorithm
Input:G (N, E) , σ, r₁ (u, v) , c (u, v) , d (u, v), MTTF_s, P_u, ω (u, v) , r_u, t_s and MTTF (u, v) ,
Output: SLA-energy Cooperative Quickest Healthcare Data Transmission (SEQHDT)
BEGIN{
Initialization:
j ← 1 ,
Procedure:
STEP0: Variable Declaration
G ← Directed Network
N ← Set of nodes
E ← Set of links
r_lnbi> (u, v) ← Reliability of the link (u, v)
c (u, v) ← Capacity of the link (u, v)
d (u, v) ← Delay of the link (u, v)
ω (u, v) ← Energy rate of the link (u, v)
P_u ← Endowed energy at each node u
r_u ← Requested service performance factor at each
node u
σ ← Healthcare data with constraints
t_s ← Requested service time
MTTF_s ← Mean time to failure of service
MTTF_(u,v) ← Mean time to failure of a link
STEP1: Prune r different capacities of links
corresponds to critical-continuous service &label of
minimum capacity:
(i) c₁ < c₂ < c₃ … < c_r
(ii) c_min (u, v) with AND rule
STEP2: Solve SPP_j w.r.t. delay time d (u, v) in G_j with
capacities c_j
For j ← 1 : r
Set j ← 1
Solve SPP_j
If No s - t path in G_j with capacity with c_j
go to STEP3
else
Let P_j is an optimal solution for SPP_j with capacity c (P_j) = c_j
end
end
STEP3:
If j = r
go to STEP4
else
set j = j + 1 and go to STEP2
end
STEP4: Find the solution
Find index h ∈ (1, 2, … r) of path array P_j such that
$T_{σ} (P_{h}) = min_{j = 1, \dots, r} T_{σ} (P_{j})$
P_h is an optimal solution of the SEQHDT
} END

Theorem 1: Let $\overset{\lor}{P}$ be an optimal solution of the SEQHDT and $(\overset{\lor}{P}) = c_{h}$ . Then, $\overset{\lor}{P}$ is an optimal solution of SPP_h and any optimal solution of SPP_h is an optimal solution.

Proof: Since $\overset{\lor}{P}$ is an s-t feasible path for the SEQHDT with capacity c_h, then $\overset{\lor}{P}$ is an s-t path in the G_h. Let (Q) be a s-t feasible path in the network G_h, then c (Q) ≥ c_h. If $d (Q) < d (\overset{\lor}{P})$ , then $T_{σ} (Q) = d (Q) + \frac{σ}{c (Q)} < d (\overset{\lor}{P}) + \frac{σ}{c_{h}} = T_{σ} (\overset{\lor}{P})$ which contradict the optimality of path $\overset{\lor}{P}$ . Furthermore, by applying the Lemma 3, the capacity of any s-t shortest path $\tilde{P}$ in G_h is $c (\tilde{P}) = c_{h}$ . Hence, $\tilde{P}$ is a s-t feasible path for SEQHDT such that $T_{σ} (\tilde{P}) = T_{σ} (\overset{\lor}{P})$ is an optimal solution.□

Theorem 2: The time complexity of the proposed SEQHDT algorithm is O (r (m + n (log (n)))).

Proof: in step 3 and 4. SEQHDT runs for the r different sub-networks, having the complexity of O (m + n (logn)) [48].□

5 Simulation results and discussion

The experiment has been conducted on a personal computer with Intel(R) CoreTMi5–7400, CPU@ 3.00 GHz, 8-GB RAM, and Windows 10 operating system in MATLAB 2010a. The SEQHDT algorithm involved computation of path using Dijkstra’s algorithm. The scope of the proposed model is simulated using hop count, qualifying service set of paths and energy efficiency. For the understanding the applicability and usefulness of the proposed algorithm the results have been presented for the standard topologies and random networks generated by Waxman random topology generator.

Standard topology:

An example of SLA-energy satisfying service is simulated on the standard directed network topology of 24-node USNET with source (s = 1) and destination (t = 24) [49]. Each link of topology is associated with delay, capacity, reliability, MTTF and energy rate. The value of link delay and capacity is considered with uniform distribution ranging [1, 100] in secs and Mb/secs, respectively. The values of link reliabilities are taken from uniform distribution ranging [0, 1]. The values of MTTF associated with links are considered with uniform distribution ranging between [1, 100] in seconds (secs). To transmit 100 Mb data between different links and nodes, let each node is associated with the fixed energy i.e. P_u = 3 ×10⁷Joule and fixed requested service performance factor (r_u). The energy rate ω (u, v) at each link is calculated by the relation 10^-4c (u, v) d² (u, v). The requested SLA for the data transmission is, requested service time t_s = 100 secs and service MTTFs=500 secs, respectively.

Find the s-t paths from different sub-networks using cost metric formed in equation (6) and find the qualifying service set (QSS) using equation (19). In the last step find the s-t path with minimum cost from the QSS. The simulation results have been simulated for the 1000 random iterations. The average number of distinct capacities and QSS are 22.1 and 6.6, respectively. The average capacity and hop count for the minimum cost s-t path from the QSS is 16.7 Mb/secs and 7.1 hops. The average energy efficiency necessitates in the data transmission and calculated by the capacity divided total energy consumed in the transmission of σ unit data and calculated as 3.46 × 10⁵bits/secs/joule.

Waxman Random Topology Generator:

To analyze the performance of the proposed SERQHDT algorithm on the large random networks a Waxman random topology generator is used [50, 51]. The generation of Waxman topology is done by placing the nodes in a one-by-one square, and the links are created between two nodes (u) and (v) by considering the probability. $P (u, v) = α e^{- (\frac{d (u, v)}{β L})}$ (20)

Where: d (u, v) is the Euclidean distances b/w u and v.

α is the maximal link probability such that α > 0.

β is the parameter to control length of the links.

L is the maximum distance between any two nodes.

The different values of α and β are considered as 0.4 and 0.1, respectively.

The proposed algorithm is verified for different set of network dimensions such as number of nodes, links, distinct capacities, energy at nodes, data traffic and SLAs. These values are shown in Table 1.

Table 1

Values of different parameters for random experiment

Sr. No.	List of Parameters	Set of parameter values
1	Number of nodes	100, 200 and 300
2	Number of links	4600, 18500 and 41500
3	Number of distinct capacities	10,100 and 1000
4	Different data traffic	1and 10 Mb
5	Energy associated with nodes	10, 100, 100 joule
6	SLAs assigned	100, 110 and 120 secs

The performance parameters are considered as mean candidate s-t QSS paths, average hop count and average energy efficiency. The mean candidate s-t QSS paths parameter is the parameter for getting the mean number of candidate optimal s-t quickest paths for the data services. Average hop count is the performance measure for calculating the energy efficiency. If the numbers of average hop count are decreased then the average energy efficiency is increased. The energy efficiency is the performance measure for efficient use of energy for data transmission services and it is measure as the amount of data traffic transferred to the total energy consumed for the data transmission across the s-t paths. Here, the amount of data has been considered in Mb, therefore here the units for energy efficiency are considered as Mb/secs/joule.

The first, second and third columns of the Tables 2–4 shows the variation of different number of capacities, nodes and links associated with the networks, respectively. The variation in the values of the mean number of candidate s-t QSS routes, average hop counts and average energy efficiency in the next consecutive columns of the Tables 2–4 for the data values 1 Mb, respectively.These results shows here are with the 95% confidence or with 5% error.

Table 2

The simulation parameters and the mean candidate s-t QSS path for the SEQHDT algorithm to transmit 1 Mb data

r	n	m	Mean candidate s-t QSS path for 10 runs
			P_u = 10			100			1000
			t_s = 100	110	120	100	110	120	100	110	120
10	100	4600	6.4	7.7	7.9	9.1	9.4	9.5	9.5	9.7	9.8
	200	18500	9.1	9.4	9.5	9.2	9.5	9.7	9.5	9.5	9.8
	300	41500	8.5	9.1	9.5	8.6	9.2	9.5	8.9	9.2	9.5
100	100	4600	38.2	47.5	54.8	54.5	62	63.9	59.2	63.8	65.2
	200	18500	46.3	53.2	53.9	55.1	60	64.4	61.8	62.1	63.5
	300	41500	49.2	53.1	62	61	65.2	65.3	59	61.2	61.8
1000	100	4600	82	86.5	88	89.2	97.1	98.5	86	93.3	99
	200	18500	86	87.2	90.1	88	97.5	98.9	83.2	86	87.2
	300	41500	83	94.2	95.6	96.6	98	99.2	92.2	98.2	98.5

Table 3

The simulation parameters and the average hop counts for the optimal path for the SEQHDT algorithm to transmit 1 Mb data

r	n	m	Average hop counts for the optimal path for 10 runs
			P_u = 10			100			1000
			t_s = 100	110	120	100	110	120	100	110	120
10	100	4600	1.9	1.9	1.7	1.5	1.3	1.2	1.6	1.4	1.4
	200	18500	1.5	1.3	1.2	1.6	1.4	1.3	1.8	1.7	1.7
	300	41500	1.8	1.7	1.7	1.5	1.2	1.2	1.8	1.7	1.6
100	100	4600	1.5	1.4	1.4	1.8	1.8	1.6	1.5	1.4	1.4
	200	18500	1.5	1.5	1	1.2	1	1	1.2	1	1
	300	41500	1.8	1.5	1.2	1.9	1.6	1.2	1.4	1.3	1.4
1000	100	4600	1.5	1.2	1.2	1.5	1.2	1.2	1	1	1
	200	18500	1.5	1.4	1.4	1.2	1.2	1	1.5	1.2	1.2
	300	41500	1.5	1.5	1.4	1.2	1.1	1.1	1.4	1.3	1.3

Table 4

The simulation parameters and the average energy efficiency for the optimal path for the SEQHDT algorithm to transmit 1 Mb data

r	n	m	Average energy efficiency for the optimal path for 10 runs
			P_u = 10			P_u = 100			P_u = 1000
			t_s = 100	110	120	100	110	120	100	110	120
10	100	4600	0.4887	0.8505	1.8091	0.1551	0.1731	0.1846	0.0568	0.4416	2.0408
	200	18500	0.1998	0.8264	0.904	0.0104	0.193	0.3086	0.0657	0.185	0.5264
	300	41500	0.1174	0.2085	0.3356	0.0111	0.2066	0.25	0.0178	0.0152	0.6944
100	100	4600	1.0649	2.1009	3.5625	0.0112	0.0331	0.0356	0.0026	0.6944	2.7778
	200	18500	0.571	0.8547	1.3086	0.0625	0.0952	1.0568	0.0204	0.0772	0.0816
	300	41500	1.5944	1.6235	2.2268	0.0116	0.0204	0.0204	0.0316	0.0435	3.1724
1000	100	4600	0.2066	0.6969	0.7223	0.277	0.0142	0.0693	0.0132	0.0865	0.8264
	200	18500	0.1155	0.1668	0.3364	0.0152	0.189	0.26	0.0408	0.8148	1.0754
	300	41500	0.8264	1.189	3.52	0.4444	1.176	1.5917	0.2268	0.8264	0.9945

From the above Table 2, results show with the variation of energy available and SLAs. If we see the results in the columns 4, 5 and 6 for the given energy, the number of selected mean candidate s-t QSS paths increased as we increased the value of SLA requested service time from 100, 110 and 120. This depicts that the SLA requested service time is the criteria to sort the SLA cooperative links for critical and continues data transmission. The usefulness of this parameter is that number of mean candidate s-t QSS paths gives the assurance to successful data transmission if any of the links in the CNN gets down. In addition, if these numbers are increased then this case is more favorable for the critical-healthcare applications.

Another usefulness of results can be seen with the variation of energy available at nodes. For the fixed SLA requested service time (t_s), the energy available at each node is varied from 10 to 1000 joule. Let’s, consider the columns 4, 7 and 10, the values of number of selected mean candidate s-t QSS paths are also increased such as 6.4, 9.1 and 9.5. This means the role of energy available at nodes is also the key factor for selecting more number of mean candidate s-t QSS paths. The rest table is explained with the same and shows the same variation with respect to SLA and energy. The role of considering number of distinct capacity and number of nodes also plays an important role to select the mean number of s-t QSS paths. If distinct capacities, number of nodes are increased then number of selected mean number of s-t paths are also increased which is a favorable case with the aspect of criticality and continuity of the data transmission.

The result in Table 3 shows that as we are increasing the values of SLA and energy available at nodes, the hop count of the best selected minimum cost s-t path is decreased. The usefulness of this performance measure is that if the numbers of hops are decreased the energy available at nodes is efficiently used. Also, this measure useful in concern with security, but here in this paper this constraint is not taken into account. From the columns 4, 5 and 6 the number of average hop counts are decreased with increasing SLA requested service time and same trend is seen from columns 4, 7 and 10 if we increased value of energy available at nodes from 10 to 1000 joule. The minimum hop count gives the data transmission with the quick possible time. The other important performance measure is used as energy efficiency (Mb/secs/joule). The Table 4 is used to explain the results to know the importance of variation of SLA and energy available. From the columns 4, 5 and 6 we can see with increase in SLA requested service time (t_s) the average energy efficiency is also increased. The energy efficiency is also increased if we increased value of energy for the fixed value of SLA requested service time. The same trend can be seen if we increased number of distinct capacities and number of nodes. To see the variation of results, the results have been seen for the different data traffic also.

The Tables 5–7 shows the results of the variation in the values of the mean number of candidate s-t QSS routes, average hop counts and average energy efficiency for the data traffic of 10 Mb. All the above discussed performance measure are shown for the 10 Mb data. The same trends of results are followed for the variation in data to be transmitted from source to destination. The Tables 5–7 are shown below to transmit the 10 Mb data. The variation of SLAs and energy is also an important factor to support all these services. However, if data traffic increased the performance measures got down because to support higher amount of data more amount of energy and time is required and sometime the requested SLAs and endowed energy is not sufficient to cooperate the data transmission. One can increased the values of SLAs and energy to make the higher values of data transmission more favorable for the criticality and continuity of service. If the service criticality is a prime constraint and can’t be compromised over any conditions then for those type of critical services other mediums has to be used for the completion of service, such as green corridors, dedicated networks etc. The results of proposed algorithm shows that the consideration of CCN as an important integral part of CPS. The Table 8 shows that the proposed SEQHDT algorithm considered both SLA and energy cooperation for the QPP model for the healthcare data transmission.

Table 5

The simulation parameters and the mean candidate s-t QSS path for the SEQHDT algorithm to transmit 10 Mb data

r	n	m	Mean candidate s-t QSS routes for 10 runs
			P_u = 10			P_u = 100			P_u = 1000
			t_s = 100	110	120	100	110	120	100	110	120
10	100	4600	6.4	7.7	7.9	9.1	9.4	9.5	9.5	9.7	9.8
	200	18500	9.1	9.4	9.5	9.2	9.5	9.7	9.5	9.5	9.8
	300	41500	8.5	9.1	9.5	8.6	9.2	9.5	8.9	9.2	9.5
100	100	4600	38.2	47.5	54.8	54.5	62	63.9	59.2	63.8	65.2
	200	18500	46.3	53.2	53.9	55.1	60	64.4	61.8	62.1	63.5
	300	41500	52.2	55	57.5	55.2	58	58.6	60	61.9	65.3
1000	100	4600	82	86.5	88	89.2	97.1	98.5	86	93.3	99
	200	18500	86	87.2	90.1	88	97.5	98.9	83.2	86	87.2
	300	41500	98.2	100.1	101.9	100.1	105.2	108.7	103	106.5	110.7

Table 6

The simulation parameters and the average hop counts for the optimal path for the SEQHDT algorithm to transmit 10 Mb data

r	n	m	Average hop counts for the optimal path for 10 runs
			P_u = 10			P_u = 100			P_u = 1000
			t_s = 100	110	120	100	110	120	100	110	120
10	100	4600	1.9	1.9	1.7	1.5	1.3	1.2	1.6	1.4	1.4
	200	18500	1.5	1.3	1.2	1.6	1.4	1.3	1.8	1.7	1.7
	300	41500	1.8	1.7	1.7	1.5	1.2	1.2	1.8	1.7	1.6
100	100	4600	1.5	1.4	1.4	1.8	1.8	1.6	1.5	1.4	1.4
	200	18500	1.5	1.5	1	1.2	1	1	1.2	1	1
	300	41500	1.5	1.2	1.1	1.3	1.1	1.1	1.1	1.1	1
1000	100	4600	1.5	1.2	1.2	1.5	1.2	1.2	1	1	1
	200	18500	1.5	1.4	1.4	1.2	1.2	1	1.5	1.2	1.2
	300	41500	1.6	1.4	1.3	1.5	1.3	1.3	1.3	1.1	1.1

Table 7

The simulation parameters and the average energy efficiency for the optimal path for the SEQHDT algorithm to transmit 10 Mb data

r	n	m	Average energy efficiency for the optimal path for 10 runs
			P_u = 10			P_u = 100			P_u = 1000
			t_s = 100	t_s = 110	t_s = 120	t_s = 100	t_s = 110	t_s = 120	t_s = 100	t_s = 110	t_s = 120
10	100	4600	0.48878	0.85057	1.80913	0.15515	0.17311	0.18467	0.0568	0.4416	2.0408
	200	18500	0.1998	0.8264	0.904	0.0104	0.193	0.3086	0.0657	0.185	0.5264
	300	41500	0.1174	0.2085	0.3356	0.0111	0.2066	0.25	0.0178	0.0152	0.6944
100	100	4600	1.0649	2.1009	3.5625	0.0112	0.0331	0.0356	0.0026	0.6944	2.7778
	200	18500	0.571	0.8547	1.3086	0.0625	0.0952	1.05684	0.0204	0.0772	0.0816
	300	41500	0.5206	1.484	1.9582	0.281	0.2491	1.2012	0.0109	0.0149	0.0244
1000	100	4600	0.2066	0.6969	0.7223	0.277	0.0142	0.0693	0.0132	0.0865	0.8264
	200	18500	0.1155	0.1668	0.3364	0.0152	0.189	0.26	0.0408	0.8148	1.0754
	300	41500	0.0118	0.4521	1.2854	0.254	1.0254	1.5921	0.6251	0.9952	1.298

Table 8

Comparison of the existing models with proposed model

Algorithm	Quickest	Reliable	Energy	SLA
Chen &Chin, 1990 [20]	✓	×	×	×
G. Xue, 1998 [52]	✓	✓	×	×
Y. K. Lin, 2003 [53]	✓	✓	×	×
H. Calvete, 2012 [54]	✓	✓	×	×
H. Calvete 2017, 2018 [41], [42]	✓	×	✓	×
A. Sharma, 2018 [21]	✓	✓	×	×
Proposed SEQHDT	✓	✓	✓	✓

The (✓) and (×) tick shows that authors have incorporated and not incorporated the model, respectively.

6 Conclusion and future scope

In this paper, a typical critical-healthcare data transmission services application of Cyber Physical System (CPS), has been highlighted by proposing a SEQHDT model with consideration of the delay, energy and SLA parameters. The novelty of proposed model for cyber physical system relies on the quickest path problem without affecting the algorithm complexity, which gives the SLA-energy cooperative QSS for critical-healthcare applications. The results of selecting QSS with the different values of requested service time and data shows that SLAs and energy plays a prominent role in the selection of SLA-energy cooperative data-path transmission for cyber physical system. The other performance measures are considered as average hop count and average energy efficiency which again strengthen the applicability of proposed algorithms for the mission critical applications. The average number of selected s-t QSS paths is increased as we increase the value of SLA requested service time (t_s) and available energy at nodes such that the possibility of getting assured data transmission also increased if any breakdown occurred in networks. It is to mention that same trend has been formed for the number of distinct capacities and number of different nodes are increased. The average energy efficiency is also increased therefore, for the higher amount of data traffic, the network with higher values of SLAs and energy is suitable for the healthcare data transmission services of CPS.

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