Infinite-server bulk queue with mmpp arrivals

We consider a queueing system with batch MMPP arrivals and an unlimited number of servers. An arriving group of customers occupies necessary number of free servers for a random time determined by a given probability distribution function. At the end of the service, the whole group releases all the servers at the same time. In the paper, we obtain the probability distribution of the number of customers in the system. To solve the problem, we use the dynamic screening method and asymptotic analysis such condition of high intensity of arrivals. It is shown that under condition the probability distribution of the number of customers in the system is Gaussian. The parameters of this Gaussian distribution are obtained in the paper. © 2020, Springer Nature Switzerland AG.

Authors
Boyarkina A.1 , Moiseeva S. 1 , Pagano M.2 , Lisovskaya E. 1, 3 , Moiseev A. 1
Journal
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Language
English
Pages
158-170
Status
Published
DOI
10.1007/978-3-030-62885-7_12
Volume
12023 LNCS
Year
2020
Organizations
  • 1 Tomsk State University, 36 Lenina Avenue, Tomsk, 634050, Russian Federation
  • 2 Department of Information Engineering, University of Pisa, Via Caruso 16, Pisa, 56122, Italy
  • 3 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
Keywords
Asymptotic analysis; Batch arrivals; Bulk service; Dynamic screening method; Infinite-server queue
Date of creation
20.04.2021
Date of change
20.04.2021
Short link
https://repository.rudn.ru/en/records/article/record/71866/
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Article
Zorin A.V., Sevastianov L.A., Tretyakov N.P.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 12023 LNCS. 2020. P. 171-185