On Little’s Formula in Multiphase Queues

Minkevičius, Saulius; Katin, Igor; Katina, Joana; Vinogradova-Zinkevič, Irina

doi:10.3390/math9182282

Mathematics

2021

DOI: 10.3390/math9182282

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On Little’s Formula in Multiphase Queues

Saulius Minkevičius

Igor Katin

Joana Katina

et al.

Abstract: The structure of this work in the field of queuing theory consists of two stages. The first stage presents Little’s Law in Multiphase Systems (MSs). To obtain this result, the Strong Law of Large Numbers (SLLN)-type theorems for the most important MS probability characteristics (i.e., queue length of jobs and virtual waiting time of a job) are proven. The next stage of the work is to verify the result obtained in the first stage.

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Cited by 3 publications

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“…In the fourteenth paper [14], a subject from queuing theory is considered, where the suggested approach consists of two stages. In the first stage, Little's law in Multiphase Systems is analyzed.…”

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Special Issue “Mathematical Methods for Operations Research Problems”

Werner

2021

Mathematics

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confidence: 99%

Special Issue “Mathematical Methods for Operations Research Problems”

Werner

2021

Mathematics

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Models for optimising the volume of material flows in the technological chain of corporate vertically integrated structures of the agricultural sector

Zagurskiy,

Sobczuk,

Lisetskyi

2024

Naukovì dopovìdì Nacìonalʹnogo unìversitetu bìoresursìv ì priro

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The relevance of this study lies in the need to optimise supply cycles and volumes in value chains, which helps to reduce costs and increase the profitability of agricultural enterprises. The purpose of this study was to investigate and optimise the costs of initial material flows in the production subsystems of corporate vertically integrated structures of the agricultural complex under conditions of non-stationary demand. To fulfil this purpose, the study investigated the relationship between the amount of raw material stock stored in the production subsystem and the time of its consumption, based on which an extended model of the economic order quantity (EOQ) was considered, which, apart from the defined costs, also considers the costs of raw material shortages associated with the inability to fulfil deliveries and losses associated with supply failures caused by the unpredictability (stochasticity) of the order flow itself. It was found that in continuous production systems there is an opportunity to reduce the costs associated with failures by using an additional regular supply batch. For this, the mathematical “point-of-order” model was built based on the theory of mass service, which allows determining not only the best point to order, but also the optimal amount of the safety stock. A model for optimising the volume of material flows was proposed, which combines the model of the economic order quantity order adapted for use in product subsystems of corporate integrated structures of the agricultural complex and the “point-of-order” model, which allows calculating the minimum size of the insurance stock of raw materials using the tools of operations research. As an example, the material flow was optimised for Kivshovata Agro LLC. The findings of the study, such as the use of analytical tools and models for determining the economic order quantity and safety stock, can be used by the management of agricultural enterprises to improve the efficiency of material flow management

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Modeling the Operation of Signal-Controlled Intersections with Different Lane Occupancy

2022

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In many cities of the world, the problem of traffic congestion on the roads remains relevant and unresolved. It is especially noticeable at signal-controlled intersections, since traffic signalization is among the most important factors that reduce the maximum possible value of the traffic flow rate at the exit of a street intersection. Therefore, the development of a methodology aimed at reducing transport losses when pedestrians move through signal-controlled intersections is a joint task for the research and engineering community and municipalities. This paper is a continuation of a study wherein the results produced a mathematical model of the influence of lane occupancy and traffic signalization on the traffic flow rate. These results were then experimentally confirmed. The purpose of this work is to develop a method for the practical application of the mathematical model thus obtained. Together with the obtained results of the previous study, as well as a systems approach, traffic flow theory, impulses, probabilities and mathematical statistics form the methodological basis of this work. This paper established possible areas for the practical application of the previously obtained mathematical model. To collect the initial experimental data, open-street video surveillance cameras were used as vehicle detectors, the image streams of which were processed in real time using neural network technologies. Based on the results of this work, a new method was developed that allows for the adjustment of the traffic signal cycle, considering the influence of lane occupancy. In addition, the technological, economic and environmental effects were calculated, which was achieved through the application of the proposed method.

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On Little’s Formula in Multiphase Queues

Cited by 3 publications

References 32 publications

Special Issue “Mathematical Methods for Operations Research Problems”

Special Issue “Mathematical Methods for Operations Research Problems”

Models for optimising the volume of material flows in the technological chain of corporate vertically integrated structures of the agricultural sector

Modeling the Operation of Signal-Controlled Intersections with Different Lane Occupancy

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