Search Results (28)

Vehicular Internet of Things (V-IoT) networks, sustained by a high-density deployment of roadside units and sensor-equipped vehicles, are currently at the edge of next-generation intelligent transportation system evolution. However, offering stable, low-latency, and energy-efficient communication in such heterogeneous and delay-prone environments is challenging due to limited spectral resources and diverse quality of service (QoS) requirements. This paper presents a Priority-Aware Spectrum Management (PASM) scheme for IoT-based vehicular networks. This dynamic spectrum access scheme integrates interweave, underlay, and coexistence modes to optimize spectrum utilization, energy efficiency, and throughput while minimizing blocking and interruption probabilities. The algorithm manages resources efficiently and gives proper attention to each device based on its priority, so all IoT devices, from high to low priority, receive continuous and reliable service. A Continuous-Time Markov Chain (CTMC) model is derived to analyze the proposed algorithm for various network loads. Simulation results indicate improved spectral efficiency, throughput, delay, and overall QoS compliance over conventional access methods. These findings establish that the proposed algorithm is a scalable solution for dynamic V-IoT environments. Full article

The coronavirus (COVID-19) expanded rapidly and affected almost the whole world since December 2019. COVID-19 has an unusual ability to spread quickly through airborne viruses and substances. Taking into account the disease’s natural progression, this study considers that viral spread is unpredictable rather than deterministic. The continuous time Markov chain (CTMC) stochastic model technique has been used to anticipate upcoming states using random variables. The suggested study focuses on a model with five distinct compartments. The first class contains Lévy noise-based infection rates (termed as vulnerable people), while the second class refers to the infectious compartment having similar perturbation incidence as the others. We demonstrate the existence and uniqueness of the positive solution of the model. Subsequently, we define a stochastic threshold as a requisite condition for the extinction and durability of the disease’s mean. By assuming that the threshold value ${\mathbf{R}}_{\mathbf{0}}^{\mathbf{D}}$ is smaller than one, it is demonstrated that the solution trajectories oscillate around the disease-free state (DFS) of the corresponding deterministic model. The solution curves of the SDE model fluctuate in the neighborhood of the endemic state of the base ODE system, when ${\mathbf{R}}_{\mathbf{0}}^{\mathbf{P}}>1$ elucidates the definitive persistence theory of the suggested model. Ultimately, numerical simulations are provided to confirm our theoretical findings. Moreover, the results indicate that stochastic environmental disturbances might influence the propagation of infectious diseases. Significantly, increased noise levels could hinder the transmission of epidemics within the community. Full article

The efficient migration of virtual machines (VMs) is critical for optimizing resource management, ensuring service continuity, and enhancing resiliency in cloud and edge computing environments, particularly as 6G networks demand higher reliability and lower latency. This study addresses the challenges of dynamically balancing server loads while minimizing downtime and migration costs under stochastic task arrivals and variable processing times. We propose a queuing theory-based model employing continuous-time Markov chains (CTMCs) to capture the interplay between VM migration decisions, server resource constraints, and task processing dynamics. The model incorporates two migration policies—one minimizing projected post-migration server utilization and another prioritizing current utilization—to evaluate their impact on system performance. The numerical results show that the blocking probability for the first VM for Policy 1 is 2.1% times lower than for Policy 2 and the same metric for the second VM is 4.7%. The average server’s resource utilization increased up to 11.96%. The framework’s adaptability to diverse server–VM configurations and stochastic demands demonstrates its applicability to real-world cloud systems. These results highlight predictive resource allocation’s role in dynamic environments. Furthermore, the study lays the groundwork for extending this framework to multi-access edge computing (MEC) environments, which are integral to 6G networks. Full article

With the rapid expansion of the aviation industry, traditional static scheduling methods have become inadequate to meet the increasingly complex demands of efficient airport operations. To enhance the operational efficiency of multi-runway airports, this paper introduced a two-stage dynamic departure scheduling method based on continuous Markov chains. The pushback rate control strategy was extended to multi-runway scenarios to identify the optimal taxiway queue threshold in stage I. In stage II, the pushback rate control strategy with a known queue threshold was introduced into a multi-objective optimization model, aiming to minimize flight delays and operational costs including pushback waiting times, taxi fuel consumption, and environmental impact. Then, continuous-time Markov chains (CTMC) were employed to track aircraft state transitions in the taxiway queue, and a nested whale optimization algorithm was proposed to optimize both the pushback sequence and runway resource allocation. Results indicate that the proposed method reduced the average taxiway queue time by 55.58%, with delay reductions of up to 73.06%, offering significant cost savings and environmental benefits while improving flight punctuality. This innovative approach highlights the potential for optimizing airport resource scheduling in complex and dynamic environments. Full article

In this paper, a stochastic continuous-time Markov chain (CTMC) model is developed and analyzed to explore the dynamics of cholera. The multitype branching process is used to compute a stochastic threshold for the CTMC model. Latin hypercube sampling/partial rank correlation coefficient (LHS/PRCC) sensitivity analysis methods are implemented to derive sensitivity indices of model parameters. The results show that the natural death rate $\left({\mu }_v\right)$ of a vector is the most sensitive parameter for controlling disease outbreaks. Numerical simulations indicate that the solutions of the CTMC stochastic model are relatively close to the solutions of the deterministic model. Numerical simulations estimate the probability of both disease extinction and outbreak. The probability of cholera extinction is high when it emerges from bacterial concentrations in non-contaminated/safe water in comparison to when it emerges from all infected groups. Thus, any intervention that focuses on reducing the number of infections at the beginning of a cholera outbreak is essential for reducing its transmission. Full article

We investigate the construction of a partial absorbing continuous-time Markov chain (CTMC) using a heuristic algorithm aimed at approximate transient analysis. The accuracy of transient state probabilities is indicated by the probability of absorbing state(s) at the specified time moment. A key challenge is the construction of a partial CTMC that minimizes the probability of reaching the absorbing state(s). The generation of all possible partial CTMCs is too computationally demanding, in general. Thus, we turn to investigation of heuristic algorithms that chose to include one state at a time based on limited information (i.e., the partial chain that is already constructed) and without any assumptions about the structure of the underlying CTMC. We consider three groups of such algorithms: naive, based on state characterization by the shortest path (obtained by Dijkstra method) and based on exact/approximate state probabilities. After introducing the algorithms, we discuss the problem of optimal partial CTMC construction and provide several examples. Then we compare the algorithm performance by constructing the partial CTMCs for two models: car sharing system and a randomly generated CTMC. Our obtained numerical results suggest that heuristic algorithms using state characterization via the shortest path offer a balance between accuracy and computational effort. Full article

This paper aims to propose a novel call for help traffic (SOS) and study its impact over Machine-to-Machine (M2M) and Human-to-Human (H2H) traffic in Internet of Things environments, specifically during disaster events. During such events (e.g., the spread COVID-19), SOS traffic, with its predicted exponential increase, will significantly influence all mobile networks. SOS traffic tends to cause many congestion overload problems that significantly affect the performance of M2M and H2H traffic. In our project, we developed a new Continuous-Time Markov Chain (CTMC) model to analyze and measure radio access performance in terms of massive SOS traffic that influences M2M and H2H traffic. Afterwards, we validate the proposed CTMC model through extensive Monte Carlo simulations. By analyzing the traffic during an emergency case, we can spot a huge impact over the three traffic types of M2M, H2H and SOS traffic. To solve the congestion problems while keeping the SOS traffic without any influence, we propose to grant the SOS traffic the highest priority over the M2M and H2H traffic. However, by implementing this solution in different proposed scenarios, the system becomes able to serve all SOS requests, while only 20% of M2M and H2H traffic could be served in the worst-case scenario. Consequently, we can alleviate the expected shortage of SOS requests during critical events, which might save many humans and rescue them from being isolated. Full article

The way we connect with the physical world has completely changed because of the advancement of the Internet of Things (IoT). However, there are several difficulties associated with this change. A significant advancement has been the emergence of intelligent machines that are able to gather data for analysis and decision-making. In terms of IoT security, we are seeing a sharp increase in hacker activities worldwide. Botnets are more common now in many countries, and such attacks are very difficult to counter. In this context, Distributed Denial of Service (DDoS) attacks pose a significant threat to the availability and integrity of online services. In this paper, we developed a predictive model called Markov Detection and Prediction (MDP) using a Continuous-Time Markov Chain (CTMC) to identify and preemptively mitigate DDoS attacks. The MDP model helps in studying, analyzing, and predicting DDoS attacks in Long-Term Evolution for Machine (LTE-M) networks and IoT environments. The results show that using our MDP model, the system is able to differentiate between Authentic, Suspicious, and Malicious traffic. Additionally, we are able to predict the system behavior when facing different DDoS attacks. Full article

The fact that the famous basic reproduction number $R_0$, i.e., the largest eigenvalue of the next generation matrix $F{V}^{-1}$, sometimes has a probabilistic interpretation is not as well known as it deserves to be. It is well understood that half of this formula, $-V$, is a Markovian generating matrix of a continuous-time Markov chain (CTMC) modeling the evolution of one individual on the compartments. It has also been noted that the not well-enough-known rank-one formula for $R_0$ of Arino et al. (2007) may be interpreted as an expected final reward of a CTMC, whose initial distribution is specified by the rank-one factorization of F. Here, we show that for a large class of ODE epidemic models introduced in Avram et al. (2023), besides the rank-one formula, we may also provide an integral renewal representation of $R_0$ with respect to explicit “age kernels” $a\left(t\right)$, which have a matrix exponential form.This latter formula may be also interpreted as an expected reward of a probabilistic continuous Markov chain (CTMC) model. Besides the rather extensively studied rank one case, we also provide an extension to a case with several susceptible classes. Full article

Recently, a mixed redundancy was introduced among the redundant design strategies to achieve a more reliable system within the equivalent resources. This study deals with a lifetime distribution for a mixed redundant system with an imperfect fault detector/switch. The lifetime distribution model was formulated using a structured continuous Markov chain (CTMC) and considers the time-to-failure (TTF) distribution of a component as a phase-type distribution (PHD). The model’s versatility and practicality are enhanced because the PHD can represent diverse degradation patterns of the components exposed to varied operating environments. The model provides accurate reliability for a mixed redundant system by advancing the approximate reliability function suggested in previous studies. Furthermore, the model would be useful in system design and management because it provides information such as the n_th moment of the system’s lifetime distribution. In numerical experiments on some examples, the mixed redundancy was confirmed to devise a more reliable system than the existing active and standby redundancies, and the improvement effect increased as the number of redundant components decreased. The optimal structure for maximizing the expected lifetime of the system changes depends on the reliability of the components and fault detector/switch. Full article

A model of a single-server queuing-inventory system (QIS) with a limited waiting buffer for consumer customers (c-customers) and catastrophes has been developed. When a catastrophe occurs, all items in the system’s warehouse are destroyed, but c-customers in the system are still waiting for replenishment. In addition to c-customers, negative customers (n-customers) are also taken into account, each of which displaces one c-customer (if any). The policy (s, S) is used to replenish stocks. If, when a customer enters, the system warehouse is empty, then, according to Bernoulli’s trials, this customer either leaves the system without goods or joins the buffer. The mathematical model of the investigated QIS is constructed in the form of a continuous-time Markov chain (CTMC). Both exact and approximate methods for calculating the steady-state probabilities of constructed CTMCs are proposed and closed-form expressions are obtained for calculating the performance measures. Numerical evaluations are presented, demonstrating the high accuracy of the developed approximate formulas, as well as the behavior of performance measures depending on the input parameters. In addition, an optimization problem is solved to obtain the optimal value of the reorder point to minimize the expected total cost. Full article

In order to investigate the impact of two immunization strategies—vaccination targeting susceptible individuals to reduce their infection rate and clinical medical interventions targeting infected individuals to enhance their recovery rate—on the spread of infectious diseases in complex networks, this study proposes a bilinear SIR infectious disease model that considers bidirectional immunization. By analyzing the conditions for the existence of endemic equilibrium points, we derive the basic reproduction numbers and outbreak thresholds for both homogeneous and heterogeneous networks. The epidemic model is then reconstructed and extensively analyzed using continuous-time Markov chain (CTMC) methods. This analysis includes the investigation of transition probabilities, transition rate matrices, steady-state distributions, and the transition probability matrix based on the embedded chain. In numerical simulations, a notable concordance exists between the outcomes of CTMC and mean-field (MF) simulations, thereby substantiating the efficacy of the CTMC model. Moreover, the CTMC-based model adeptly captures the inherent stochastic fluctuation in the disease transmission, which is consistent with the mathematical properties of Markov chains. We further analyze the relationship between the system’s steady-state infection density and the immunization rate through MCS. The results suggest that the infection density decreases with an increase in the immunization rate among susceptible individuals. The current research results will enhance our understanding of infectious disease transmission patterns in real-world scenarios, providing valuable theoretical insights for the development of epidemic prevention and control strategies. Full article

Fifth-generation (5G) networks provide network slicing capabilities, enabling the deployment of multiple logically isolated network slices on a single infrastructure platform to meet specific requirements of users. This paper focuses on modeling and analyzing resource capacity planning and reallocation for network slicing, specifically between two providers transmitting elastic traffic, such during as web browsing. A controller determines the need for resource reallocation and plans new resource capacity accordingly. A Markov decision process is employed in a controllable queuing system to find the optimal resource capacity for each provider. The reward function incorporates three network slicing principles: maximum matching for equal resource partitioning, maximum share of signals resulting in resource reallocation, and maximum resource utilization. To efficiently compute the optimal resource capacity planning policy, we developed an iterative algorithm that begins with maximum resource utilization as the starting point. Through numerical demonstrations, we show the optimal policy and metrics of resource reallocation for two services: web browsing and bulk data transfer. The results highlight fast convergence within three iterations and the effectiveness of the balanced three-principle approach in resource capacity planning for 5G network slicing. Full article

The 5G network is designed to serve three main use cases: enhanced mobile broadband (eMBB), massive machine-type communications (mMTC), and ultra-reliable and low-latency communications (uRLLC). There are many new technological enablers, including the cloud radio access network (C-RAN) and network slicing, that can support 5G and meet its requirements. The C-RAN combines both network virtualization and based band unit (BBU) centralization. Using the network slicing concept, the C-RAN BBU pool can be virtually sliced into three different slices. 5G slices require a number of Quality of service (QoS) metrics, such as average response time and resource utilization. In order to enhance the C-RAN BBUs utilization while protecting the minimum QoS of the coexisting three slices, a priority-based resource allocation with queuing model is proposed. The uRLLC is given the highest priority, while eMBB has a higher priority than mMTC services. The proposed model allows the eMBB and mMTC to be queued and the interrupted mMTC to be restored in its queue to increase its chance to reattempt the service later. The proposed model’s performance measures are defined and derived using a continuous-time Markov chain (CTMC) model and evaluated and compared using different methodologies. Based on the results, the proposed scheme can increase C-RAN resource utilization without degrading the QoS of the highest-priority uRLLC slice. Additionally, it can reduce the forced termination priority of the interrupted mMTC slice by allowing it to re-join its queue. Therefore, the comparison of the results shows that the proposed scheme outperforms the other states of the art in terms of improving the C-RAN utilization and enhancing the QoS of eMBB and mMTC slices without degrading the QoS of the highest priority use case. Full article

This work focuses on the enhancement of the charging reliability of both scheduled (SEVs) and opportunistic (UEVs) electric vehicle (EV) users in an EV fast charging station (FCS). The proposed charging coordination strategies allow UEVs to exploit unused charging resources to optimally utilize the limited charging resources of FCS. However, the optimum utilization of limited charging resources of an FCS while assuring a reliable charging process for plugged-in EVs under random failures of electric vehicle supply equipment (EVSE) is a real challenge for the FCS controller. When the FCS admits UEVs in addition to SEVs, assuring a satisfactory quality of service to both EV user categories is also dispensable. Therefore, we analyze the performance of reservation of off-board mobile chargers (MOBCs) to enhance the charging reliability of EV users while achieving high charging resource utilization. This work proposes resource allocation and charging coordination strategies for an FCS where MOBCs are used to enhance the charging reliability of both SEVs and UEVs. Moreover, the proposed dynamic charging resource coordination strategies are analyzed with a continuous time Markov-chain (CTMC). The presented results from the CTMC model demonstrate that the proposed strategies outperform the EV charging process of the FCS in terms of high resource utilization and reliability while guaranteeing a satisfactory quality of service to EV users. Full article