Application of Machine Learning Methods to Solving Problems of Queuing Theory

Vishnevsky, Vladimir; Gorbunova, A. V.

doi:10.1007/978-3-031-09331-9_24

Cited by 6 publications

(2 citation statements)

References 26 publications

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“…It depends on the number of tasks in the customer. In the article [27], you can familiarize yourself with the use of neural networks for the analysis of fork-join systems and other complex problems of queuing theory (for example, [28,29]).…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Fork–Join System with Markovian Arrival Process Arrivals and Phase-Type Service Time Distribution Using Machine Learning Methods

Vishnevsky,

Klimenok,

Sokolov

et al. 2024

Mathematics

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This paper presents a study of fork–join systems. The fork–join system breaks down each customer into numerous tasks and processes them on separate servers. Once all tasks are finished, the customer is considered completed. This design enables the efficient handling of customers. The customers enter the system in a MAP flow. This helps create a more realistic and flexible representation of how customers arrive. It is important for modeling various real-life scenarios. Customers are divided into K≥2 tasks and assigned to different subsystems. The number of tasks matches the number of subsystems. Each subsystem has a server that processes tasks, and a buffer that temporarily stores tasks waiting to be processed. The service time of a task by the k-th server follows a PH (phase-type) distribution with an irreducible representation (βk, Sk), 1≤k≤K. An analytical solution was derived for the case of K=2 when the input MAP flow and service time follow a PH distribution. We have efficient algorithms to calculate the stationary distribution and performance characteristics of the fork–join system for this case. In general cases, this paper suggests using a combination of Monte Carlo and machine learning methods to study the performance of fork–join systems. In this paper, we present the results of our numerical experiments.

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Section: Introductionmentioning

confidence: 99%

Investigation of the Fork–Join System with Markovian Arrival Process Arrivals and Phase-Type Service Time Distribution Using Machine Learning Methods

Vishnevsky,

Klimenok,

Sokolov

et al. 2024

Mathematics

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“…While the first steps in the successful application of machine learning to evaluate the performance characteristics of simple and complex queueing systems have already been taken, the total number of works on this topic still remains modest. As for reviews, we can only refer to a recent paper by Vishnevsky and Gorbunova [ 1 ] which proposes a systematic introduction to the use of machine learning in the study of queueing systems and networks. Before we formulate our specific problem we would like also to make a small contribution to the popularisation of machine learning in the queueing theory by describing briefly the latest works.…”

Section: Introductionmentioning

confidence: 99%

Optimal Scheduling in General Multi-Queue System by Combining Simulation and Neural Network Techniques

Efrosinin

Vishnevsky

Stepanova³

2023

Sensors

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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.

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On Estimating the Average Response Time of High-Performance Computing Environments

Gorbunova¹,

Vishnevsky²

2022

Lecture Notes in Computer Science

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Application of Machine Learning Methods to Solving Problems of Queuing Theory

Cited by 6 publications

References 26 publications

Investigation of the Fork–Join System with Markovian Arrival Process Arrivals and Phase-Type Service Time Distribution Using Machine Learning Methods

Investigation of the Fork–Join System with Markovian Arrival Process Arrivals and Phase-Type Service Time Distribution Using Machine Learning Methods

Optimal Scheduling in General Multi-Queue System by Combining Simulation and Neural Network Techniques

On Estimating the Average Response Time of High-Performance Computing Environments

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