Differential Security Barriers for Virtual Emotion Detection in Maritime Transportation Stations With Cooperative Mobile Robots and UAVs

A Maritime Transportation System (MTS) accomplishes diverse tasks including efficient route, information management, transportation stations. In particular, security and surveillance should be one of critical topics in IoT-supported MTS. In this paper, we introduce a secure framework that creates differential security barriers for virtual emotion detection in IoT-assisted maritime transportation systems. We formally define a problem whose goal is to maximize the number of differential security barriers by mobile robots and UAVs. To solve the problem, we propose two different schemes to provide an improved security detection in priority area so that the proposed methods create the maximum number of security barriers to fit with discriminative security levels in MTS subareas. Then, we analyze their performances through various settings and scenarios with detailed discussions.

SECTION I. Introduction

During recent decades, the studies of mobile robots attracted much interests of researchers thanks to its numerous applicabilities. From its basic moving operation, sensory feedback, information processing, communication capabilities, it has been utilized for industries to perform specific tasks which humans can not accomplish directly due to harsh environment and conditions [1]. Also, in cooperation with recent advances including artificial intelligence, machine learning and reinforced learning, mobile robots are expanding their applicabilities into various practical fields including manufacture of several products, delivery services, information guidance, public services, etc [2]–​[4]. And, it is highly anticipated that mobile robots will take critical roles in a wide range of IoT (Internet of Things)-enabled environments and sensor-based systems [5]–​[12].

UAVs (Unmanned Aerial Vehicles) have several advantages covering rapid flight, relatively small sized vehicles, video, audio information processing abilities, etc [13]–​[15]. In particular, instead of a single large UAV, a group of multiple small-sized UAVs can bring improved performances of cost reduction, scalability, minimum delay, task completion [16], [17]. With those useful availabilities, it is also expected that a fleet of UAVs is utilized for a wide range of applications such as maritime transportation system, rescue operations, monitoring areas, surveillance by barriers, delivery services, mobile system [18]–​[24].

On the other hand, the maritime research domain addresses all maritime activities covering ocean, transportation system, borderline sites, cargo, people, vessels, etc. Particularly, the MTS (Maritime Transportation System) is considered as recent emerging branch of maritime domain [25], [26]. Essentially, the MTS can be composed of several nets and layers including ports, port facilities, vessels, boats, transportation stations, border sites. Also, in order to support those nets and layers of MTS, there are important issues of efficient routes, information management, regulated international framework, risk management, liability as well as security, surveillance [27]–​[30]. Fig. 1 depicts possible services and their supports by mobile robots and UAVs in MTS. With the combination of mobile robots and UAVs in MTS, they are able to support cargo, transportation, screening test, patrol, security check, virtual emotion service, transit and delivery service between maritime transportation stations and inland stations.

Fig. 1.

A brief overview of services and applications using mobile robots and UAVs in MTS.

Besides, the research branch of security has been enlarged tremendously due to its extraordinary importance and necessity [31]–​[39]. In particular, a novel security concept of barrier firstly has been introduced by Kumar et al. [40]. Then, its applicability has been expanded to numerous applications and services such as camera sensor, surveillance, emotion applications [41], [42], [42]–​[44]. Moreover, if barrier is newly utilized for the purpose of security and surveillance based on virtual emotion in MTS, recent advanced devices of mobile robots and UAVs can be contained as primary members of such a security barrier construction. The IoT-enabled MTS can embrace differential priority security sub-areas and the relevant events and sub-area status can be changed frequently. Hence, the issue of how to construct enhanced security barriers promptly in the requested priority region should be studied as one of emergent research branches in IoT-assisted MTS.

So, based on the above motivations, we summarize the key contributions of this paper as follows.

1. In this paper, we introduce a framework, referred as DiffS, which builds differential security barriers in cooperation with mobile robots and UAVs toward secure maritime transportation system. So, the proposed system reinforces the security of the requested maritime transportation area consequently. To the best of our knowledge, this is the first approach that security barriers for virtual emotion detection using mobile robots and UAVs are applied to IoT-enabled maritime transportation stations with differential perspectives and regional weights.

2. We formally defined the problem whose objective is to maximize the number of differential security barriers by mobile robots and UAVs such that the requested primary subsection meets the given detection accuracy and every subsection is monitored by at least security barrier. Also, the defined problem is presented with ILP (Integer Linear Programming) formulation.

3. To solve the problem, we devised two different schemes which return the maximum number of differential security barriers satisfying bounded distance of system components, required detection accuracy after system initialization with dividing sub-sections, verification of components and detection ranges, setting up initial barriers. Also, the proposed methods reinforce the discriminative security levels of multiple number of MTS area.

The remaining part of this paper is proceeded as follows. Next, the notations, system settings, assumptions in the proposed system are described as well as the defined problem is represented with ILP formulation. In Section III, the proposed algorithms are explained to resolve the defined problem. Then, in Section IV, after extensive simulations of the devised algorithms, their performance are evaluated and are discussed with detailed discussion. Finally, this paper is concluded in Section V.

SECTION II. DiffS: A Framework for Differential Security Barriers in MTS

In this section, we first specify system settings and assumptions which are required before implementing the proposed framework. Also, after the explanation of the critical definitions, we formally define a main problem with ILP formulation that covers objective function and conditions.

A. System Settings, Assumptions and Notations

The proposed system is operated by the below settings and assumptions.

1. The whole IoT-enabled maritime transportation systems can be split into several sub-regions and each sub-area has different security levels to be monitored where the security level can be changed according to the system request.

2. The components of the proposed system cover mobile robots, UAVs where each component has heterogeneous capabilities including different detection ranges, resources and all components are equipped with wireless transmitter, receiver, virtual emotion derivation procedures. Based on wireless signal, reflection and derivation procedures [45], each component detects at least five emotion types such as joy, pleasure, neutral, sorrow, rage.

3. Every autonomous mobile robot moves in the ground by centralized system. Also, all autonomous UAVs obey the rule of FAA (Federal Aviation Administration) [15] and they have line-based movements while they are operated in the air.

4. The detected emotion information is sent to other system entities for system update and maintenance.

Also, the notations and their descriptions that are used in the proposed system are summarized in the Table I.

TABLE I Notations

B. Differential Security Barriers in MTS

Here, we present two important definitions used in the proposed framework: IoT-enabled MTS virtual emotion barriers and differential security barriers which are defined below.

Definition 1 (IoT-Enabled MTS Virtual Emotion Barriers):

Given that a set of smart devices equipped with wireless transmitter and receiver are positioned in square-shaped IoT-supported MTS, the IoT-enabled MTS virtual emotion barriers, called as MTSVEmoBar, are barriers with line-based formations that can detect the virtual emotion of the person who is passing into the given MTS area.

Definition 2 (Differential Security Barriers):

Given that the whole IoT-assisted MTS area is divided into several sub-sections with differential security levels, the differential security barriers, referred as DiffSBar, are the special type of MTSVEmoBar that reinforce the high priority security sub-section based on detected virtual emotion where each sub-section has different security priority level and the level is updated frequently depending on the system status and request.

Fig. 2 gives expression to the applicable status of the IoT-enabled MTS virtual emotion barriers, namely MTSVEmoBar. As it can be seen in Fig. 2, there are two MTSVEmoBar in MTS area $S$ , which are composed of several system components with mobile robots and UAVs with heterogeneous capabilities. After those line-based MTSVEmoBar are constructed, virtual emotion can be detected through wireless signal and its reflection on mobile robots and UAVs when person is passing through $S$ . And, the detected virtual emotion information such as rage emotion information can be utilized to reinforce the security of the given area $S$ .

Fig. 2.

An example of IoT-enabled MTS virtual emotion barriers using mobile robots and UAVs.

C. Problem Definition and ILP Formulation

Now, the MaxDiffSBar problem is formally represented with its description and ILP formulation.

Definition 3 (MaxDiffSBar Problem):

When initial MTSV EmoBar are constructed in whole MTS area and the high priority MTS sub-section is decided, the MaxDiffSBar problem is to maximize the total number of DiffSBar with the given detection accuracy in the requested high priority security sub-section. And, the conditions are satisfied that the movement distance of each movable component is no more than the given distance and at least one MTSVEmoBar is active at other sub-sections consequently.

As it can be seen above, the objective of the defined MaxDiffSBar problem is to maximize the total number of DiffSBar in sub-sections with differential security priority levels. By Kumar et al. [40], it is possible to apply sleep-wakeup scheduling scheme. It follows that after searching for the maximum number of DiffSBar, the applied sleep-wakeup scheduling allows DiffSBar to have the transition between sleep mode for energy saving and wake up mode for working DiffSBar alternately. Therefore, the maximum number of DiffSBar results in the maximum lifetime of the proposed framework ultimately.

Fig. 3 delineates the DiffSBar and the defined MaxDiffSBar problem. As shown in Fig. 3, a whole MTS area $S$ was classified with four different sub-sections and sub-section 1 is assumed to be the high priority security sub-section. After initial MTSVEmoBar are built in the whole area $S$ , the DiffSBar within sub-section 1 with the high priority security level can be created by the support of mobile robot and UAV with limited movement in other sub-sections. Then, MaxDiffSBar problem is to maximize the total number of DiffSBar with the given detection accuracy in the high priority security sub-section such that other sections should have at least one MTSVEmoBar. For instance, four different DiffSBar can be generated in the high security sub-section 1 by mobile robot and UAV in Fig. 3.

Fig. 3.

A description of DiffSBar and MaxDiffSBar problem.

Then, MaxDiffSBar problem using ILP with integer variables is presented below.\begin{align*} P_{i}=&~\begin{cases} \displaystyle 1, & \text {if the component} ~c_{i}~\text {is interconnected} \\ \displaystyle 0, & \text {otherwise.} \end{cases} \\ Q_{i, k}=&\,\,\begin{cases} \displaystyle 1, & \text {if} ~c_{i}~\text {is a member of} ~b_{k} \\ \displaystyle 0, & \text {otherwise.} \end{cases} \\ W_{i, k}=&\,\,\begin{cases}\displaystyle {ll} 1, & \text {the moving distance of} ~c_{i}~\text {is less than} ~u \\ \displaystyle & \text {when} ~c_{i}~\text {is movable to} ~b_{k} \\ \displaystyle 0, & \text {otherwise.} \end{cases} \\ X_{k}=&\,\,\begin{cases} \displaystyle 1, & \text {if} ~b_{k}~\text {satisfies detection accuracy} ~t \\ \displaystyle 0, & \text {otherwise.} \end{cases} \\ Y_{l, k}=&\,\,\begin{cases} \displaystyle 1, & \text {if each} ~S_{\text {low}}~\text {has at lease one} ~b_{k} \\ \displaystyle 0, & \text {otherwise.} \end{cases} \\ Z_{k}=&\,\,\begin{cases} \displaystyle 1, & \text {if} ~b_{k}~\text {is active as}~ {\text {DiffSBar}} \\ \displaystyle 0, & \text {otherwise.} \end{cases}\end{align*} The objective function (1) of MaxDiffSBar problem is to maximize the total number of DiffSBar in $S_{high}$ on condition that the moving distance of each movable component is less than the requested distance and at least one MTSVEmoBar should be maintained in other $S_{\text {low}}$ . Note that $\alpha $ is the total number of differential security barriers. Then, its constraints are specified as follows.\begin{align*}&\textbf {Max}~\alpha = \sum ^{n}_{k = 1}\left({\prod ^{n}_{i = 1}\prod ^{m}_{l = 1}Q_{i, k} \cdot W_{i, k} \cdot X_{k} \cdot Y_{l, k} \cdot Z_{k}}\right) \tag{1}\\&\text {s.t.}~ \sum ^{n}_{i = 1}P_{i} \leq 2 \quad (\forall i) \tag{2}\\&\hphantom {\text {s.t.}~}\sum ^{\alpha }_{k = 1}Q_{i, k} \leq 1 \quad (\forall i) \tag{3}\\&\hphantom {\text {s.t.}~}\sum ^{n}_{i = 1}W_{i, k} \leq u\quad (\forall i) \tag{4}\\&\hphantom {\text {s.t.}~}\sum ^{n}_{k = 1}X_{k} \leq 1 \quad (\forall k) \tag{5}\\&\hphantom {\text {s.t.}~}\sum ^{m}_{l = 1}Y_{l, k} \leq 1\quad (\forall l) \tag{6}\\&\hphantom {\text {s.t.}~}Q_{i, k} \leq Z_{k} \quad (\forall i, \forall k).\tag{7}\end{align*}

From constraint (2), it is required that every component should have at most two edges with other components within DiffSBar. Constraint (3) forces that the system component $c_{i}$ must be counted at most once as a member of DiffSBar. Also, constraint (4) imposes that the moving distance condition $u$ is satisfied when $c_{i}$ in $b_{k}$ is moved from other positions. Constraint (5) verifies that the detection accuracy condition should be met if $b_{k}$ is considered as DiffSBar. And, constraint (6) checks that every $S_{\text {low}}$ has to maintain at least one MTSVEmoBar when a group of DiffSBar are constructed in $S_{high}$ . The constraint (7) confines that if $c_{i}$ is part of $b_{k}$ , then $c_{i}$ should be part of the completed DiffSBar.

SECTION III. Proposed Schemes

To solve MaxDiffSBar problem, we propose three different algorithms: MTS-Initialization, Partial-Shift-Increment, Whole-Shift-Completion. In this section, all of the developed algorithms are specified with their execution procedures and pseudocodes in detail.

A. Algorithm 1: MTS-Initialization

The proposed framework requires the implementation MTS-Initialization method firstly, which accomplishes system initialization of various tasks and settings and also finds as many initial MTSVEmoBar in the initial state where system components are randomly scattered. Then, the MTS-Initialization follows the below procedures.

1. Identify the square-shaped whole MTS area $S$ .

2. Verify $n$ number of system components $C$ including mobile robots and UAVs within $S$ where every component has random positions initially.

3. Validate that all components have different detection ranges where $R = \{r_{1}, r_{2}, \ldots, r_{n}\}$ .

4. Update $C$ as $C'$ and $R$ as $R'$ , respectively.

5. For each component $c_{i}$ , create a list of neighbors if $Euc(c_{i}, c_{j}) \leq r_{i} + r_{j}$ where $c_{i}, c_{j} \in C$ and $r_{i}, r_{j} \in R$ .

6. By applying Edmonds-Karp algorithm [46], we iterate the below steps until there is no additional MTSVEmoBar.

   • Search for a new independent MTSVEmoBar $b_{k}$ from current set of components $C'$ .

   • If a new independent MTSVEmoBar $b_{k}$ is found, add $b_{k}$ into a set of MTSVEmoBar $B$ .

   • The components within the new MTSVEmoBar $b_{k}$ is removed from $C'$ .

1. Divide $S$ into $m$ number of sub-sections where we have $S_{1}, S_{2}, S_{3}, S_{4}$ if $m$ = 4. Then, assign security priority to each sub-section.

2. Return $B$ as the result.

In brief, the motivation of the MTS-Initialization is to supply with the verification of deployed mobile robots and UAVs and their detection ranges, dividing the whole MTS area into sub-sections, assigning discriminative security levels to sub-sections, setting up initial MTSVEmoBar so that the proposed framework operates the essential task of barriers for virtual emotion detection in MTS area. Fig. 4 shows several situations while Algorithm 1 is implemented. Fig. 4(a) depicts an initial state that the components are located randomly in $S$ and then, initial MTSVEmoBar are generated as shown in Fig. 4(b). Also, Fig. 4(c) represents the partitioned state with four sub-sections.

Fig. 4.

Procedures and relevant status of Algorithm 1: MTS-Initialization.

Algorithm 1 MTS-Initialization

Inputs: $S, C, R, n, m$ , Output: $B$

1:

set $B = \emptyset $ ;

2:

identify $S$ ;

3:

verify $C = \{c_{1}, c_{2}, \ldots, c_{n}\}$ ;

4:

validate $R = \{r_{1}, r_{2}, \ldots, r_{n}\}$ ;

5:

$C' \leftarrow C$ ;

6:

$R' \leftarrow R$ ;

7:

create a list of neighbors for each component $c_{i}$ ;

8:

while True do

9:

Search for a new MTSVEmoBar $b_{k}$ ;

10:

set $B \gets B \cup b_{k}$ ;

11:

set $C' \gets C' - \{$ components within $b_{k}\}$ ;

12:

end while

13:

divide $S$ into $S_{1}, S_{2}, S_{3}, S_{4}$ with security priority;

14:

return $B$ ;

Moreover, MTS-Initialization’s pseudocode is explained at Algorithm 1.

B. Algorithm 2: Partial-Shift-Increment

After MTS-Initialization is executed for system initialization, the proposed Partial-Shift-Increment scheme with partial shift strategy is performed with the following steps.

1. Identify barrier members in each sub-section.

2. Decide the high security priority area $S_{high}$ .

3. Calculate cumulative detection accuracy of all barriers in $S_{high}$ .

4. If barriers $b_{full}$ in $S_{high}$ fulfill $t$ , keep those barriers and add them to $D$ .

5. If there exists a barrier $b_{k}$ that does not satisfy $t$ in $S_{high}$ , the below sub-steps are iterated until the barrier $b_{k}$ meets the condition of $t$ .

   • Step 1: Search for the new candidate component $c_{i}$ with the smallest detection accuracy within $b_{k}$ .

   • Step 2: Shift $c_{i}$ with another member $c_{j}$ from another barrier within other non-priority sub-sections $S_{\text {low}}$ if the moving distance of $c_{j}$ is less than $u$ and at least one barrier in should be maintained in all $S_{\text {low}}$ .

   • Step 3: If the barrier $b_{k}$ meets the condition of $t$ , add $b_{k}$ to $D$ . Otherwise, go to Step 1 to find additional component to be replaced.

6. Return the total number of DiffSBar $|D|$ as $\alpha $ value.

The motivation of Partial-Shift-Increment algorithm is that the total number of DiffSBar is ultimately created to fit with the assigned security levels of sub-sections after the successful operation of MTS-Initialization is observed. The involved idea is to search for the shifting match between the system component with the smallest detection accuracy and the movable component candidate so that such a partial match results in possible maximum number of DiffSBar. Fig. 5 portrays several situations when Partial-Shift-Increment approach is executed. Fig. 5(a) depicts a weak point with the low detection accuracy in the initial MTSVEmoBar. In Fig. 5(b), we can see possible candidate components to replace them with weak points if they are satisfied with moving distance condition. And, Fig. 5(c) presents the shifted status by proper candidate components so that the total number of DiffSBar in $S_{high}$ is increased.

Fig. 5.

Procedures and relevant status of Algorithm 2: Partial-Shift-Increment.

Furthermore, Partial-Shift-Increment’s pseudocode is described at Algorithm 2 with formal notations.

Algorithm 2 Partial-Shift-Increment

Inputs: $S, C, R, B, n, m, t, u$ , Output: $|D|$

1:

set $D = \emptyset $ ;

2:

determine the high security priority area $S_{high}$ ;

3:

estimate cumulative accuracy of all barriers in $S_{high}$ ;

4:

if barriers $b_{full}$ in $S_{high}$ satisfy $t$ then

5:

set $D \gets D \cup b_{full}$ ;

6:

end if

7:

while there is a barrier $b_{k}$ that does not satisfy $t$ do

8:

step 1: find a new $c_{i}$ with the smallest accuracy in $b_{k}$ ;

9:

step 2: shift $c_{i}$ with $c_{j}$ from another barrier if the moving distance of $c_{j}$ is less than $u$ and at least one barrier in $S_{\text {low}}$ is maintained;

10:

if step 3: $b_{k}$ meets $t$ then

11:

set $D \gets D \cup b_{k}$ .

12:

else

13:

go to step 1;

14:

end if

15:

end while

16:

return $|D|$ ;

C. Algorithm 3: Whole-Shift-Completion

We develop Whole-Shift-Completion approach whose basic idea is leaving one barrier in the non-event area and relocating all nodes to strengthen the security of the requested event area with high priority. The Whole-Shift-Completion scheme is implemented according to the below procedures.

1. Bring $D$ from Algorithm 2 and accept it as $D'$ of the initial result.

2. The below sub-steps are iterated until there is no new whole shift candidate barrier in other sub-sections $S_{\text {low}}$ .

   • Identify if there exists possible whole shift candidate barrier $b_{k}$ in $S_{\text {low}}$ .

   • Check if $b_{k}$ fulfills both detection accuracy condition $t$ and moving distance limit $u$ for all components within $b_{k}$ .

   • If satisfied, $b_{k}$ is moving to $S_{high}$ .

   • Add $b_{k}$ to $D'$ .

3. Return the total number of DiffSBar $|D'|$ as $\alpha $ value.

Concisely, the motivation of Whole-Shift-Completion algorithm facilitates the maximum number of DiffSBar according to the assigned security priorities in MTS field by satisfying complex scenes of required detection accuracy and bounded moving distance of system elements. The applied idea aims to seek the whole shift candidates and then, the maximum number of DiffSBar is increased gradually whenever the whole shift is processed. Fig. 6 represents various situations when Whole-Shift-Completion scheme is performed. Fig. 6(a) depicts the status of finding whole shift candidates of barriers in other sub-sections $S_{\text {low}}$ satisfying both conditions of detection accuracy and moving distance for those candidates. Also, Fig. 6(b) describes the situation of shifting the whole shift candidates to the high priority security area $S_{high}$ . Fig. 6(c) shows the status after whole shift completion into $S_{high}$ is done by candidates.

Fig. 6.

Procedures and relevant status of Algorithm 3: Whole-Shift-Completion.

Furthermore, Whole-Shift-Completion’s pseudocode is presented at Algorithm 3 in accurate notations.

Algorithm 3 Whole-Shift-Completion

Inputs: $S, C, D, R, B, n, m, t, u$ , Output: $|D'|$

1:

$D' \leftarrow D$ ;

2:

while there is a barrier $b_{k}$ that does not satisfy $t$ do

3:

verify if there is possible whole shift candidate $b_{k}$ in $S_{\text {low}}$ ;

4:

check if $b_{k}$ fulfills both conditions of $t$ and $u$ for every component;

5:

if both conditions are satisfied then

6:

$b_{k}$ has whole-shift to $S_{high}$ ;

7:

set $D' \gets D' \cup b_{k}$ ;

8:

end if

9:

end while

10:

return $|D'|$ ;

SECTION IV. Evaluation of Proposed Schemes

A. Experimental Analysis

In this section, we evaluate the performance of the proposed schemes based on numerical results through extensive simulations with various communication ranges, the number of components, different maritime transportation station sizes, etc. As a system initialization, MTS-Initialization is firstly implemented by $C^{++}$ code which returns the set of IoT-enabled MTS virtual emotion barriers $B$ when the system components with heterogeneous detection ranges are randomly positioned in the maritime transportation area $S$ . Based on the result of MTS-Initialization, two different approaches Partial-Shift-Increment and Whole-Shift-Completion are executed which return the total number of differential security barriers $|D|$ , $|D'|$ as their outputs, respectively. If we specify the execution environment such as system settings, codes and tools, every scheme is executed at various sizes of regular quadrilaterals with the heights and widths including 1000 $\times1000$ , 1050 $\times1050$ , $1100\times1100$ , $1150\times1150$ . The total number of system components is varying from 100 to 250. Also, the minimum detection ranges of system components is between 70 and 120 as well as the interval of random communication range is between 30 and 45. And, the moving distance of system component is limited as 500. The accuracy values among components are calculated depending on distance, communication range and those values are ranging from 0.6 to 1.0 and the cumulative accuracy value is estimated by multiplying the accuracy value in the considered barrier. In addition, it is noted that all numerical results obtained from the proposed approaches represents the average output value of 100 completely different settings. Each setting has different the initial positions of components, the detection ranges, etc.

For the first set of experiments, after MTS-Initialization’s implementation, Partial-Shift-Increment and Whole-Shift-Completion are performed independently in 1000 $\times1000$ area with minimum communication ranges from 70 to 120. When Partial-Shift-Increment scheme is proceeded, the cumulative accuracy of possible active component for the construction of DiffSBar is greater than equal to 0.8 in the targeted sub-section of high priority when the whole area $S$ is divided to four sub-sections $S_{1}, S_{2}, S_{3}, S_{4}$ . Also, if Whole-Shift-Completion algorithm is demonstrated, the whole structured candidates of DiffSBar in other sub-sections except targeted region where its accumulative accuracy value is greater than 0.8 are moved to the high priority security region. And, for such a scene, the moving distance of every component in the candidate barrier is less than 500. Fig. 7(a) shows the result when $n=100$ and Fig. 7(b) presents the output with $n =150$ . Also, Fig. 7(c) depicts the obtained result of $n =200$ and Fig. 7(d) presents the archived value if $n =250$ . As seen in Fig. 7, the performance of Whole-Shift-Completion approach is better than Partial-Shift-Increment approach for the total number of DiffSBar. And, we can verify that the result value increases as the communication range increases. Furthermore, when $n$ value and communication range have greater values, Whole-Shift-Completion approach has much better performance than Partial-Shift-Increment approach.

Fig. 7.

Comparison for the total number of differential security barriers $\alpha $ by different number of system components in $1000 \times 1000$ environment.

When we deliberate on the second group of simulations, after MTS-Initialization is firstly carried out, Partial-Shift-Increment and Whole-Shift-Completion are implemented with $n =100$ and 1000 $\times1000$ region. Similarly, the whole area $S$ is divided into four sub-sections $S_{1}, S_{2}, S_{3}, S_{4}$ and the targeted area with high priority security is selected from those four sub-sections. The second set of simulations focuses on the performance analysis of different intervals of random communication ranges. Fig. 8(a) represents the outcome when the interval of random communication range is 30 and Fig. 8(b) shows the output value in case of the interval of random communication range = 35. And, Fig. 8(c) depicts the gained results when the interval of random communication range is put into the experiments as 40 and Fig. 8(d) shows the performance if the interval of random communication range is 45. As it can be checked in Fig. 8, Whole-Shift-Completion scheme conducts better performance of the total number of DiffSBar than Partial-Shift-Increment method as a whole according to different intervals. In particular, the performance difference between Whole-Shift-Completion and Partial-Shift-Increment more increases as the minimum communication range has bigger value.

Fig. 8.

Comparison for the total number of differential security barriers $\alpha $ by various interval of random communication ranges with $n =100$ in $1000 \times 1000$ environment.

As the third group of experiments, based on the outcomes of MTSVEmoBar by MTS-Initialization, both Partial-Shift-Increment and Whole-Shift-Completion algorithms are carried into execution with $n =100$ . In the third set of simulations, the whole area $S$ is separated with four sub-sections $S_{1}, S_{2}, S_{3}, S_{4}$ and the targeted area with high priority security is chosen from those four sub-sections, too. This group of experiments accounts for various sizes of the whole area, which have 1000 $\times1000$ , $1050\times1050$ , $1100\times1100$ , $1150\times1150$ , respectively. Fig. 9(a) is open to the view of the results in 1000 $\times1000$ and Fig. 9(b) shows the outcome when 1050 $\times1050$ is given. Also, not only Fig. 9 displays the obtained output in case of 1100 $\times1100$ but also Fig. 9(c) represents the results if 1150 $\times1150$ is put into the experiment. As it can be seen in Fig. 9(d), we are able confirm that as a whole, Whole-Shift-Completion scheme achieves better performance than Partial-Shift-Increment scheme depending on different sizes of the whole area. Besides, if the communication range is increasing in the system, Whole-Shift-Completion shows much better performance than Partial-Shift-Increment. For instance, the performance difference between Partial-Shift-Increment and Whole-Shift-Completion with communication range = 120 is greater than the result with communication range = 70.

Fig. 9.

Comparison for the total number of differential security barriers $\alpha $ by different area sizes with $n =100$ .

For the fourth set of simulations, according to the results of by MTS-Initialization, both Partial-Shift-Increment and Whole-Shift-Completion schemes are performed with detection accuracy limit or cumulative accuracy of possible active component for the construction from 70 to 95 in 1000 $\times1000$ area. And, this group of experiments achieves the minimum communication range ranging from 100 to 130. Fig. 10(a) represents the outcomes when $n =100$ and Fig. 10(b) shows the output with $n =150$ for various cumulative detection accuracy. Also, Fig. 10(c) presents the results when $n =200$ and Fig. 10(d) depicts the consequence in case of $n =250$ . As it can be verified in Fig. 10, we demonstrate that Whole-Shift-Completion scheme returns better performance of the total number of DiffSBar than Partial-Shift-Increment method based on the comprehensive results. As the detection accuracy restriction is more relaxed, Whole-Shift-Completion method shows better performance than Partial-Shift-Increment. Then, it is observed that the result value of total number of DiffSBar decreases as the detection accuracy limit increases.

Fig. 10.

Comparison for the total number of differential security barriers $\alpha $ by different number of system components in $1000 \times 1000$ environment.

Finally, for the fifth set of experiments, after MTS-Initialization’s execution, Partial-Shift-Increment and Whole-Shift-Completion are performed with $n =100$ as well as with different detection accuracy ranging from 70 to 95. Similar to above experiments, the whole area $S$ is divided into four sub-sections and the targeted region with high priority security is chosen from those four sub-sections. Essentially, this group of scenes considers different sizes of the whole area $S$ , which become 1000 $\times1000$ , $1050\times1050$ , $1100\times1100$ , $1150\times1150$ , respectively. Fig. 11(a) depicts the results if 1000 $\times1000$ is put into the experiment and Fig. 11(b) shows the outcomes with the area size of 1050 $\times1050$ . Also, Fig. 11(c) indicates the result with the region size of 1100 $\times1100$ and the obtained result of the size of 1150 $\times1150$ is shown in Fig. 11(d). As it can be seen in Fig. 9, we can identify that the performance of Whole-Shift-Completion approach is better than Partial-Shift-Increment approach. Moreover, it is demonstrated that the performance of the total number of DiffSBar drops down as the requirement of detection accuracy goes up consequently.

Fig. 11.

Comparison for the total number of differential security barriers $\alpha $ by different area sizes with $n =100$ .

B. Complexity Analysis for Proposed Algorithms

In this section, we estimate the complexity of the proposed Algorithm 1, 2, 3 and discuss their performances.

First, if we estimate the complexity of Algorithm 1, it creates of neighbors or edges for each system component $c_{i}$ . If it is transformed into graph model, the set of system components $C$ is equal to the set of vertices $V$ and the set of edges is same as the set of edges $E$ . Then, Algorithm 1 searches for MTSVEmoBar within iterations and the process is equivalent to finding of max flow value. So, by Edmonds-Karp algorithm [46], the complexity of Algorithm 1 is $O(VE^{2})$ .

Second, if we calculate the complexity of Algorithm 2, it verifies the high security sub-areas takes $O(1) $ as well as checks all barriers (i.e. $D_{high}$ ) in high security area. Then, within while iterations, Algorithm 2 finds a new system component $c_{i}$ with the smallest accuracy within iterations and the number of iterations for the process is $n$ . And, Algorithm 2 shifts the component and the number of shifts is $n$ . Also, add it to DiffSBar with $O(1) $ . If so, the total number of iterations will be $O(1) + D_{high} + n + n + O(1) $ . Since $O(1) $ and $D_{high}$ are constants, the asymptotic upper bound is $O(n)$ . Hence, the complexity of Algorithm 2 is $O(n)$ .

Third, if the complexity of Algorithm 3 is estimated, it executes iterations to verify if there is possible whole shift candidate from all founded barriers (i.e. $D_{\text {low}}$ ) in low security region. Then, it checks that for every component, the found whole shift candidate fulfills the given conditions of detection accuracy and moving distance bound and the number of iterations is $n$ . Also, Algorithm 3 adds the selected candidate to DiffSBar with $O(1) $ . If so, the total number of iterations will be $D_{\text {low}} + n + O(1) $ . Because $D_{\text {low}}$ and $O(1) $ are constants, the asymptotic upper bound is $O(n)$ . Therefore, as asymptotic upper bound as the worst case, the complexity of Algorithm 3 is estimated as $O(n)$ .

In addition, we compare with existing studies authored by Kumar et al. [47] and Boppana et al. [48] in wireless sensor networks. Although the previous study by Kumar et al. [47] does not deliberate on multiple number of sub-sections with differential security levels in MTS area, virtual emotion, detection accuracy requirement, bounded moving distance of system components. They proposed two polynomial time algorithms to optimally solve the sleep-wake up problem for constructing barriers alternately when sensors are deployed randomly. The first Stint algorithm is proposed to solve barrier coverage problem when sensor lifetime are homogeneous and the second Prahari algorithm is developed for the case that the lifetime of sensors are heterogeneous, different. By Kumar et al. [47], the complexity of Stint algorithm is $O(VE^{2})$ and the complexity of Prahari algorithm is $O(kV^{3} / log(V))$ where $k$ is the required number of barriers. Also, though Boppana et al. [48] does not cover does sub-sections with differential security levels in MTS area, virtual emotion, detection accuracy requirement, bounded moving distance of system components, the problem of finding maximum number non-crossing barriers can be transformed into the MIS (maximum independent set) problem that is NP-hard. And, the MIS problem can be solved by applying existing approximation algorithm of Boppana et al. [48] which has $O(|n| / (log|n|)^{2})$ .

SECTION V. Concluding Remarks

In this paper, we introduced a differential framework, DiffS, which forms differential security barriers for virtual emotion detection in cooperation with a group of mobile robots and UAVs. The proposed DiffS was designed to fit with IoT-enabled maritime transportation systems so as to strengthen security in the requested high priority security section. After MaxDiffSBar problem with ILP formulation was defined, we devised three different algorithms: MTS-Initialization, Partial-Shift-Increment, Whole-Shift-Completion, respectively. Then, after we performed comprehensive experiments with various settings, components and parameters, the detailed discussions were discussed with the comparisons of their performances. As future works, we will study security reinforcement in various shaped target regions such as convex hull, polygon, hexagon, etc. Also, we plan to expand the proposed framework with a consideration of more realistic environment covering SINR (signal to interference plus noise ratio), velocity of the sensors and sensing targets.