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In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector’s indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers’ sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace–Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer’s length (understood as the sum of the volume vector’s indications). Moreover, we present some numerical computations illustrating theoretical results.

This research focused on the helicopter turboshaft engine dynamic model, identifying task solving in unsteady and transient modes (engine starting and acceleration) based on sensor data. It is known that about 85% of helicopter turboshaft engines operate in steady-state modes, while only around 15% operate in unsteady and transient modes. Therefore, developing dynamic multi-mode models that account for engine behavior during these modes is a critical scientific and practical task. The dynamic model for starting and acceleration modes has been further developed using on-board parameters recorded by sensors (gas-generator rotor r.p.m., free turbine rotor speed, gas temperature in front of the compressor turbine, fuel consumption) to achieve a 99.88% accuracy in identifying the dynamics of these parameters. An improved Elman recurrent neural network with dynamic stack memory was introduced, enhancing the robustness and increasing the performance by 2.7 times compared to traditional Elman networks. A theorem was proposed and proven, demonstrating that the total execution time for N Push and Pop operations in the dynamic stack memory does not exceed a certain value O(N). The training algorithm for the Elman network was improved using time delay considerations and Butterworth filter preprocessing, reducing the loss function from 2.5 to 0.12% over 120 epochs. The gradient diagram showed a decrease over time, indicating the model's approach to the minimum loss function, with optimal settings ensuring the stable training. [ABSTRACT FROM AUTHOR]

Background: Temporomandibular disorders (TMDs) are the most prevalent non-dental pain issues in the maxillofacial region. Despite advancements, diagnosing and managing TMDs continues to pose challenges. This study aimed to assess the efficacy of cannabidiol (CBD) formulations, with different concentrations, in patients experiencing sleep bruxism and muscle-related TMDs, with a particular emphasis on their myorelaxant, pain-relieving, and bruxism-reducing properties. Methods: The Research Diagnostic Criteria for Temporomandibular Disorders (RDC/TMDs) was utilized as the diagnostic framework. Sixty patients completed the study, which followed a parallel-group, three-arm, randomized, double-blind clinical trial design, with a 1:1:1 allocation ratio across three groups: 1a, 1b, and 2. Groups 1a and 1b received CBD formulations at concentrations of 10% and 5%, respectively, while Group 2 received a placebo formulation. The trial consisted of four main visits, namely screening, baseline, first follow-up after 14 days, and second follow-up after 30 days, during which surface electromyography (sEMG), the visual analogue scale (VAS) for pain assessment, and Bruxoff examinations were conducted. Results: The reduction in pain, as measured by the visual analogue scale (VAS), among patients using the 10% CBD formulation was 57.4% (p < 0.05), accompanied by a decrease in sEMG activity by 42.1% (p < 0.05). Conversely, individuals using the 5% CBD formulation experienced a 40.8% (p < 0.05) decrease in pain. Regarding the decrease in the sleep bruxism index, users of the 10% CBD formulation saw the highest reduction of 51% (p < 0.05). These findings underscore the efficacy of the proposed treatment in both experimental groups, with a notable advantage observed in Group 1a. Conversely, the outcomes of the selected variables for the control group did not exhibit significant differences throughout the study. Conclusions: The intraoral use of CBD formulations in patients with TMDs have proven to be a successful treatment for reducing pain, muscle tension, and bruxing activity in individuals with sleep bruxism and muscle-related TMDs. Specifically, a concentration of 10% CBD has demonstrated superior results compared to 5% CBD. [ABSTRACT FROM AUTHOR]

The sustainable implementation of resources and the transition to low-carbon construction is on the world's daily agenda. This paper describes the development of criteria for the efficient management of material resources in low-carbon construction. Net income, gross profit, balance sheets, and equity are proposed as indicators that serve as criteria for assessing the efficient use of resources. Nonlinear regression models were the methodological basis for the establishment of cause-and-effect relationships of the volume of construction of transport structures. It was established that since construction companies do not purchase materials for storage, the cost of materials for use in low-carbon technological construction work is directly proportional to the cost of construction. The volume of production in the construction industry is determined by construction costs. More efficient use of low-carbon materials reduces cost and construction waste. In this paper, we have established the relationship between the indicator of efficiency for the functioning of the construction enterprises in Ukraine and the use of low-carbon materials for the construction of transport structures. The practical value of the obtained results for low-carbon construction management lies in proving the relationship between the performance indicators of the construction enterprise (net profit, gross profit, output volume, balance sheets, and equity capital) and the use of low-carbon material resources. Our results form the basis for future research into the use of a cost-based model for low-carbon economy transition in municipalities and regions. [ABSTRACT FROM AUTHOR]

Producers are encouraged to reduce their energy consumption of manufacturing systems by applying less-energy-intensive modern technologies and advanced machine tools and operating methods at the system level. In the paper, organizational and analytical solutions are combined to model the sustainable production system. Managers can study the behavior of a production system organized using energy-saving rules by changing key parameters of the input model (arrival intensity, bottleneck service rate, buffer size, setup and shutdown time) to analyze the queue size of the production system and therefore performance. A discrete-time queueing model of a single-bottleneck production line with a finite input buffer capacity is proposed. Jobs occur according to a binomial process and are processed individually, one by one, according to the natural FIFO service discipline, with a general discrete-type cumulative distribution function. The total number of jobs present in the system is bounded by a non-random fixed value N. Every time the system becomes empty, an energy-saving mechanism is started: the processing machine (server) is turned off during a geometrically distributed shutdown time. Similarly, the first job arriving into the empty system initializes a geometrically distributed setup time. Identifying renewal moments in the evolution of the model, a system of difference equations is built for the transient queue-size distribution conditioned by the state of the system at the opening. The solution is obtained explicitly in terms of probability-generating functions. In addition, the Drum-Buffer-Rope concept is proposed to reduce the energy consumption of the production line. The throughput of the production system is maximized by adjusting the time between the order arrivals and the size of the input buffer to the capacity of the bottleneck. Turning off a machine under certain conditions and slowing down non-critical machines are strategies to reduce energy consumption. A detailed illustrating numerical and simulation study of the considered model is attached as well, in which the sensitivity of the queue-size behavior to changes of the key input model parameters is investigated. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the analysis was to divide Polish regions (as a single region we mean

Purpose: The article aims to build a mathematical model of a bike-sharing station based on an appropriate queueing system and show the model's usefulness in practice. Design/methodology/approach: In designing the model, constructing a queueing system described by exponential distributions with a finite accumulating buffer was used. The existence of the steady state of the system and the global balance principle were used to obtain analytical results. Findings: The most important analytical results are the stationary probability distribution of the number of rented bikes, the so-called loss probability (the probability that the customer has to resign from sharing due to the lack of bikes), as well as the average (mean) values of the number of rented bikes. Originality/value: The paper fits into the broadly understood trend of research related to the smart city concept. The proposed model may be beneficial in practice when designing specific solutions related to the development of bicycle rental stations. [ABSTRACT FROM AUTHOR]

A queueing system of the M/G/n-type, n ≥ 1, with a bounded total volume is considered. It is assumed that the volumes of the arriving packets are generally distributed random variables. Moreover, the AQM-type mechanism is used to control the actual buffer state: each of the arriving packets is dropped with a probability depending on its volume and the occupied volume of the system at the pre-arrival epoch. The explicit formulae for the stationary queue-size distribution and the loss probability are found. Numerical examples illustrating theoretical formulae are given as well.

In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments are presented. A cost optimization problem is solved using an evolutionary strategy for a class of queueing systems described by exponential and Erlang distributions.

Purpose: Currently, in Poland, the process of patient registration at the hospital emergency department (SOR) is carried out in accordance with the S.T.A.R.T. (Simple Triage And Rapid Treatment) standard. According to this procedure, based on a preliminary interview, patients are selected and assigned to one of five risk categories, described by colors: red, orange, yellow, green, or blue. Since this standard is relatively new (introduced in 2019), its analysis using quantitative, not only qualitative, methods are highly desired. Design/methodology/approach: The so-called mean-value approach for studying the proposed queueing model is used in the paper. Findings: For each category of patients, the mean number of patients present in the system, the mean queue length, and the average values of waiting time for admission by a doctor and time spent in the emergency department are found. Two priorities are considered: nonpreemptive (absolute) and preemptive-resume (relative). Numerical calculations illustrate theoretical results. Originality/value: Explicit representations for key queueing characteristics are found analytically. Moreover, illustrating numerical results simulating the "behavior" of a real hospital emergency department are presented and discussed. [ABSTRACT FROM AUTHOR]

In the paper, a finite-capacity queueing model is considered in which jobs arrive according to a Poisson process and are being served according to hyper-exponential service times. A system of equations for the time-sensitive queue-size distribution is established by applying the paradigm of embedded Markov chain and total probability law. The solution of the corresponding system written for Laplace transforms is obtained via an algebraic approach in a compact form. Numerical illustration results are attached as well. [ABSTRACT FROM AUTHOR]

This article proposes a queueing model of the operation of a wireless sensor network node, in which a threshold strategy for starting the node after a period of no transmission is used. In this model, transmission of packets is resumed when the number of packets in the accumulation buffer reaches a predefined level. In the literature, most of the results for models with limited access to the service station are obtained in equilibrium. In this paper, a formula for the Laplace transform of the transient queue-size distribution is obtained and written using the key input parameters of the system. The analytical apparatus uses the concept of the embedded Markov chain, the formula for total probability, renewal theory and some supporting algebraic results. Numerical examples are attached as well. [ABSTRACT FROM AUTHOR]

One of the most important characteristic of each queueing model is time to buffer overflow. In the paper the distribution of that time in a single-channel manufacturing system, modelled by a Markovian finite-buffer queue with machine breakdowns, is studied. By using the analytical approach based on the idea of embedded Markov chain, total probability law and linear algebra, the formula for Laplace transform of the time to buffer overflow conditional distribution is found. Numerical illustration is presented.

Increase flexibility of manufacturing requires implementation of effective planning IT tools. Planning and scheduling problems traditionally consider the production resources as the only constraints. Since the raw material and intermediate transferring times are relevant in relation to the production times, it is required to model the material handling equipment and its activities. The problem of scheduling subject to manufacturing and logistical constraints based on data-driven models generation method is presented. A KbRS and FlexSim systems are used as a scheduling tool.

The paper presents application of ant colony optimisation algorithm for scheduling multi-resources operations in flexible job shop type of production systems. Operations that require the participation of two or more resources are common in industrial practice, when planning are subject not only machines, but also other additional resources (personnel, tools, etc.). Resource requirements of operation are indicated indirectly by resource groups. The most important parameters of the resource model and resource groups are also described. A basic assumptions for ant colony algorithm used for scheduling in the considered model with multiresources requirements of operations is discussed. The main result of the research is the schema of metaheuristic that enables searching best-score solutions in manufacturing systems satisfying presented constraints.

In the manuscript, a probability distribution of the queue length is studied in a model with group Markov arrivals, arbitrarily distributed service times and finite waiting room. After the period of suspension of service due to lack of packets, each new busy period is preceded by a random setup time. Integral equations for time-dependent queue-length distribution are derived by identifying renewal moments in the operation of the system and by applying total probability law. The representation for the solution of the system is found in terms of Laplace transforms. Computational examples illustrating the impact of system parameters on the queue-length distribution are included. [ABSTRACT FROM AUTHOR]

Non-stationary behavior of departure process in a finite-buffer MX=G=1=K-type queueing model with batch arrivals, in which a threshold-type waking up N-policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the Nth message occurrence, where the threshold value N is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a compact-form representation for the mixed double transform (probability generating function of the Laplace transform) of the probability distribution of the number of messages completely served up to fixed time t is obtained. The considered queueing system has potential applications in modeling nodes of wireless sensor networks (WSNs) with battery saving mechanism based on threshold-type waking up of the radio. An illustrating simulational and numerical study is attached. [ABSTRACT FROM AUTHOR]

The method of maintenance and production task scheduling is proposed to make the production system insensitive to a disruption. The method enables the maintenance of high values of schedule evaluation indicators in variable conditions, such as stability robustness and quality robustness. The frequency of a machine failure is described by the Maxwell distribution. Formulae for different reliability characteristics are given. The parameters of the distribution are estimated using maximum likelihood, empirical moments and a method based on the renewal theory. The advantage of the last method is the ability to achieve accurate predictions of failure-free time of a machine, when there is a lack of complementary and reliable historical data. In the related literature, only the first method is used to estimate unknown parameters of the probability distribution. The methods are applied to job-shop scheduling problems to evaluate their impact on achieving predictive schedules. [ABSTRACT FROM AUTHOR]

A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer over ow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer over ows is also given. Numerical examples are attached as well. [ABSTRACT FROM AUTHOR]

A single-channel FIFO queueing model with finite buffer capacity and the multiple vacation policy is investigated, in which jobs arrive according to a compound Poisson process and are being processed individually with a general-type distribution function of the service time. A multiple vacation period, consisting of a number of independent generally-distributed server vacations, is being started each time when the system becomes empty. During this period, the processing of jobs is suspended. Successive server vacations are being initialised until at least one job is present in the buffer at the completion epoch of one of them. A compact formula for the Laplace transform of the distribution of the time to the first buffer overflow, conditioned by initial number of packets present in the buffer, is found. The analytical approach is based on the paradigm of embedded Markov chain, integral equations and Korolyuk's potential idea. Numerical illustrating examples are attached as well. [ABSTRACT FROM AUTHOR]

A model of a single-machine production system with finite magazine capacity is investigated. The input ow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overows is also given. Numerical examples are attached as well. [ABSTRACT FROM AUTHOR]