https://orcid.org/0000-0002-1522-562X
Figures
Abstract
Private networks have become popular for secure data sharing and anonymous communication in many domains: enterprise environments, military, journalism, telecommunication, healthcare, to name a few. It has been used with or without internet connection. Its primary purpose is to provide confidentiality, bypass unlawful activities, and protect against common threats such as interception, modification, and censorship. In addition, several private network technologies exist to support secure communications. However, they mostly rely on encryption only. The transmitted data is classified into different confidentiality levels. This research presents a smart private network architecture scheme that transmits constraint-based classified packets. The main directive of this work is the proposed constraint. This constraint is meant to enforce that if two packets belong to the same confidentiality level, they can’t be transmitted through the two routers simultaneously. Therefore, the studied problem is an NP-hard problem. This paper presents the following contributions: (i) proposes a new architecture paradigm for outsourcing a constraint-based multi-classified data sharing securely and transmitted through two routers; (ii) introduces several algorithms to prove the feasibility for this NP-Hard problem; and (iii) implements the algorithms solutions using C++ and compares their performance. Different metrics are used to measure the performance of the proposed algorithms. Randomized Longest Transmission time first algorithm scored the best algorithm with a percentage of 73.5% and an average gap of 0.002 according to the experimental results. It is remarkable worthy to note that the execution time of all the algorithms is less than 0.001 s.
Citation: Sarhan A, Jemmali M (2023) Novel intelligent architecture and approximate solution for future networks. PLoS ONE 18(3): e0278183. https://doi.org/10.1371/journal.pone.0278183
Editor: Sathish A.P. Kumar, Cleveland State University, UNITED STATES
Received: July 2, 2022; Accepted: November 11, 2022; Published: March 1, 2023
Copyright: © 2023 Sarhan, Jemmali. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the manuscript and its Supporting information files.
Funding: This work was funded by the University of Jeddah, Jeddah, Saudi Arabia, under grant No. (UJ-21-DR-62). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
1 Introduction
The “communication gap” between the experts who are working on network development and those working on technology development for security purposes has led to a significant lack of both methodologies to manage the complexity of security needs and the flexibility of security methods deployment. Network security design relies on the Open System Interface (OSI) model, which provides protocol standardization, flexibility, and modularity [1] In fact, the Internet revolution which has been developed in the past 20 years, classified computer network development and advancement into several stages [2]. The so-called “Active Networks” programmable functionality started in the 1st stage. In the second stage, open interfaces were developed to communicate between the control and data planes. Finally, Network Virtualization (NV) for better routing flow and the “OpenFlow API and network operating systems (N.O.S.s)” was developed in other stages.
The exponential increase in data production resulted in a need for emerging solutions for data management using artificial intelligence (AI), machine learning (ML), and analytical tools. However, despite the importance of the produced information and their analysis to deal with issues concerning pandemic risks, disease prevention, or climate changes, exposing these data through any stage during their lifecycle becomes a serious cybersecurity concern because of the expandability of the Internet.
Based on TCP/IP protocol suite, IPv4 and IPv6 addressing, the Internet has expanded into a worldwide network (WWW), which has become universally accessed and enabled billions of devices and people to connect, exchange, and share information [3]. However, the anonymous nature of the Internet, including its architectural design, failed to provide a suitable solution to address many security, privacy, and performance issues, leading to a significant increase in cyberattack incidents [3, 4]. Technology virtualization includes Software-Defined Networking (SDN) and Network Function Virtualization (NFV) are considered new approaches for building, designing, and managing future programmable networks to overcome the density of the internet infrastructure.
Recently, a new direction or movement of the Internet has taken place owed to the progress in the wireless network domain and innovative mobile device capabilities. Furthermore, infrastructure less wireless network technology like mobile ad hoc network (MANET) is a decentralized network that does not rely on routers or access points to forward the data; instead, it is being formed from mobile nodes that can be created and joined “on the fly” and forward the data based on network connectivity, and the routing algorithms [5]. Despite the various applications that MANET support, it poses several challenges and is vulnerable to various attacks [6].
On a more advanced level, the commercialization of the Internet and the introduction of new technologies like the fifth generation (5G), transformed the communication architecture or the cyber-physical to provide connectivity to connect people, things, devices, applications, transport, and even cities. However, anything that relies on emerging concepts and technologies like everything IP, everything Data, Long Term Evolution (LTE), and IoT, have brought challenges concerning security, privacy, and trust [7]. For example, nearly 90 percent of the infrastructure has been owned by the private sectors, which brings a concern to safeguard data outsourced or routed by U.S.A military or government organizations. To answer the demand of future computer networks, several experimental networking projects were designed for next-generation networks (NGNs), For instance, the global environment for network innovations (GENI), the PlanetLab, and the project of future Internet design (FIND) program. However, the complexity and weakness of the current network protocols make it difficult to keep up with the rapid growth and advancement in communications and applications. For instance, the system administrators and users have limited knowledge of the networking infrastructure. This, in turn, resulted in the inability to apply security tools to protect the environment due to the complexity and weakness of the current internet network protocols.
Literature has well studied the network packets timing, scheduling, and movements problems. Network Packet scheduler specifies the packets that need to transit and those that need to wait at each time. Several sequential and parallel scheduling algorithm solutions have been proposed to minimize packet routing timing and maximize the queue size [8]. The advancement in innovative communications technologies in various domains has presented a vast range of applications in several areas, such as environmental surveillance, biomedicine, and video security monitoring. Thus additional issues to the network routing problems like latency, energy consumption, and security have emerged. Several routing scheduling algorithms methods, policies, and heuristics have been proposed to deal with issues related to routing security and privacy, optimization, delay, energy consumption, recovery time, and overhead in many modern network technology such as WirelessHART Mesh Networks, Wireless Sensor Networks, Industrial Wireless Mesh Networks, and Wireless Body Sensor Networks [9].
Protecting networks depends on ensuring the following security requirements: confidentiality to protect data from unauthorized users, integrity to protect data from unauthorized modification, and availability to protect data from being damaged or lost. Furthermore, the damage of the communication infrastructures can cause data to be damaged during war or natural disasters such as earthquakes, tsunamis, and floods. Therefore, there is a need for data control solutions in such emergencies [10]. The ongoing evolution of artificial intelligence (AI) technologies makes it possible to create emergency data allocation algorithmic techniques that deal with such incidents as proposed in [11] using the scheduler and router-based window constraints. The window is used by an intelligencer via a scheduler to control the network and create a “static urgent window pass” to reserve a time slot or pause accessing the router when dealing with scheduling problems during data transmission of confidential and urgent data based on given constraints [10, 12]. Failure to provide any security requirements leads the Networks architecture to be prone to numerous cybersecurity attacks such as eavesdropping, sybil, selective, smurf, sinkhole, masquerading, byzantine, location disclosure attacks, blackhole, wormhole, and man-in-the-middle [13].
Access control contributes to the security requirements of securing the network in terms of confidentiality, integrity, and availability (CIA). However, such security requirements pose some limitations in dynamic environments. Therefore, a new generation of access control mechanisms has been demeaned to cope with today’s dynamic digital environments. The classification of information into top-secret, secret, confidential, and unclassified has existed for a long time. Several Multilevel security policy models and systems have been proposed. Several problems and concerns have been pointed out concerning the practicality of MLS. They are summarized as follows. (i) The cost and difficulty of building them; (ii) the need to rebuild several applications to cope with MLS; and (iii)the complexity of the classification of data. With the technological improvements, several variations of traditional and untraditional access control mechanisms have been proposed to safeguard against unauthorized access. These mechanisms are encrypted-based or encryption-independent. Discretionary Access Control (DAC), Mandatory Access Control (MAC), Role-Based Access Control (RBAC), Attribute-Based Access Control (ABAC), and Context-Aware role-based Access Control (CAAC) are all access control techniques and frameworks [14].
The main motive of this research is to advance state-of-the-art research in computer networks by proposing a future network vision that can be highly secured. A major problem is stopping or minimizing data leakages for sensitive outsourced information, which has become a significant problem nowadays. It also proposes a model that is capable to protect data of individuals in particular fields, for instance, during critical coverages for individuals (e.g., Journalists, Media outlets). Furthermore, the model investigates nontraditional methods or techniques existed in state-of-the-art. For example, our method was a reduction of an NP-Hard problem that deals with two machines. This paper aims to propose an intelligent private network architecture that disseminates classified network packets based on the constraint. It also proposes a robust network paradigm that relies on two routers to address critical data privacy issues in particular environments and circumstances. The proposed scheme outsources data securely and privately in a critical environment. The approach has the following advantages: (i) It introduces an idea or vision for a secure future network using intelligent algorithms; (ii) Supports individuals (e.g, Journalists, Media outlets) to securely and privately exchange sensitive information with their hosts; (iii) provides a unique two-router network architecture for transmitting network packets based on a constraint-based classification; (iv) Presents algorithms using known and unknown techniques such as dispatching rules, local insertion search, randomization method, and lifting procedure; (v) Introduces a group of heuristic algorithms that deal with an NP-hard problem and applies it in the computer network area; (vi) Solves the problem in an acceptable optimal time, as it is shown in the result section. The disadvantages of our approach are listed as follows: (i) The two-router problem in our scheme is a reduction of a known NP-hard problem. Thus, solving such a problem using multiple hops could be time-consuming and might require more effort and techniques to heuristically solve it using algorithms with O(n3). (ii) The time complexity to solve the problem relying on multiple hops could be very complicated because using two routers in our scheme problem reduces a known NP-hard problem. (iii) The exact solution for the problem requires a lower bound to be used in a branch-and-bound algorithm in the future; thus, an optimal solution can be given for our problem using the developed algorithm in this paper. Overall, this paper aims to propose a smart private network architecture that disseminates classified network packets based on the constraint.
It includes eight sections presented as follows. First, we introduce the related work in section 2. Then, the studied problem is described in Section3. Third, we present the novel proposed architecture and the different components in Section 4. Next, a detailed description of a novel lifting procedure is presented in Section 5. Fifth, we present the proposed solution algorithms in Section 6. Furthermore, we show the experimental setup and performance comparison between the algorithms in Section 7. Finally, some concluding remarks with reference to the future work are included in Section 8.
2 Literature review
Literature has investigated threats for the transmitted data across all network layers in various distributed computing systems, applications, and technologies. The analysis of the threats showed attacks against one or more of the C.I.A. triad- confidentiality, integrity, availability, including authentications, non-repudiation, and in various emerging and intelligent communications and technologies domains. For example, attacks on wireless mobile ad hoc networks are investigated in [15], attacks on wireless sensor networks [16], and cloud computing environments are discussed in [17]. Furthermore, due to a lack of end-to-end novel security solutions, several attacks have been against evolving technologies, for instance, those depending on artificial intelligence (AI) [18], augmented reality (AR) [19], Software-Defined Networking (SDN) paradigm [20] and Blockchain addressed in [21]. Attacks against new business models and e-health applications presented in [22].
The internet protocols have been viewed as a set of layers or protocol stack described according to the open system’s interconnections (OSI) into a seven-layered network [23]. Several protocols such as IPSec, SSL, and DNSSEC which have been proposed to provide end-to-end security solutions. For example, since routing information is subject to being intercepted or modified when routed through unknown networks, IPSec protocol has been developed to ensure end-to-end encryption for the Internet protocol (IP) user data and traffic.
The geographical distribution of various enterprises, sites and offices worldwide has led to the need for point-to-point or site-to-site private networks and secure connections. Virtual private network (VPN) has become popular for creating a private network to share resources and disseminate data over insecure networks. The secure channels in the VPN use the IPSec protocol. Unlike VPN, Virtual Private LAN services (VPLS) have been designed to control new evolving patterns, such as NFV and SDN. It has been popular for providing multipoint-to-multipoint connectivity, including other features, such as robust security and low operational cost. Still security in VPLS is a big concern [24].
Mobile ad hoc network MANET has been adopted due to its numerous advantages. The routing functionality in MANET is integrated into its nodes. Both topology-based and position-based routing protocols have been adopted in MANET. However, due to its decentralized nature and lack of efficient algorithm, designing routing protocol in MANET has been considered a complex issue [25]. In [26], the authors extended the greedy perimeter stateless routing protocol (GPSR)to enhance the position-based routing protocols for MANET. In addition, they used fuzzy logic to adjust the lifetime of entries in the nod’s neighborhood matrix (IFPE).
The invention of 5G mobile communications and the advancement in computer network architectures, including SDN, NFV, and smart communication wireless devices, has made traditional data management systems unable to handle massive data. Accordingly there is a need to process higher data rates, guarantee lower data latency, and manage big data. To these ends, newer network architecture design and better algorithms embedded with security and decision-making capabilities are required [27]. Furthermore, Network routing should deal with policy compliance and avoid the dependence on algorithmic optimization [3]. For example, they used a scheduler in their scheme [12] to prioritize highly confidential classified packets in circumstances where the guarantee of the transmission of such packets could be uncertain. Furthermore, the authors used a single router with a static window pass [10, 12] to experiment with several proposed heuristics and thus prove the practicality of their work. In addition, in [28], the authors used the scheduler to solve the problem of identical routers into network.
Data are publicly classified into several classes: top-secret, secret, restricted, and public, and others use such other terms like regulatory, public, confidential (highly confidential), and internal. Data classification using security policies has been used in many domains military, business, and healthcare [29]. For instance, a secure data and identity multilevel security outsourcing scheme are proposed in [30].
Multilevel security (MLS) controls the disclosure of data in trusted and unsafe environments. Only authorized individuals can access, modify, or delete data. The current network behavior is static, which makes the network sluggish in unstable network environments (e.g., traffic patterns or topology changes, or link failures)-thus there is a need for a Multilevel security policy that can be adopted under any circumstances [31]. Ali et al. proposed a blockchain-based IoT network multilevel security architecture that provides multilevel protection of data. The scheme uses cipher ChaCha20 and cellular automata to gain more security and randomness. The same authors claimed that their scheme enhances security and protects against all kinds of attacks by providing multiple levels of encryption; however, their scheme is not flexible and cannot minimize the chances of leakages [32]. In [33], the authors proposed a scheme that transmitted the data securely between cloud service and Internet of vehicles (IoV) devices. Their scheme uses an M-tree-based elliptic curve and digital signature algorithm (ECDSA) to provide key management for multilevel security infrastructure. In [34], The authors proposed a MLS scheme that enforced the flow policy of information among the inter-node within the network to minimize chances for attacks. Their scheme enforces the MLS policy on the software-defined networks SDN switches by moving the job to the controller. Unlike the proposed MLS methods, our scheme MLS policy ensures the absence of transmitting an identical level of secure information simultaneously.
Several schemes used reputation systems mechanisms to ensure a trusted routing environment. In [35], the authors proposed a trusted-based routing protocol model that recommends the trusted routing node to improve security. In [36, 37] authors embed a trust-based mechanism in the routing path for routing path scheduling. Other authors used Blockchain and trusted public key protocols [38] to create decentralized inter-domain trusted routing systems and use smart contracts [39] to follow a trusted route to the destination. Detection of malicious nodes using reinforcement learning by automatically discovering the packets number transmitted to node’s neighbor nodes was studied in [40]. In [41], the authors proposed a scheme to ensure the privacy of the source location to maintain safety time. The scheme selects multiple phantom nodes based on a dynamic routing generation process, adds a randomly directed path, and transmits the packets through different phantom nodes to ensure security [42].
Even though, there is a strong need for a multilevel secure data dissemination solution in a military-based environment, not enough research and investment in this domain exist-despite the need to use such a solution in the current era where collaboration between businesses and governmental organizations becomes necessary. Furthermore, even though several access-control mechanisms have been deployed for secure data dissemination [30, 43–45], they are not fully practical in dealing with the multilevel protection of classified big data or data streams needed in a military-based environment. In fact, the current paper proposes a model that relies on two router-based architecture to schedule securely and then disseminate conflict-based multilevel packet security in a critical situation. In addition, other researches related to the representation of the network traffic are developed in [46, 47].
The suggested techniques presented in this paper can be exploited and operated to be adopted to the problems developed in [48–52]. We believe that our approach is important since it provides optimal security due to its multilevel security that minimizes the level of leaked information in case of cybersecurity attacks compared to other approaches. For example, the highly secure dissemination of packets in our approach justifies our important architectural choice of two routers since two packets that belong to the same level of security are prohibited from being transmitted at the same time, and this only can be accomplished in the main time through more than one router. Thus, if an adversary could capture one highly secure packet at one point through one router, it would not be able to capture a second one simultaneously since our architecture promotes transmitting classified packets with multiple levels of security. Additionally, a review of the literature showed the lack of research on this NP-Hard problem, and we were the first to present it in [53]. Finally, we introduced several heuristics that can help reach metaheuristics or an exact solution for the problem in the future. The proposed algorithms in [54–60].
Unlike many researches that focused on solving the problem of exchanging or outsourcing data securely and privately at the application layer and try to solve it using known techniques or traditional methods to protect outsourced information, our innovative approach addresses the problem from a different point of view and study the problem at the network layer and propose heuristics solution reduced from known NP-Hard problem and apply in the network security field. Furthermore, the presented algorithms in [53] were based only on the dispatching rules; however, this paper uses several techniques for the problem, such as dispatching rules, the local insertion search, the randomization method, and the lifting procedure.
3 Problem description
The problem in focus is described as follows. In a private network wherein several files must be transmitted through two routers, it is assumed that each group of files is classified in a confidentiality level denoted by Cli with i = {1, ⋯, nCl} where nCl is the number of confidentiality level. These files will be divided into packets, and each packet related to each file will be classified into the corresponding Cl. The total packets are grouped in the set PT. Thus, we denote npt for the number of packets.
The index of the packet is denoted by j and the packet is denoted by Ptj. The confidentiality level of the packet Ptj is denoted by Clpj. The packet Ptj has an estimated transmission time (Time of Packet Transmission) denoted by tpj. After scheduling the packet j, the cumulative transmission time on the first router Ro1 is denoted by , and on the second router Ro2 is denoted by
. This cumulative transmission time represents the finishing transmission time of packet j.
PT1 refers to the set of packets transmitted through Ro1 and PT2 to the set of packets transmitted through Ro2. Consequently, PT = PT1 ⋃ PT2 and npt = |PT1| + |PT2|.
Once all packets are transmitted, the calculation of the total transmission time on router Ro1 is denoted by Tr1 and on router Ro2 is denoted by Tr2. Therefore, the maximum estimated transmission time for the two routers is given in Eq 1.
(1) Proposition 1 The maximum estimated transmission time for the two routers (Trmax) can be written as detailed in Eq 2.
(2) Proof 1 The cumulative transmission time of the packet j (finishing transmission time of packet j) on the first router Ro1 is
and on the second router Ro2 is
. The maximum finishing transmission time for all packets in router Ro1 is
. The maximum finishing transmission time for all packets in router Ro2 is
. The total transmission time on router Ro1 is Tr1 and on router Ro2 is Tr2. Thus,
and
.
One packet cannot be simultaneously transmitted through the two routers in a fixed time. The objective is to give an algorithm that can minimize the value Trmax respecting the proposed confidentiality constraint presented in this paper. This constraint is to enforce packets belonging to the same confidentiality level to be transmitted through routers simultaneously which means that, in a fixed time interval it is not possible to transmit packets that belongs to the same confidentiality level. Indeed, in the same time interval, the transmission of two packets belonging to the same confidentiality level is not allowed.
The problem of the minimization of the maximum estimated transmission time for the two routers under the confidentiality constraint is an NP-Hard problem as proved in [53].
Example 1 Suppose that a problem of transmission network with npt = 15. The number of confidentiality level nCl is equal to 3. The estimated transmission time tpj for each packet Ptj is illustrated in Table 1.
The confidentiality levels for each packet are given in Table 2. It is noticeable that packets Pt1, Pt9, Pt10, and Pt14 belong to the same confidentiality level Cl1, which means that these packets must not, in any case, be transmitted simultaneously at the same time on the two routers.
The schedule shown in Fig 1 illustrates the scheduling of packets on the two routers without consideration of the confidentiality constraint. This figure shows that Trmax = 129. The schedule is as follows. The transmitted packets through the router Ro1 are {6, 12, 8, 4, 10, 1, 15} and through the router Ro2 the transmitted packets are {7, 3, 13, 5, 2, 14, 9, 11}.
It is worthy to note that this schedule cannot be considered as a feasible solution for the studied problem. Indeed, a feasible solution to the studied problem must satisfy the confidentiality constraint. Two contradictions of the confidentiality constraint have occurred for the schedule illustrated in Fig 1. The packets {6, 7} were transmitted in the same interval even though they belong to the same confidentiality level Cl2. The same holds true with the packets {9, 10} which were transmitted in the same interval even though they belong to the same confidentiality level Cl1.
Now, concerning the constraint proposed in the studied problem, the schedule given in Fig 1 cannot be accepted. For this reason, a feasible solution must be presented. In fact, it is illustrated in the schedule shown in Fig 2. This figure shows that Trmax = 130. The schedule is as follows. The packets {14, 8, 15, 12, 1, 6, 13} are transmitted through router one Ro1 and the packets {2, 7, 5, 11, 4, 3, 9, 10} are transmitted through router two Ro2.
4 Proposed architecture and components
This section details a novel architecture of data transmission into the network. The important advantage of this architecture is adding the component called “scheduler” into the well-known architecture. In addition, a new constraint called “confidentiality constraint” is imposed for the transmission of packets. This constraint precises the confidentiality level required by the administrator or the intelligencer (i.e., an intelligencer is a person that has a very high priority to manage and control the network and each data transmitted through the network. In addition, the intelligencer is responsible for attributing the confidentiality level to each file. As a result, all packets constituting the file will have the same confidentiality level).
We present the following example of the confidentiality levels to clarify the proposed idea.
- Cl1: Very restricted. This level can encompass all highly sensitive data (files) that can affect national or military security.
- Cl2: Restricted. This level can encompass all sensitive data (files).
- Cl3: Confidential. This level can encompass all delicate data (files).
- Cl4: Internal. This level can encompass all non-sensitive data (files) that can’t be disclosed to the public.
- Cl5: Public. This level can encompass all revealed data (files) that may be exposed to the public.
Each confidentiality level Cli encompasses a fixed number of packets. This number is denoted by npi ∀i ∈ {1, ⋯, nCl}.
Proposition 2 The total number of packets is given in Eq 3.
(3) Proof 2 The sum of all packets in each confidentiality level is the total packets npt.
Fig 3 shows the confidentiality level categorization. The confidentiality level Cli has a set of packets ∀ i ∈ {1, ⋯, nCl}.
The novel architecture with two routers that can show the addition of the new component “Scheduler” is illustrated in Fig 4. The proposed architecture is composed of five components. These components are described as follows.
- Data collection: This component is responsible for specifying the files to be sent. It is managed by the intelligencer of the network.
- File categorization: This component is responsible for specifying the confidentiality level. The intelligencer specifies the confidentiality level for each file.
- Scheduler: This component is responsible for solving a scheduling problem for the transmission of packets through the network. It is managed or represented by a scheduler, and the solution to the scheduling problem is selected after running several algorithms, and the best solution will be selected.
- Routers: Two routers are the entities of this component.
- Data Recipient: This component is represented by the receiver of the data.
The novel proposed architecture illustrated in Fig 4 allows manipulating the dispersion and transmission of data.
5 Lifting procedure (LP)
This section describes a new proposed lifting procedure that can be applied to any given algorithm for the studied problem. This application can enhance the algorithm and gives a better result. The idea of this lifting procedure is as follows. Given an algorithm A that solves approximately the studied problem-we denote by Roma the router that has the maximum Trk with k = {1, 2}. We denote by Romi the router that has the minimum Trk. The lifting procedure role is to search the first packet scheduled in Roma and remove it to Romi at the last position to be the last packet scheduled in Romi. This gives a new schedule for the studied problem. In fact, a new value of Trmax must be recalculated, and the best solution must be chosen.
Example 2 Assume that the number of packets npt = 15 and the number of confidentiality levels nCl=3. Table 3 presents the distribution of tpj for each packet Ptj. This example shows the resulting schedule before and after applying the lifting procedure.
Fig 5 illustrates the schedule before applying the lifting procedure for Example 3. This figure shows that in Ro1 the packets {14, 5, 1, 6, 11, 3} are transmitted and in Ro2 the packets {10, 12, 15, 7, 8, 2, 13, 9, 4} are transmitted. For this schedule Trmax = 192.
Fig 6 illustrates the schedule after applying the lifting procedure in Example 3. This figure shows that the packets {14, 5, 1, 6, 11, 3, 10} are transmitted through Ro1 and the packets {12, 15, 7, 8, 2, 13, 9, 4} are transmitted through Ro2. For this schedule Trmax = 175.
It is clear from Figs 5 and 6 that the lifting procedure gives a better remarkable result. Indeed, for the schedule before the using lifting procedure of this example, the total time is Trmax = 192 compared to the result after applying the lifting procedure, which is equal to Trmax = 175. So, the difference is 17 units.
6 Proposed algorithms
This section presents detailed instructions to show the functionality of twelve algorithms developed to solve the studied problem. The algorithms are based on the dispatching rules, the local insertion search, the randomization method, and the proposed lifting procedure. The first and second algorithms are based on the dispatching rules using the non-decreasing order and the non-increasing order algorithm. The third algorithm uses a local insertion search approach, and the fourth and the fifth algorithms use a randomization method. The sixth algorithm is based on the critical confidentiality level in which detailed information is presented about the critical confidentiality level. Finally, the six remaining algorithms are lifting of all six presented algorithms.
6.1 Longest transmission time first algorithm (LTF)
This algorithm is based on selecting the packet that has the longest estimated transmission time. The selected packet will be transmitted through the most available router. The transmission which is-based on the latter selection is continued until all packets are transmitted.
Proposition 3 The complexity of the LTF algorithm is O(nlogn).
Proof 3 To sort packets, a Quicksort algorithm is applied. As known, Quicksort’s time complexity is O(nlogn). After that, each packet is assigned to a selected router which takes O(n) operations for all packets. So, the LTF’s time complexity is O(nlogn).
Example 3 describes the scheduling of the packets on the two routers following LTF algorithm.
Example 3 Assume that the number of packets is npt = 8 and the number of confidentiality levels is nCl = 3.
Fig 7 illustrated the obtained schedule after applying LTF algorithm. The obtained sequences after applying LTF are {6, 4, 8} on Ro1 and {1, 3, 5, 7, 2} on Ro2. This schedule gives the values tr1 = 66 and tr2 = 54 with a total estimated transmission time Trmax value of 66.
6.2 The smallest transmission time first algorithm (STF)
This algorithm is based on selecting the packet that has the Smallest estimated transmission time. The selected packet will be transmitted through the most available router. The transmission based on the latter selection is continued until all packets are transmitted.
Proposition 4 The complexity of the STF algorithm is O(nlogn).
Proof 4 To sort packets, a Quicksort algorithm is applied. As known, Quicksort’s time complexity is O(nlogn). After that, each packet is assigned to a selected router which takes O(n) operations for all packets. So, the STF’s time complexity is O(nlogn).
Example 4 describes the scheduling of the packets on the two routers following STF algorithm.
Example 4 For this example, we choose to apply the STF algorithm in the example detailed in Table 4. Fig 8 shows the obtained schedule after applying STF algorithm. The obtained sequences after applying STF is {5, 8, 1, 6} on Ro1 and {2, 7, 4, 3} on Ro2 this given a total transmission time Trmax value of 64.
Based on Example 3 and 4, the results are Trmax = 66 and Trmax = 64 by applying LTF algorithm and STF algorithm, respectively. Therefore, for the instances in Table 4, the result obtained by STF is better than the one obtained by LTF. This remark is not general. This means that the result cannot be the same for all the instances.
6.3 Search, test, and insert algorithm (STI)
First, we have to introduce the definition of the idle-time in a schedule.
Definition 1 The idle-time is a slot time or interval time when there is no packet transmission.
Based on the definition-above, this time interval is not exploited and can give a bad result for the scheduling problem on routers. Therefore, in this subsection, the algorithm tends to avoid idle-time and minimize the number of idle-time in routers by inserting packets in these time intervals. Hereinafter, the set of idle-time is denoted by IT1 and IT2 in the first router and the second one, respectively. ni1 and ni2 denote the number of the idle-time in Ro1 and Ro2, respectively. Therefore, and
.
The SI algorithm’s first step is to choose the type of sort order of the packets. There are two types of sort orders packets available to be applied. The first one is the non-decreasing order of the estimated transmission time of the packets, and the second is the non-increasing order of the estimated transmission time of the packets.
The first idle-time or
is obtained after the start of scheduling the packet on the two routers. ptj must be tested to insert an unscheduled packet in the obtained idle-time. If there is no possibility to schedule any unscheduled packet, the packet ptj is scheduled, and an idle-time is provoked. Then, the same instructions are called until all packets are scheduled.
Hereinafter, the functions that sort the elements of a given list Li in the increasing order and decreasing order are denoted by InS() and DcS(), respectively.
In algorithm 1, we present an illustration of the search and the insertion packets in the idle-times when the InS is applied (SIPI procedure).
We denote SDI() for the function that searches and determines the idle-times when a packet ptj is selected to be assigned. This function updates the ni2 and ni1 values.
We denote ST() for the function that returns the starting time of the obtained idle-times for the scheduled packets.
We denote PIS(r) for the function that searches the possibility of scheduling the packet ptj on the router r. This function returns 1 if it is possible to schedule the packet ptj, otherwise it returns 0.
Algorithm 1 Procedure (SIPI)
1: Call InS(PT)
2: Set ni1 = 0 and ni2 = 0
3: for (j = 1 to npt) do
4: Set test1 = 0 and test2 = 0
5: Call SDI()
6: for (k = 1 to ni1) do
7: Call ST()
8: if (PIS(1) = 1) then
9: Set test1++
10: calculate
11: end if
12: end for
13: for (k = 1 to ni2) do
14: Call ST()
15: if (PIS(2) = 1) then
16: Set test2++
17: calculate
18: end if
19: end for
20: if (test1 ≠ 0 OR test2 ≠ 0) then
21:
22: end if
23: end for
24: Calculate Trmax
25: Return Trmax
The SIPI procedure is functioning as follows. Firstly, we call the procedure InS() applied on all packets. The numbers of idle-times ni1 and ni2 are initialized to 0. A loop from 1 to the number of packets is applied to schedule packets in Ro1 and Ro2. This loop is described from instruction 3 to 23. For each packet (for each value of j), we Call SDI() (Instruction 5) and we loop from 1 to the number of idle-times in Ro1 trying to insert the packet j. If the insertion can be feasible, so we calculate , otherwise a test for the next idle-time will take place (Instructions 6–12). After that, we loop from 1 to the number of idle-times in Ro2 trying to insert the packet j. If the insertion can be feasible, so we calculate
, otherwise a test for the next idle-time will take place (Instructions 13–19). Finally, the minimum cumulative time will be picked (Instructions 20–22).
The algorithm of the search and the insertion of the packets in the idle-times when the DcS is applied uses the same instructions in Algorithm 1, but it replaces InS(PT) by DcS(PT). This algorithm is denoted by SIPD()
Now, the instructions of the search and insert algorithm (STI) are illustrated in Algorithm 2.
Algorithm 2 Search and insert algorithm (STI)
1: Set C1 = SIPI(PT)
2: Set C2 = SIPD(PT)
3: Determine Trmax = min(C1, C2)
4: Return Trmax
The Search and insert algorithm (STI) is functioning as follows. We call SIPI(PT) and SIPD(PT). The best value is picked.
Proposition 5 The complexity of the STI algorithm is O(n2).
Proof 5 To sort packets, a Quicksort algorithm is applied. So InS(PT)’s and DcS(PT)’s time complexities are O(nlogn). Then, the SDI() function takes n2 comparisons so that a quadratic complexity O(n2). The ST() function has constant complexity. Therefore, SIPI(PT)’s time complexity is O(n2) and the same for SIPD(PT) algorithm. So overall, the STI’s time complexity is O(n2).
6.4 Randomized Longest Transmission time first algorithm (RLT)
Firstly, we sort all packets according to the decreasing order of their estimated transmission time. Now, we schedule the first-longest estimated transmission time with probability β and the second-longest estimated transmission time with probability 1 − β. In practice, the value of β is equal to 0.3.
We denote SWP() for the procedure that swaps two packets given as inputs.
The instructions described in Algorithm 3 show the functionality of RLT algorithm.
Algorithm 3 Algorithm (RLT)
1: Call DcS(PT)
2: for (it = 1 to 500) do
3: for (j = 1 to npt − 1) do
4: x = 1 + rand()%100.
5: if(x < 30) then
6: SWP(PT, j, j + 1)
7: end if
8: calculate
9: calculate
10: if () then
11: Ro(j) = Ro1
12: else
13: if () then
14: Ro(j) = Ro2
15: end if
16: end if
17: Calculate Tcj
18: end for
19: if (j = npt) then
20: Set j++
21: Goto Step 8
22: end if
23: Calculate
24: end for
25: Calculate
26: Return Trmax
The randomized longest transmission time first algorithm (RLT) is functioning as follows. Firstly, we call DcS(PT) (Instruction 1) to sort all packets according to the decreasing order of their estimated transmission time. After that, an iterative loop is applied 500 times (Instruction 2) to randomly choose the packet that will be scheduled. Indeed, for each iteration, a loop of npt − 1 will take place (Instruction 3) and for each packet, a random generation of a number between 1 and 100 will be applied (Instruction 4). If this number is less than 30 (Instruction 5) then we swap the packets j and j + 1 (Instruction 6). We schedule the selected packet on the most available router (Instructions 8–17). Next, the last remaining packet will be scheduled (Instructions 19–21). After that, is calculated (Instruction 23). After the termination of all iterations, the minimum value of Trmax is determined (Instruction 25).
Proposition 6 The complexity of the RLT algorithm is O(nlogn).
Proof 6 As mentioned above, the Quicksort algorithm is used to sort packets. So DcS(PT)’s time complexity is O(nlogn). Then, each packet is assigned to a selected router which takes n operations. Since the randomize function has a constant complexity, the RLT’s time complexity is O(nlogn).
6.5 Randomized smallest Transmission time first algorithm (RST)
This algorithm is like RLT but instead of DcS(PT) we use InS(PT). Then, the RST’s complexity time is O(nlogn).
6.6 Critical confidentiality level algorithm (CCL)
Firstly, we define the critical confidentiality level. The packets having the same confidentiality level Cli are grouped in a set denoted by PTi with i = {1, ⋯, nCl}. The sum of the estimated transmission time of all packets in PTi is denoted by Sti.
Definition 2 The critical confidentiality level denoted by C is the confidentiality level that has the maximum Sti ∀i = {1, ⋯, nCl}.
Definition 3 The fictive packet denoted by FPi is a new proposed packet with the estimated transmission time Sti ∀i = {1, ⋯, nCl}.
Proposition 7 The number of the fictive packet is nCl.
Example 5 Suppose that the estimated transmission time and the confidentiality levels distribution for each packet are the same given in Table 1.
Table 5 illustrated the generation of the fictive packets. The estimated transmission time of the fictive packets FP1, FP2, and FP3 are 87, 72 and 75 respectively.
Hereinafter, the function DFP() is developed to calculate the total estimated time of each confidentiality level and to determine the FPs.
The instructions of CCL are illustrated in Algorithm 4. The complexity of this algorithm is O(nlogn).
Algorithm 4 Critical confidentiality level algorithm (CCL)
1: Call DFP(PT, Cl, nCl)
2: Call DcS(FP)
3: for (k = 1 to nCl) do
4: Calculate
5: Calculate
6:
7: end for
8: Calculate
9: Return Trmax
The critical confidentiality level algorithm (CCL) is functioning as follows. Firstly, we call DFP() and DcS (Instructions 1–2). After that, a loop from 1 to the number of confidentiality level will take place to determine and
(Instructions 4–5). The minimum value will be stored in
(Instruction 6). Finally, Trmax is calculated (Instruction 8).
Proposition 8 The complexity of the CCL algorithm is O(nlogn).
Proof 7 The complexity of DFP function is O(n). As mentioned above, the Quicksort algorithm is used to sort packets. So DcS(FP)’s time complexity is O(nlogn). Then, each packet is assigned to the most available router which takes O(n) operations. So, the CCL’s time complexity is O(nlogn).
6.7 Lifting algorithms
All algorithms proposed previously can be enhanced by applying the lifting procedure LP defined in Section 5. The lifting algorithm of LTF, STF, STI, RLT, RST, and CCL will be ,
,
,
,
and
, respectively. Since LP’s time complexity is O(n), then all lifting algorithms maintain the same complexity class proven above.
7 Experimental results
The experimental results and the statistical analyses are detailed in this section. The proposed algorithms are coded in C++. The computer running all developed programs has the characteristics for the processor Intel(R) Core (TM) i5–1035G1CPU @1.00GHz and for the memory 8GB RAM.
7.1 Problem instances
To measure the performance of the proposed algorithms, it is mandatory to test them on several instances. The different classes of instances depend on how the generation of the estimated transmission time tpj will be. In this paper, we opted for the uniform distribution to generate all instances. This distribution is denoted by U[s, e], with s being the starting value of tpj, and e the ending value that can’t be exceeded. Four different classes are developed as follows:
- Class A: tpj in U[1, 30].
- Class B: tpj in U[10, 30].
- Class C: tpj in U[1, 50].
- Class D: tpj in U[20, 50].
The number of packets npt is varying in {15, 25, 45, 65, 90, 110}. The number of confidentiality level nCl is varying in {3, 5, 7, 9}. For each npt value all nCl values are tested. For each npt, nCl, and Class, 10 instances are given. In total (6 × 4 × 4 × 10) = 960 instances are generated and tested. It is worthy noting that the confidentiality level Clpj for a packet ptj is generated uniformly between [1, Clpj].
7.2 Metrics
The experimental study will only be important after having measured the performance via measurement metrics in order to be able to interpret them afterward. The metrics used in this paper to measure the performance of the proposed algorithms are as follows:
- A+: best returned value of the Trmax after the execution of all algorithms.
- A: returned value of Trmax by the studied algorithm.
- Pr: percentage of instances when A+ = A.
-
.
- AvG: average of Gp for a group of instances.
- AT: average execution time in seconds. When this time is less than 0.001 s the symbol “-” is placed.
7.3 Discussions
In this subsection, a discussion of the experimental results is presented. Firstly, an overview of Pr, AvG, and AT for all proposed algorithms is described. Next, the impact of applying the lifting procedure is illustrated. A comparison of the average gap AvG for all algorithms according to the number of packets npt, nCl, and Class is discussed.
Table 6 presents the overview of Pr, AvG, and AT for all proposed algorithms. It shows that the best algorithm that gives the highest percentage of 73.5% is . The average obtained gap for this algorithm is 0.002. It is remarkable in this respect that all the running times for all algorithms are less than 0.001 s. This proves that the proposed algorithms give a result in a very impressive time. The second best algorithm is RLT with a percentage of 72.8% and an average gap of 0.003.
Now, we compare the best algorithm given in literature which is MDETA as detailed in [53] with the best-proposed algorithm . We denoted by MV the minimum obtained between
and MDETA after running all the 960 instances. The results show that
reaches MV value in 91% of instances, while MDETA reaches the MV value in only 41% of instances. This proves that the proposed algorithm
is the best algorithm compared with the results in the literature.
Table 7 presents the impact of applying the lifting procedure. This table shows that the lifting procedure gives a better result for the algorithms RLT and CCL.
Each tuple (npt), nCl, Class is denoted by the variable Tu. For the instances given in this experimental results, Tu = {1, ⋯, 96}. The first value of Tu is 1 and is represented by the tuple (15, 3, 1). The last value of Tu is 96 and is represented by the tuple (100, 9, 4). Fig 9 illustrated the variation of the average gap values when Tu changes for algorithm . This figure shows that the remarkable peaks are recorded for Tu = {4, 36, 68} which represented the tuples (15, 3, 4), (45, 3, 4), and (90, 3, 4) respectively. The average gap of 0.012 is obtained when Tu = {4, 68}. However, when Tu = 36 the average gap is equal to 0.011.
Table 8 compares the average gap AvG for all algorithms according to the number of packets npt. It shows that the minimum average gap AvG of 0.001 is reached for the algorithm when npt = 25. However, this minimum AvG value is reached for algorithm
three times when npt = {65, 90, 110}. It is noted that, for all algorithms excluding RLT and
, the average gap AvG decreases when the number of packets npt increases. The maximum average gap of 0.093 is obtained by algorithm STF when npt = 15.
Table 9 on the other hand, compares the average gap AvG for all algorithms according to the number of confidentiality level nCl. The minimum reached average gap AvG of less than 0.001 is recorded for algorithm when nCl = 9 and for algorithm RLT when nCl = 9. In addition, the second best average gap AvG of 0.001 is reached for algorithm
when nCl = {5, 7} and for the algorithm RLT when nCl = {5, 7}. The maximum average gap of 0.063 is obtained by the algorithm STF when nCl = 3.
Table 10 presents the comparison of the average gap AvG for all algorithms according to the different classes Class. For the best algorithm, the minimum average gap of 0.001 is obtained when Class = {1, 3}. However, for Class 2 the average gap is equal to 0.002, and for Class 4 the average gap is equal to 0.004. Finally, the maximum average gap of 0.056 is obtained for Class 3 by the algorithm STF.
8 Conclusion and prospects
8.1 Conclusion
This research studied the problem of scheduling multilevel classified network packets on two routers based on a constraint. We proposed an architectural paradigm that can be deployed for a private network. The paradigm can be used for the secure dissemination of classified data in a military-based environment. This is a known NP-hard in the strongest sense.
We proposed six heuristic algorithms and their enhancements versions using the lifting procedure. The proposed heuristics are LTF, STF, STI, RLT, RST, and CCL. So, in total, we proposed twelve algorithms. We compared the proposed algorithms’ average gap based on the number of packets npt, nCl, and Class. Our observation based on the performed experimentation indicates that algorithm performed the best, recording a percentage rate of 73.5%, and an average gap of 0.003. The second best algorithm in line is RLT. RLT percentage rate was 72.8%, and the average gap was 0.002. The lifting procedure gave the RLT and CCL algorithms a better result, and the average gap decreases for all algorithms, excluding
, and RLT, when the number of packets npt increases. We also noticed that the minimum reaches average gap AvG of less than 0.001 according to the number of confidentiality level nCl was for algorithm RLT when nCl = 9.
8.2 Prospects
Future work will be based mainly on five directives. The first directive is meant to enhance the proposed algorithms using several meta-heuristics by calling the proposed algorithms the initial solution. The second directive is to develop a lower bound and an exact solution for the studied problem compared with the obtained results. The third directive is to elaborate an extension of the studied problem by considering the problem when the number of routers exceeds 2. The fourth directive is to employ supervised machine learning classification to intelligently label and then transmit the network packets through three or more routers. The last directive is the simulation of the proposed network and algorithms in a real-life scenario with demonstration and testing in real hardware and the investigation of multilevel data security using multi-agent systems.
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