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This work is a review of current trends in the stray flux signal processing techniques applied to the diagnosis of electrical machines. Initially, a review of the most commonly used standard methods is performed in the diagnosis of failures in induction machines and using stray flux; and then specifically it is treated and performed the algorithms based on statistical analysis using cumulants and polyspectra. In addition, the theoretical foundations of the analyzed algorithms and examples applications are shown from the practical point of view where the benefits that processing can have using HOSA and its relationship with stray flux signal analysis, are illustrated.

Data centers are a vital and fundamental infrastructure component of the cloud. The requirement to execute a large number of demanding jobs places a premium on processing capacity. Parallelizing jobs to run on multiple cores reduces execution time. However, there is a decreasing marginal benefit to using more cores, with the speedup function quantifying the achievable gains. A critical performance metric is flow time. Previous results in the literature derived closed-form expressions for the optimal allocation of cores to minimize total flow time for a power-law speedup function if all jobs are present at time 0. However, this work did not place a constraint on the makespan. For many diverse applications, fast response times are essential, and latency targets are specified to avoid adverse impacts on user experience. This paper is the first to determine the optimal core allocations for a multicore system to minimize total flow time in the presence of a completion deadline (where all jobs have the same deadline). The allocation problem is formulated as a nonlinear optimization program that is solved using the Lagrange multiplier technique. Closed-form expressions are derived for the optimal core allocations, total flow time, and makespan, which can be fitted to a specified deadline by adjusting the value of a single Lagrange multiplier. Compared to the unconstrained problem, the shortest job first property for optimal allocation is maintained; however, a number of other properties require revising and other properties are only retained in a modified form (such as the scale-free and size-dependence properties). It is found that with a completion deadline the optimal solution may contain groups of simultaneous completions. In general, all possible patterns of single- and group-completion need to be considered, producing an exponential search space. However, the paper determines analytically that the optimal completion pattern consists of a sequence of single completions followed by a single group of simultaneous completions at the end, which reduces the search space dimension to being linear. The paper validates the Lagrange multiplier approach by verifying constraint qualifications.

Timely status updating in mobile edge computing (MEC) systems has recently gained the utmost interest in internet of things (IoT) networks, where status updates may need higher computations to be interpreted. Moreover, in real-life situations, the status update streams may also be of different priority classes according to their importance and timeliness constraints. The classical disciplines used for priority service differentiation, preemptive and non-preemptive disciplines, pose a dilemma of information freshness dissatisfaction for the whole priority network. This work proposes a hybrid preemptive/non-preemptive discipline under an M/M/1/2 priority queueing model to regulate the priority-based contention of the status update streams in MEC systems. For this hybrid discipline, a probabilistic discretionary rule for preemption is deployed to govern the server and buffer access independently, introducing distinct probability parameters to control the system performance. The stochastic hybrid system approach is utilized to analyze the average age of information (AoI) along with its higher moments for any number of classes. Then, a numerical study on a three-class network is conducted by evaluating the average AoI performance and the corresponding dispersion. The numerical observations underpin the significance of the hybrid-discipline parameters in ensuring the reliability of the whole priority network. Hence, four different approaches are introduced to demonstrate the setting of these parameters. Under these approaches, some outstanding features are manifested: exploiting the buffering resources efficiently, conserving the aggregate sensing power, and optimizing the whole network satisfaction. For this last feature, a near-optimal low-complex heuristic method is proposed.

Dense network deployment is now being evaluated as one of the viable solutions to meet the capacity and connectivity requirements of the fifth-generation (5G) cellular system. The goal of 5G cellular networks is to offer clients with faster download speeds, lower latency, more dependability, broader network capacities, more accessibility, and a seamless client experience. However, one of the many obstacles that will need to be overcome in the 5G era is the issue of energy usage. For energy efficiency in 5G cellular networks, researchers have been studying at the sleeping strategy of base stations. In this regard, this study models a 5G BS as an M[X]/G/1 feedback retrial queue with a sleeping strategy to reduce average power consumption and conserve power in 5G mobile networks. The probability-generating functions and steady-state probabilities for various BS states were computed employing the supplementary variable approach. In addition, an extensive palette of performance metrics have been determined. Then, with the aid of graphs and tables, the resulting metrics are conceptualized and verified. Further, this research is accelerated in order to bring about the best possible (optimal) cost for the system by adopting a range of optimization approaches namely particle swarm optimization, artificial bee colony and genetic algorithm.

A system manager makes dynamic pricing and dispatch control decisions in a queueing network model motivated by ride hailing applications. A novel feature of the model is that it incorporates travel times. Unfortunately, this renders the exact analysis of the problem intractable. Therefore, we study this problem in the heavy traffic regime. Under the assumptions of complete resource pooling and common travel time and routing distributions, we solve the problem in closed form by analyzing the corresponding Bellman equation. Using this solution, we propose a policy for the queueing system and illustrate its effectiveness in a simulation study.

This study discusses the existence of tracking N-dimensional Brownian nanoparticle in an interactive medium, where this tracking is based on Brownian motion analysis. A group of N nanosensors begin the tracking process at the origin of N dimensional space, where the nanosensors serve an important role in detecting and monitoring this nanoparticle. Each nanosensor oscillates as it passes through the origin of its planer surface (to the right and left) in the presence of a succession of random points on each axis. The space's plans cross on a real line, with the origin (0,0,...,0). Because of this uncertainty, we may be able to calculate the overall distance in each tracking step as a function of a discounted effort-reward parameter. We show analytically how this parameter influences demonstrating the existence of this model and lowering the computationally expected value of the first collision time between a nanosensor and a nanoparticle.

In this paper, we consider a queueing-inventory system with modified delayed vacation under Bernoulli schedule. If the inventory is empty upon completion of the service, the server will take the modified delayed vacation. During the modified delayed vacation period, if the replenishment is completed, the customer will still be served as normal. After this period, the server will take Bernoulli schedule, where the server reverts to normal work with probability q(0≤q≤1) or takes multiple vacations with probability 1-q. The customers arrive according to a Poisson process. Upon customer arrival, if the inventory is not empty, the customer accepts the service and leaves the system carrying a product. The service time, lead time, modified delayed vacation time and multiple vacations time are all assumed to be exponentially distributed. We derive the stability condition of the system and the matrix geometric solution of steady-state probabilities using an algorithm. Then performance measures of the system are derived. Finally, numerical results are presented to demonstrate the impact of system parameters on performance measures and the expected cost function.

We consider a queueing system in which the arrivals occur according to batch Markovian arrival process. There is a single server in the system. The server offers services in batches of varying sizes from 1 to b, where b is pre-determined finite positive integer. Upon completion of a service, the server will become idle if there is no customer waiting in the queue of infinite size. Otherwise, the server will offer services to the waiting customers by picking the minimum of b and the number waiting from the head of the queue. Thus, the services are offered for batches of size r varying from 1 to b. Assuming that the service times follow a phase type distribution with representation depending on r we analyze the queueing system in the steady-state using matrix-analytic methods. We report some interesting illustrative numerical examples point out that the type of the arrival (in other words, the variability in the inter-arrival times) and the type of batch size distribution have a significant effect on the some performance measures.

Batch service queueing systems are basically classified into two types: a time-based system in which the service facilities depart according to inter-departure times that follows a given distribution, such as the conventional bus system, and a demand-responsive system in which the vehicles start traveling provided that a certain number of customers gather at the waiting space, such as ride-sharing and on-demand bus. Motivated by the recent spreading of demand-responsive transportation, this study examines the M/MX/∞ queue. In this model, whenever the number of waiting customers reaches a capacity set by a discrete random variable X, customers are served by a group. We formulate the M/MX/∞ queue as a three-dimensional Markov chain whose dimensions are all unbounded and depict a book-type transition diagram. The joint stationary distribution for the number of busy servers, number of waiting customers, and batch size is derived by applying the method of factorial moment generating function. The central limit theorem is proved for the case that X has finite support under heavy traffic using the exact expressions of the first two moments of the number of busy servers. Moreover, we show that the M/MX/∞ queue encompasses the time-based infinite server batch service queue (M/MG(x)/∞ queue), which corresponds to the conventional bus system, under a specific heavy traffic regime. In this model, the transportation facility departs periodically according to a given distribution, G(x), and collects all the waiting customers for a batch service for an exponentially distributed time corresponding to the traveling time on the road. We show a random variable version of Little’s law for the number of waiting customers for the M/MG(x)/∞ queue. Furthermore, we present a moment approach to obtain the distribution and moments of the number of busy servers in a GI/M/∞ queue by utilizing the M/MG(x)/∞ queue. Finally, we provide some numerical results and discuss their possible applications on transportation systems.

This paper develops a comprehensive analytical model for the M/M/S/M+ queueing system with customer abandonment. The transition rate diagram and associated transition probabilities are derived to characterize the system dynamics. Key performance metrics are obtained, including the mean number of customers in the system, the mean waiting time in the system, the probability of an empty system, the probability of finding all servers busy, and the abandonment probability. Specific focus is given to characterizing the abandonment behavior, deriving expressions for the mean abandonment time and the mean number of abandoned customers. The mathematical formulation provides insights into the impacts of arrival rates, service rates, customer impatience levels and system capacity on performance. Potential applications span various domains where customer abandonment significantly affects system design and resource provisioning, such as call centers, healthcare facilities, transportation services and e-commerce platforms. The analytical queueing model enables quantifying fundamental tradeoffs between service quality metrics like customer waiting times and the potential revenue losses from abandonments. The results can guide capacity planning, staffing optimization, and decision support for design and control of queueing systems with impatient customers.