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We study the robustness of the c μ -rule for the optimal allocation of a resource consisting of one unreliable server to parallel queues with two different classes of customers. The customers in queues can be served with respect to a FIFO retrial discipline, when the customers at the heads of queues repeatedly try to occupy the server at a random time. It is proved that for scheduling problems in the system without arrivals, the c μ -rule minimizes the total average cost. For the system with arrivals, it is difficult directly to prove the optimality of the same policy with explicit relations. We derived for an infinite-buffer model a static control policy that also prescribes the service for certain values of system parameters exclusively for the class-i customers if both of the queues are not empty, with the aim to minimize the average cost per unit of time. It is also shown that in a finite buffer case, the c μ -rule fails. [ABSTRACT FROM AUTHOR]

The problem of optimal scheduling in a system with parallel queues and a single server has been extensively studied in queueing theory. However, such systems have mostly been analysed by assuming homogeneous attributes of arrival and service processes, or Markov queueing models were usually assumed in heterogeneous cases. The calculation of the optimal scheduling policy in such a queueing system with switching costs and arbitrary inter-arrival and service time distributions is not a trivial task. In this paper, we propose to combine simulation and neural network techniques to solve this problem. The scheduling in this system is performed by means of a neural network informing the controller at a service completion epoch on a queue index which has to be serviced next. We adapt the simulated annealing algorithm to optimize the weights and the biases of the multi-layer neural network initially trained on some arbitrary heuristic control policy with the aim to minimize the average cost function which in turn can be calculated only via simulation. To verify the quality of the obtained optimal solutions, the optimal scheduling policy was calculated by solving a Markov decision problem formulated for the corresponding Markovian counterpart. The results of numerical analysis show the effectiveness of this approach to find the optimal deterministic control policy for the routing, scheduling or resource allocation in general queueing systems. Moreover, a comparison of the results obtained for different distributions illustrates statistical insensitivity of the optimal scheduling policy to the shape of inter-arrival and service time distributions for the same first moments. [ABSTRACT FROM AUTHOR]

Optimal control problems are applied to a variety of dynamical systems with a random law of motion. In this paper we show that the random degradation processes defined on a discrete set of intermediate degradation states are also suitable for formulating and solving optimization problems and finding an appropriate optimal control policy. Two degradation models are considered in this paper: with random time to an instantaneous failure and with random time to a preventive maintenance. In both cases, a threshold-based control policy with two thresholds levels defining the signal state, after which an instantaneous failure or preventive maintenance can occur after a random time, and a maximum number of intermediate degradation states is applied. The optimal control problem is mainly solved in a steady-state regime. The main loss functional is formulated as the average cost per unit of time for a given cost structure. The Markov degradation models are used for numerical calculations of the optimal threshold policy and reliability function of the studied degrading units. [ABSTRACT FROM AUTHOR]

In this paper we study the possibility to use the artificial neural networks for trees classification based on real and approximated values of the sap flow density flux describing water transport in trees. The data sets were generated by means of a new tree monitoring system TreeTalker©. The Fourier series-based model is used for fitting the data sets with periodic patterns. The multivariate regression model defines the functional dependencies between sap flow density and temperature time series. The paper shows that Fourier coefficients can be successfully used as elements of the feature vectors required to solve different classification problems. Here we train multilayer neural networks to classify the trees according to different types of classes. The quality of the developed model for prediction and classification is verified by numerous numerical examples. [ABSTRACT FROM AUTHOR]

In this paper we find stability conditions of a two-class retrial system with unreliable server, in which the new customer joins a class-dependent orbit queue regardless of the state of the server. The interrupted customer joins the top of the corresponding orbit and tries to occupy the server after a class-dependent exponential retrial time. To find stability conditions, we apply two different approaches, regenerative approach and the stability analysis of a Markov chain (the MC approach) which has been developed in Fayolle et al. (Topics in the constructive theory of countable Markov chains, Cambridge University Press, Cambridge, 1995). The former approach allows to obtain a transparent and intuitive necessary stability condition. Then we apply the MC approach to obtain the stability criterion of the embedded two-dimensional Markov chain describing the state of orbits at the instances when the server becomes free. We use a necessary stability condition obtained by the regenerative method to present the stability criterion in a compact form. Moreover we discuss a modified controllable system and compare stability zones of these two systems. Some numerical examples based on simulation results are included as well which illustrate the theoretical issues. [ABSTRACT FROM AUTHOR]

Segmentation or change point detection is a very common topic in time series analysis, anomaly detection and pattern recognition. In our previous paper the time series generated by sensors with 3D accelerometers were analysed. It was noticed that such series consist of segments of independent and correlated observations. Hence the appropriate methods for change point detection for both data types must be implemented simultaneously. This paper provides an auxiliary comparison analysis which we intend to implement later for the above mentioned acceleration data. The available methods require usually a long execution time, so that it is time-consuming if several methods should be compared. In the framework of the present publication we want to give additional help for detecting a suitable change point detection method and for finding a good parameter setting. Our analysis is performed on simulated time series, that are normally distributed with constant but unknown mean and changes in variance. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of optimal routing for the pair of two-server heterogeneous queues operating in parallel and subsequent optimal allocation of customers between the servers in each queue. Heterogeneity implies different servers in terms of speed of service. An open-loop control assumes the static resource allocation when a router has no information about the state of the system. We discuss here the algorithm to calculate the optimal routing policy based on specially constructed Markov-modulated Poisson processes. As an alternative static policy, we consider an optimal Bernoulli splitting which prescribes the optimal allocation probabilities. Then, we show that the optimal allocation policy between the servers within each queue is of threshold type with threshold levels depending on the queue length and phase of an arrival process. This dependence can be neglected by using a heuristic threshold policy. A number of illustrative examples show interesting properties of the systems operating under the introduced policies and their performance characteristics. [ABSTRACT FROM AUTHOR]

This paper presents a Markovian queueing model for a hybrid channel consisting of two links with different throughputs. The busy faster link is assumed to be unreliable, with possible partial and complete failures. Partial failures lead to a reduction in the service rate, while complete failure stops the service. Repairs return the faster server to a non-failed state. The problem of the optimal allocation of customers between the servers is considered. The optimality of a threshold-based policy that depends on the failure state of the faster server is proved. The dynamic behaviour of the system for the given threshold policy is described by a four-dimensional Markov process that can be treated as a QBD process with a large number of boundary states. Stationary analysis of the system is performed by means of a matrix-geometric approach, and the main performance measures are derived. [ABSTRACT FROM AUTHOR]

Some degradation models with random life resources for technical and biological objects are introduced and studied. Conditional hazard rate function given fixed consumed resource is in the focus of consideration. [ABSTRACT FROM AUTHOR]

The paper deals with a finite-source queueing system serving one class of customers and consisting of heterogeneous servers with unequal service intensities and of one common queue. The main model has a non-preemptive service when the customer can not change the server during its service time. The optimal allocation problem is formulated as a Markov-decision one. We show numerically that the optimal policy which minimizes the long-run average number of customers in the system has a threshold structure. We derive the matrix expressions for performance measures of the system and compare the main model with alternative simplified queuing systems which are analysed for the arbitrary number of servers. We observe that the preemptive heterogeneous model operating under a threshold policy is a good approximation for the main model by calculating the mean number of customers in the system. Moreover, using the preemptive and non-preemptive queueing models with the faster server first policy the lower and upper bounds are calculated for this mean value. [ABSTRACT FROM AUTHOR]

This paper deals with heterogeneous queues where servers differ not only in service rates but also in operating costs. The classical optimisation problem in queueing systems with heterogeneous servers consists in the optimal allocation of customers between the servers with the aim to minimise the long-run average costs of the system per unit of time. As it is known, under some assumptions the optimal allocation policy for this system is of threshold type, i.e., the policy depends on the queue length and the state of faster servers. The optimal thresholds can be calculated using a Markov decision process by implementing the policy-iteration algorithm. This algorithm may have certain limitations on obtaining a result for the entire range of system parameter values. However, the available data sets for evaluated optimal threshold levels and values of system parameters can be used to provide estimations for optimal thresholds through artificial neural networks. The obtained results are accompanied by a simple heuristic solution. Numerical examples illustrate the quality of estimations. [ABSTRACT FROM AUTHOR]

The paper studies a controllable multi-server heterogeneous queueing system where servers operate at different service rates without preemption, i.e., the service times are uninterrupted. The optimal control policy allocates the customers between the servers in such a way that the mean number of customers in the system reaches its minimal value. The Markov decision model and the policy-iteration algorithm are used to calculate the optimal allocation policy and corresponding mean performance characteristics. The optimal policy, when neglecting the weak influence of slow servers, is of threshold type defined as a sequence of threshold levels which specifies the queue lengths for the usage of any slower server. To avoid time-consuming calculations for systems with a large number of servers, we focus here on a heuristic evaluation of the optimal thresholds and compare this solution with the real values. We develop also the simple lower and upper bound methods based on approximation by an equivalent heterogeneous queueing system with a preemption to measure the mean number of customers in the system operating under the optimal policy. Finally, the simulation technique is used to provide sensitivity analysis of the heuristic solution to changes in the form of inter-arrival and service time distributions. [ABSTRACT FROM AUTHOR]

Subclinical ketosis is a metabolic disease in early lactation. It contributes to economic losses because of reduced milk yield and may promote the development of secondary diseases. Thus, an early detection seems desirable as it enables the farmer to initiate countermeasures. To support early detection, we examine different types of data recordings and use them to build a flexible algorithm that predicts the occurrence of subclinical ketosis. This approach shows promising results and can be seen as a step toward automatic health monitoring in farm animals. [ABSTRACT FROM AUTHOR]

The paper provides reliability analysis of a cold double redundant renewable system assuming that both life-time and repair time distributions are arbitrary. The proposed approach is based on the theory of decomposable semi-regenerative processes. We derive the Laplace–Stieltjes transform of two main reliability measures like the distribution of the time between failures and the time to the first failure. The transforms are used to calculate corresponding mean times. It is further derived in closed form the time-dependent and time stationary state probabilities in terms of the Laplace transforms. Numerical results illustrate the effect of the type of distributions as well as their parameters on the derived reliability and probabilistic measures. [ABSTRACT FROM AUTHOR]

The need for accurate positioning and tracking of mobile sensor nodes arises in many applications. To compute position estimates from raw measurements in positioning systems, Bayesian filtering techniques such as Kalman, histogram, or particle filters are frequently employed. A major disadvantage of these techniques is the fact that they compute only a single position estimate in every timestep and, therefore, do not utilize the available information to the full extent. The work presented in this article improves over this current state of the art by instead estimating full node trajectories and, therefore, the most plausible sequence of positions in every timestep. We present two distinct algorithms—for a discrete and for a continuous state-space—and highlight the particular advantages of each variant. Achievable results are shown by simulation and measurement to be more accurate than the traditional Bayesian filtering approach. The most prominent advantage of much more accurate total track length estimation is particularly emphasized. [ABSTRACT FROM AUTHOR]

The last few decades have been characterised by a very active application of smart technologies in various fields of industry. This paper deals with industrial activities, such as injection molding, where it is required to monitor continuously the manufacturing process to identify both the effective running time and down-time periods. Supervised machine learning algorithms are developed to recognize automatically the periods of the injection molding machines. The former algorithm uses directly the features of the descriptive statistics, while the latter one utilizes a convolutional neural network. The automatic state recognition system is equipped with an 3D-accelerometer sensor whose datasets are used to train and verify the proposed algorithms. The novelty of our contribution is that accelerometer data-based machine learning models are used to distinguish producing and non-producing periods by means of recognition of key steps in an injection molding cycle. The first testing results show the approximate overall balanced accuracy of 72–92% that illustrates the large potential of the monitoring system with the accelerometer. According to the ANOVA test, there are no sufficient statistical differences between the comparative algorithms, but the results of the neural network exhibit higher variances of the defined accuracy metrics. [ABSTRACT FROM AUTHOR]

The objectives of this study were (1) to develop an algorithm for the acceleration sensor of the Smartbow Eartag (Smartbow GmbH, Weibern, Austria) to distinguish between postures (lying and standing or locomotion) and to detect 6 kinds of activities (milk intake, water intake, solid feed intake, ruminating, licking or sucking without milk intake, and other activities) in dairy calves and (2) to evaluate this sensor for identifying these behaviors in dairy calves compared with observations from video. Accelerometers were applied to the left ears of 15 preweaned Holstein dairy calves. Calves were kept in a group pen and received milk replacer from an automatic calf feeder. Based on 38 h of acceleration data and video observation, an algorithm was established to detect the predefined behaviors. Using cross-validation, video recordings were used to analyze whether a behavior was detected correctly by the developed algorithm. For posture, sensitivity (94.4%), specificity (94.3%), precision (95.8%), and accuracy (94.3%) were high. Cohen's kappa was calculated as 0.88. For the 6 defined activities, overall (i.e., aggregated for all activities) accuracy was 70.8% and kappa was calculated as 0.58. Some activities (e.g., ruminating, feed intake, other activities) were identified better than others. In conclusion, the developed algorithm based on the acceleration data of the Smartbow Eartag was successful in detecting lying behavior, rumination, feed intake, and other activities in calves, but further development of the underlying algorithm will be necessary to produce reliable results for milk and water intake. [ABSTRACT FROM AUTHOR]