Research Article  Open Access
Yiwei Liao, Guosheng Zhao, Jian Wang, "Autonomous Cognitive Model and Analysis for Survivable System", Mathematical Problems in Engineering, vol. 2020, Article ID 3618284, 11 pages, 2020. https://doi.org/10.1155/2020/3618284
Autonomous Cognitive Model and Analysis for Survivable System
Abstract
The research on autonomous recognition mechanism for survivability has vigorously been growing up. A method of autonomous cognitive model and quantitative analysis for survivable system was proposed based on cognitive computing technology. Firstly, a cognitive model for survivable system with crosslayer perception ability was established, a selffeedback evolution mode of cognitive unit based on monitordecideexecute loop structure was improved, and a selfconfiguration of cognitive unit is realized. Then, combined with the cognitive state transition graph, the analysis of cognitive performance for survivable systems based on dynamic cognitive behavioral changes was constructed. Finally, the cognitive processes of survivable system were described by using formal modeling. Simulation validated the influence degree of test parameters on system survivability from two perspectives of the probability of intrusion detection systems vulnerability and attacks detected. Results show that enhancing the rate of monitoring actions change and the rate of performing actions change obviously improved the cognitive performance of survivable system.
1. Introduction
Survivability is a hot topic in the research on the nextgeneration Internet security. According to Westmark [1] and Ellison [2] definition, survivability can be illustrated from three properties: resistance, recognition, and recovery. Among them, recognition reflects the system’s autonomous cognition of its own survival situations and securities of the scene and environment. Current research focuses more on the definition of survivability [1, 2], quantitative and qualitative evaluation [3–5], formal description [6–8], trusted protection [9], recovery [10], and other topics in resistance and recovery. But the research on recognition has just begun and is growing.
At present, consensuses on the research of survivability mechanism have been achieved at home and abroad as follows. Recognition refers to the ability that the system possesses to “know” and “feel” the current system’s survival situation [11]. Survivabilityoriented recognition gives priority to the perception and cognition of the security status of the whole system environment, which can be regarded as the identification of basic key services’ decline in survivability and of the attack and intrusion event sets [12]. Recognition means the system’s response and adaptability when systems face malicious intrusion [13], which can reflect systems’ ability to assess its own security status and surrounding working environment, which can be analyzed from its recognition rate of security incidents and the recognition time of nonsecurity incidents. Recognition can be achieved by constraining reference thresholds of cognition parameters, while autonomy can be achieved by the central control process of the autonomous recognition unit [14]. Recognition can be obtained by establishing a hierarchical perception model and making the policy library drive the selfmanagement mode of the monitordecideexecute (MDE) loop structure [15]. Cognitive Computing is a summary of the characteristics of the nextgeneration intelligent Internet’s core concepts [16]. Cognitive computing in the era of big data is approaching cognitive science, with the abilities of selflearning, selfadaptation, and selfperception to realize the humanbrainlike recognition and judgment. In this paper, based on previous survivability researches, an autonomous cognitive model of survivable system is raised, and the model is formalized by using semiMarkov stochastic process algebra [17, 18], which provides theoretical guidance for the study of survivable system’s cognitive ability.
2. Autonomous Cognitive Model
The system’s cognitive needs are mapped to the dynamic selection of multiobjective cognitive results at multiple cognitive levels. Meanwhile, the crosslayer perception is used to obtain the autonomous reasoning, dynamic decisionmaking, and resource reallocation of survivable systems, and to realize the selfadaptation to dynamic changes of the cognitive needs and environment security. In addition, cognitive model should reach a balance between formal description and cognitive abstraction, so it can not only accurately describe and reflect the system’s recognition, but also facilitate reasoning, thus providing theoretical support for the study of cognitive ability of survivable system.
2.1. CrossLayer Recognition
According to different emphasis on cognitive process, cognitive needs, and cognitive elements, the survivable system can be divided into three cognitive layers, namely, access cognitive layer, network cognitive layer, and service cognitive layer, as shown in Figure 1.
Access cognition layer reflects the recognition of the communication capability of available transmission channels, which supports protocol conversion and adaptation of various available channels, and achieves high reliable information transmission through the recognition of channels’ communication capability.
The network cognitive layer shows the unified cognition of cognitive specifications in the cognitive process and goals of cognitive needs. It can realize dynamic reconfiguration and planning constraints of cognitive network resources.
The service cognitive layer reflects the recognition of the matching ability of providing Internet resources required for applications and users. It can serve high QoS service in complex environment, where massive, incomplete, or even malicious service scenarios exist.
2.2. SelfFeedback Mode of Cognitive Units
The cognitive unit structure is similar to Agent in the traditional sense, the basic unit of the realization of cognitive model [19–21], which is also the symbol of the autonomous cognitive ability of survivable system. With the selffeedback ability added on the basis of the existing cognitive unit structure, an improved cognitive loop structure is achieved as shown in Figure 2. This structure is a selffeedback evolving structure driven by the selfconfiguring strategy library of cognitive elements (MDE: MonitorDecideExecute), which can adjust behaviors, topology, and service parameters with the changes of working environment and task objectives inside and outside the survivable system. Apart from the function of perceiving contexts of normal network events, the structure can also deal with internal and external security threats to enable survivable systems to independently adapt to environment and demand changes.
The selffeedback mechanism of cognitive unit is shown in Figure 3, which includes local, domainlevel, and global feedbacks. Each layer is composed of several cognitive units to achieve global, domain, and local cognition of the system’s cognitive behaviors. Results of local feedback can obtain the local optimal solution to the goal of cognitive needs; global feedback can coordinate the feedback results at domain and local levels and obtain the global optimal or suboptimal solution.
Cognitive units can obtain selfconfiguration of cognitive elements with a selffeedback mechanism. There are two cases:
2.2.1. Preset SelfConfiguration
When matchable strategies are found in existing strategy libraries, the configuration strategy in the preset cognitive rule set will analyze and reason the system, as shown in Figure 4.
2.2.2. Acquired SelfConfiguration
When matchable strategies cannot be found in strategy library, effective rules achieved after acquisition will be stored as acquired rules in the configuration strategy library, as shown in Figure 5.
3. Cognitive Process of Formal Modeling
In order to formally describe the transition between different states of the system under attacks, faults, or accidental failures, and to better understand the dynamic evolution process of the survivable system’s survival situations, a cognitive survival state transition diagram [14] is introduced, as shown in Figure 6.
The tool Version v25 of the PEPA Eclipse Plugin [22] of the Computer Science Foundation Laboratory of the University of Edinburgh is used to simplify the calculation process. The formal description of the cognitive survival state for the survivable system in Figure 6 is as follows:(i)Intruder: = (searching, h). Attack;(ii)Attack: = (starck_attack, p). (attack, k). Attack + (starck_attack, g). Intruder;(iii)General: = (attack, z1). Compromised + (failing, z2). Compromised + (error, z3). Compromised;(iv)Compromised: = (probe, w1). Detection + (mask, w2). General;(v)Detection: = (start_probe, L1). (emergency1, p1). SelfDestruction; + (start_probe, L2). (healing, L3). SelfHealing;(vi)SelfHealing: = (start_healing, L3). (sealheaking, s1). General + (start_healing, L4). (emergency2, p2). SealDectruction + (strat_healing, L5). (selfhealing, s2). SelfHealing;(vii)SelfDestruction: = (start_destroy, L6). (destroy, delta: L (s)). (backup, s3). General
The parameters and their meanings are shown in Table 1.

The cognitive model of survivable systems can be formalized as a quintuple form (Mde, Objects, Domain), where Mde = Mde_{1}, Mde_{2}, ... Mde_{m}} represents the resource constraint sets of m cognitive units, C = C (Mde_{i}) represents the cognitive sublayer at layer j, including i cognitive unit resources; Objects = {Object_{1}, Object_{2}, ..., Objects} is a set of cognitive needs’ objectives. The single objective Object_{k} is associated with the i^{th} cognitive sublayer C_{j} = C (layeri) and satisfies the mapping function : Object_{k}⟶C_{j}. If there are multiple cognitive needs objectives in a cognitive sublayer, it can be expressed by a union set: Object_{s1}Object_{s2}…Object_{sq}; Domain represents the set of cognitive domains, and each subnet i is regarded as Domain Domain_{i}; = {_{1}, _{2}, L, _{n}} i is the set of action decision result functions.
Survivable systems provide key services to the outside world, and users request services. Therefore, from the perspective of service supply, the survivable system is modeled as two ends: User and Server. The User end can be represented as process. The formal description of user end is(i)Monitor = (monitor, m). Decide;(ii)Decide = (decide, r1). Execute + (uncertain, r2). Learn;(iii)Learn = (learning, r3). Decide;(iv)Execute = (execute, r4). Monitor + (service1, s1). Monitor + (servce2, s2). Monitor +...+ (servcet, st). Monitor
And a model for Server end is made, objective kObjects, and the process of Server end is represented as , where iDomain, jC (layer_{i}), which satisfy :k⟶j. For different Domain_{i} processes, the rate and number of action changes are different. Therefore, the cognitive process can be shown as {service^{k}}
And service is the collection of all service interactions. For all the cognitive needs of the system, the formal description of server end is Modelcognitive = {  (k) = User  {monitork, executek} Sever }, kobjects, j{C (layer1), C (layer2), ..., C (layerp), i Domain
4. Quantitative Analysis
The PEPA Workbench and Eclipse Plugin cognitive tool is used to quantitatively analyze the model of survivable system, and the quantitative analysis results are obtained from the perspective of steadystate probability.
4.1. Solution of SteadyState Probability
For SMPEPA, if any component P satisfies the formula: , will be called as the derivation of , and the collection will be the collection of all derivations of P. The state space X_{s} is the collection of all nodes of the derivative graph of SMPEPA, and SMP corresponding to SMPEPA is built: {X, T} = {X_{n}, T_{n}, n = 0, 1, 2, …}, where, X_{n}X_{S}, and when m = n = l = 1, we get
Attack’, Failure’, Accident’, General’ are derivations of component Attack, Failure, Accident, General, respectively. Q (t) of SMP satisfiesp_{ij} = P{X_{n} _{+} _{1} = j, X_{n} = i} represents the state transition rate between i, j; H_{ij} = P{T_{n} _{+} _{1}−T_{n} ≤ t  j = X_{n} _{+} _{1}, i = X_{n}} represents the distribution probability obeyed by action change rates between i and j.
The stablestate probability of Markov can be obtained after the following calculations [23]:
Let X_{S} be any state space and let the corresponding Markov Chain, P = (p_{ij}) be a state transition matrix:
After doing reduction of the model, when the delay of action obeys the exponential distribution, the probability of transition from state α to state l is p_{al} = , where is the delay parameter of actions. And when the delay time parameter obeys the general distribution of action d, because its priority is higher than other actions, the probability of transition to the determined state q is 1, and the probability of transition to the rest is 0.
Therefore, the steadystate rate of embedded semiMarkov Chain satisfies = (V_{G}, V_{C}, V_{D}, V_{SH}, V_{SD}) is a stationary probability vector embedded in semiMarkov Chain.
When the duration of behaviors in SMPEPA model obeys exponential distribution, the solution of the model can be transformed into solving the duration Markov Chain corresponding to PEPA. Assuming that the steadystate probability distribution of duration Markov chains is , soπ = {π_{1}, π_{2},…} is the steadystate probability vector.
4.1.1. State Transition Matrix
Because a survivable system application scenario for the corresponding goal is different, its internal and external environment are also different; at the same time, it is limited by many constraints, etc., so according to different application scenario for the conditions for survival systems can be divided into five states: normal survival state (general), compromise survival state (compromised), cognitive detection state (detection), the recovery state (selfhealing), and selfdestructive state (selfdestruction). From the state set, the state space X = {G, V, D, SH, SD} can be obtained, and then the DTMC chain, just an example, can be obtained, as shown in Figure 7.
The abovementioned parameters’ probability values are shown in Table 2.
 
The state transition matrix P. 
4.1.2. Quantification of Evaluation Indicators
Based on the state transition matrix P, the corresponding relationship between the evaluation index and the state transition probability is established [15]: Recognition: p1, TC⟶G Resistance: p1 + (1−p1) p2, TC⟶G, TC⟶D Recovery: 1−p3−p4, TSH⟶G Reliability: 1−πSD
Among them, TC ⟶ G means the time interval between threat detection and threat processing; TC ⟶ D means the time interval of resisting invasion or attack; TSH ⟶ G is the time interval of system selfrecover; πSD is the steadystate probability of system in selfdestructive state; T_{C ⟶ G}, T_{C ⟶ D}, T_{SH ⟶ G} can be obtained from the actual operation of survivable systems through bypass network monitoring tools.
4.1.3. Solution of Approximate SteadyState Probability
According to the steadystate distribution value of the steadystate rate embedded in semiMarkov Chain, the five calculating formulas of steady states are as follows:
Here, we make the average staying time of selfdestructive SD obey subexponential distribution, distribution parameters 和_{,} while the average staying time of other states obeys exponential distribution, which is also consistent with the actual network situation, then the average staying time of five states is shown as formula (7).
The formula to get the steadystate probability based on the semiMarkov process is
The steadystate probability of semiMarkov process can be solved finally. To simplify the analysis process, a global cognitive unit is assumed to consist of two domain cognitive units, Domain_1 and Domain_2. The approximate steadystate probabilities derived from each cognitive unit are shown in Table 3.

4.2. Quantitative Analysis and Simulation
In this paper, PEPA Workbench is used to process data files, and the tool, Version v25 of the PEPA Eclipse Plugin of the Computer Science Foundation Laboratory of Edinburgh University, is adopted to quantitatively analyze the performance of the proposed cognitive model in terms of resistance, recognition, and recovery.
Due to the addition of cognitive computing features in the model, state space X_{S} can be further divided into collection X_{1} and X_{2} to represent cognitive and noncognitive survivable state collections. Each local derivation in X_{2} contains noncognitive survivable state and indefinite state in the following form: X_{1} = {xx = DeGradation...}. Similarly, the steadystate probability collection, , can also be divided into two parts, corresponding to the subcollection C_{D} in X_{1} and the subcollection C_{UD} in X_{2}, respectively.
The test parameters are listed in Table 4.

In order to better measure the impact of the selected index parameters on the cognitive performance of survivable systems, the resistance parameter h and the cognitive parameter z_{1} are first examined. And then the values of h and z1 are adjusted to maintain the rest of the parameters unchanged. The experimental results are shown in Figures 8 and 9.
In Figure 8, parameter h means the probability of attackers finding system flaws and, correspondingly, means the system’s resistance to attacks. The smaller the value of h is, the stronger the antiattack ability of the system becomes. With h decreasing, the survivability index of the system increases gradually. But the resistance of the system is not endless. When the value of h reaches 1e09, the survivability index of the system approaches 1.0 and gradually becomes stable. No matter how strong the attack defense is, it is possible to be invaded. The curve shows the defense trend that it will return to the origin and start a new round of survivability evolution process. As long as new flaws are added to the system and the flaws recognition rate of attackers are increased in unit time, the survival index curve will always show a trend similar to Figure 8.
Figure 9 shows the curve of system survivability index. z1 represents the probability of attacks being recognized by the system. When the initial recognition rate is close to zero, the survivability index of the system is about 0.08, and the local cognitive units begin to update the acquisition rules independently. With the recognition rate increasing, the system keeps adjusting its state and updates the results of selffeedback behavior transitions to the global cognitive level, and the survivability index gradually increases, which improves the fact that the selfconfiguration mechanism in the crosslayer cognitive network further strengthens the system’s survivability. When z_{1} increases to 0.7, the survivability index begins to climb rapidly, which shows that improving the system’s attack recognition rate delivers better effects on enhancing the system’s survivability, rather than strengthening its resistance.
From the DTMC corresponding to the cognitive survival state collections, we can see that there are three possible states of selfrecovery actions, L_{3}, L_{4} and L_{3} as assumed. And the selfrecovery rate V = L_{3}/L_{3} + L_{4} + L_{5} in Figure 10 shows the changes of system survivability indexes when the selfrecovery rates are 0.532, 0.758, 0.914, and 0.997, respectively. It also unveils the fact that, with the increase of the interval time of selfrecoveries, the survivability index curve declines steadily. When the intervals are the same, the larger the value of selfrecovery rate V is, the higher the survivability index of the system becomes. When the value of V is 0.997, the survivability index is close to the highest, 1.0, the system performs the best selfrecovery ability. It can be seen that improving the system recovery is one of the most feasible ways to improve the system survivability.
For survivable systems, different indicators affecting cognitive performance are tested. The main parameters and their implications are shown in Table 5. In view of the cognitive model in this paper, the relationship between the above parameters and the cognitive ability of survivable system is analyzed and tested accordingly.

Reliability is one of the important indicators affecting the cognitive ability of survivable systems. Failure of cognitive units has great impacts on the cognitive performance of systems. The relationship between E_{SD} and reliability is shown in Figure 11. Parameters of E_{SD} decline along the transverse axis, and the height of the histogram decreases as well, which proves that the reliability of the system gets weakened as the interval of failure time decreases; that is, the higher the failure frequency is, the weaker the reliability becomes. When E_{SD} is 1/50 × E_{SD}, the reliability is still above 0.9, while when E_{SD} is reduced to 1/100 × E_{SD}, the reliability drops sharply to less than 0.1. That is, because the number of cognitive units that provide normal service decreases with the increase of failure frequency, the reliability of the system is weakened dramatically, thus causing significant impacts on the system’s cognitive ability.
Recovery is an important indicator to measure the system’s cognitive ability. Figure 12 demonstrates the relationship between E_{SH} and recovery. The system’s recovery falls with E_{SH} growing, which shows that the longer the recovery time is, the more poor the recovery performance will be. In particular, when the E_{SH} value is 100 × E_{SH}, the system’s recovery decreases to about 0.2. The survivable system cannot avoid attacks, faults, or other accidents under such complex working environment. If the selfrecovery time is too long, the duration of staying in unsafe states will be longer, thus affecting the cognitive survivable system’s cognitive ability.
The relationship between the rate of monitor behaviors’ transitions (m represents different rates) and recognition is shown in Figure 13. From the figure, we can see that every curve climbs upwards, demonstrating that the system’s recognition gets stronger as t increases. At first, the four curves rise significantly and then tend to grow steadily and slowly. That is because the time t starts to advance from 0, meaning that the system begins to work from nonworking states. Then, the system’s recognition increases rapidly from 0. And when t advances to a certain value, the recognition ability will also remain at a stable state. When m is 1.0, the curve of recognition stays at the lowest level, while when m is 5.0, the curve is at the highest level, which shows that the bigger the m value is, or the faster the execution rate of transition behaviors is, the stronger the recognition of the system will be. Because the time delay of executing monitoring behavior decreases, the number of monitoring units in working states increases, which improves the efficiency of perception and detection of the internal and external environment of the system, so the system’s cognitive ability gets stronger.
The transition rate of monitoring behaviors, namely, the relationship between e and recognition, is shown in Figure 14. We can see that every curve climbs upwards along the transverse axis, demonstrating that the system’s recognition gets stronger as t increases. When the value of t is relatively small, the four curves rise rapidly and then tend to grow steadily and slowly; that is because the time t starts to advance from 0, meaning that the system begins to work from nonworking states. Then, the system’s recognition increases rapidly from 0. And when t advances to a certain value, the recognition ability will also remain at a stable state. The four curves are obtained when e is 0.2, 0.4, 1.5, and 2.0, respectively. When e = 0.2, the corresponding curve is at the lowest level, and when e = 2.0, the corresponding curve is at the highest level, which means that the bigger the value of e is, the stronger the system’s recognition ability becomes. Because the time delay of executing monitoring behavior decreases, the number of monitoring units in working states increases, which improves the efficiency of perception and detection of the internal and external environment of the system, so the system’s cognitive ability gets stronger.
5. Conclusion
Cognitive model of survivable system is the abstraction of cognitive ability of survivable system and the key to enhance the system’s cognitive ability.
This paper studies the autonomous cognitive model and analysis method of survivable systems. The selffeedback structure of cognitive unit is improved, and the formal modeling of cognitive process is carried out by describing the transition map of cognitive survival state. In addition, the paper has obtained standardized results with the application of PEPA Workbench model tool. Next, we will further improve the cognitive structure and formal model of survivable systems and conduct research on the enhanced design of survivable system with autonomous cognitive model.
Data Availability
The data set can be obtained free of charge from http://kdd.ics.uci.edu/databases/kddcup99/kddcup99.html.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This present research work was supported by the National Natural Science Foundation of China (Nos. 61202458 and 61403109); the Natural Science Foundation of Heilongjiang Province of China (No. F2017021); the Harbin Science and Technology Innovation Research Funds (No. 2016RAQXJ036).
References
 V. R. Westmark, “A definition for information system survivability,” in Proceedings of the 37th Annual Hawaii International Conference on System Sciences, pp. 2086–2096, IEEE Computer Society Press, Big Island, HI, USA, January 2004. View at: Publisher Site  Google Scholar
 R. J. Ellison, R. C. Linger, T. Longstaff, and N. R. Mead, “Survivable network system analysis: a case study,” IEEE Software, vol. 16, no. 4, pp. 70–77, 1999. View at: Publisher Site  Google Scholar
 G. S. Zhao, H. Q. Wang, and J. Wang, “Study on situation evaluation for network survivability based on grey relation analysis,” MiniMicro Systems, vol. 27, no. 10, pp. 1861–1864, 2006. View at: Google Scholar
 J. Wang, H. Q. Wang, and G. S. Zhao, “Situation tracking assessment for network survivability based on sequential Monte Carlo,” Journal of Harbin Institute of Technology, vol. 40, no. 5, pp. 802–806, 2008. View at: Google Scholar
 J. Wang, H. Q. Wang, and G. S. Zhao, “A situation assessment method for network survivability,” Wuhan University Journal of Natural Sciences, vol. 11, no. 6, pp. 1785–1788, 2006. View at: Google Scholar
 J. Wang, H.Q. Wang, and G.S. Zhao, “Formal modeling and quantitative evaluation for information system survivability based on PEPA,” The Journal of China Universities of Posts and Telecommunications, vol. 15, no. 2, pp. 88–113, 2008. View at: Publisher Site  Google Scholar
 J. Wang, H. Q. Wang, and G. S. Zhao, “Automated analysis and validation for survivability of distributed missioncritical systems,” Chinese High Technology Letters, vol. 19, no. 6, pp. 572–579, 2009. View at: Google Scholar
 G. S. Zhao, H. Q. Wang, and J. Wang, “A novel formal analysis method of network survivability based on stochastic process algebra,” Tsinghua Science & Technology, vol. 12, no. 1, pp. 175–179, 2007. View at: Publisher Site  Google Scholar
 J. A. Zinky, D. E. Bakken, and R. E. Schantz, “Architectural support for quality of service for CORBA objects,” Theory and Practice of Object Systems, vol. 3, no. 1, pp. 55–73, 1997. View at: Publisher Site  Google Scholar
 G. S. Zhao, J. Wang, and Z. X. Li, “A method of autonomous emergency rejuvenation for survivable system,” MiniMicro Systems, vol. 35, no. 10, pp. 2284–2289, 2014. View at: Google Scholar
 Z. H. Yu, S. M. Lin, and H. Q. Chen, Network SecurityResearch on Survivability and Network Modeling, Beijing, China, 2012.
 Report on Software Survivability[EB/OL]. http://www. doc88.com/p147660727345.html. Beijing, 2012.
 G. S. Zhao, W. D. Wang, and W. Zhang, “Research of cloud survivability,” Telecommunications Science, vol. 9, pp. 52–59, 2011. View at: Google Scholar
 G. S. Zhao, H. L. Liu, and J. Wang, “Study on the autonomous recognition mechanism for survivable systems,” Chinese High Technology Letters, vol. 24, no. 10, pp. 999–1006, 2014. View at: Google Scholar
 J. Wang and G. S. Zhao, “Cognitive model and quantitative analysis for survivable system based on SMPEPA,” Journal of Huazhong University of Science and Technology (Nature Science Edition), vol. 43, no. 5, pp. 99–103, 2015. View at: Google Scholar
 D. S. Modha, R. Ananthanarayanan, S. K. Esser, A. Ndirango, A. J. Sherbondy, and R. Singh, “Cognitive computing,” Communications of the ACM, vol. 54, no. 8, pp. 62–71, 2011. View at: Publisher Site  Google Scholar
 J. T. Bradley, “SemiMarkov PEPA: modelling with generally distributed actions,” International Journal of Simulation, vol. 6, no. 34, pp. 43–51, 2005. View at: Google Scholar
 H.Q. Wang, H.W. Lü, Q. Zhao, X.K. Dong, and G.S. Feng, “Model and quantification of autonomic dependability of missioncritical systems,” Journal of Software, vol. 21, no. 2, pp. 344–358, 2010. View at: Publisher Site  Google Scholar
 R. Thomas, D. Friend, L. Dasilva, and A. Mackenzie, “Cognitive networks: adaptation and learning to achieve endtoend performance objectives,” IEEE Communications Magazine, vol. 44, no. 12, pp. 51–57, 2006. View at: Publisher Site  Google Scholar
 P. Balamuralidhar and R. Prasad, “A context driven architecture for cognitive radio nodes,” Wireless Personal Communications, vol. 45, no. 3, pp. 423–434, 2008. View at: Publisher Site  Google Scholar
 C. Fortuna and M. Mohorcic, “Trends in the development of communication networks: cognitive networks,” Computer Networks, vol. 53, no. 9, pp. 1354–1376, 2009. View at: Publisher Site  Google Scholar
 Laboratory For Foundations of Computer Science, Version v25 of the PEPA Eclipse Plugin[EB/OL].http://www.dcs.ed.ac.uk/pepa/downloads.
 J. D. Nicholas, Parallel Computation of Response Time Densities and Quantiles in Large Markov and Semimarkov models, Imperial College, London, UK, 2004.
Copyright
Copyright © 2020 Yiwei Liao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.