Asymptotic diffusion analysis of RQ system M/M/1 with unreliable server

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Abstract

The paper considers a single-line retrial queueing system with an unreliable server. Queuing systems are called unreliable if their servers may fail from time to time and require restoration (repair), only after which they can resume servicing customers. The input of the system is a simple Poisson flow of customers. The service time and uptime of the server are distributed exponentially. An incoming customer try to get service. The server can be free, busy or under repair. The customer is serviced immediately if the server is free. If it is busy or under repair, the customer goes into orbit. And after a random time it tries to get service again. The study is carried out by the method of asymptotically diffusion analysis under the condition of a large delay of requests in orbit. In this work, the transfer coefficient and diffusion coefficient were found and a diffusion approximation

About the authors

Nataliya M. Voronina

National Research Tomsk Polytechnic University

Email: vnm@tpu.ru
ORCID iD: 0000-0001-9044-5211
Scopus Author ID: 57802914700
ResearcherId: AAD-2035-2019

Senior Lecturer of Department of Information Technology of School of Information Technology and Robotics Engineering

30 Lenina Ave, Tomsk, 634050, Russian Federation

Svetlana V. Rozhkova

National Research Tomsk Polytechnic University; National Research Tomsk State University

Author for correspondence.
Email: rozhkova@tpu.ru
ORCID iD: 0000-0002-8888-9291
Scopus Author ID: 6603581666
ResearcherId: F-5512-2017

Doctor of Physics and Mathematics Sciences, Professor of Department of Mathematics and Mathematical Physics of School of Nuclear Technology Engineering, National Research Tomsk Polytechnic University, Professor of Department of Probability Theory and Mathematical Statistics Institute of Applied Mathematics and Computer Science, National Research Tomsk State University

30 Lenina Ave, Tomsk, 634050, Russian Federation; 36 Lenina Ave, Tomsk, 634050, Russian Federation

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