Delay analysis of a queue with re-sequencing buffer and Markov environment

There are simple service disciplines where the system time of a tagged customer depends only on the customers arriving in the system earlier (for example first-in-first-out (FIFO)) or later (for example LIFO) than the tagged one. In this paper we consider a single-server queueing system with two infinite queues in which the system time of a tagged customer may depend on both the customers arriving in the system earlier and later than the tagged one. New regular customers arrive in the system according to Markov arrival process (MAP) flow, occupy one place in the buffer and receive service in FIFO order. External re-sequencing signals also arrive at the system according to (different) MAP flow. Each re-sequencing signal transforms one regular customer into a delayed one by moving it to another queue (re-sequencing buffer), wherefrom it is served with lower priority than the regular ones. Service times of customers from both queues also have MAP distribution different from those which govern arrivals. Queueing system with memoryless ingredients (arrival, service, resequencing) has already been a subject of extensive research. In this paper we investigate how the essential analytical properties of scalar functions, which made the analysis of the memory less system feasible, can be extended to the case of a Markov environment.

Authors
Razumchik R. 1, 2 , Telek M.3, 4
Number of issue
1-2
Language
English
Pages
7-28
Status
Published
Volume
82
Year
2016
Organizations
  • 1 Russian Acad Sci, Fed Res Ctr Comp Sci & Control, Inst Informat Problems, Moscow, Russia
  • 2 Peoples Friendship Univ Russia, Moscow, Russia
  • 3 MTA BME Informat Syst Res Grp, Budapest, Hungary
  • 4 Tech Univ Budapest, Budapest, Hungary
Keywords
Delay analysis; Re-sequencing buffer; Matrix analytic methods; Kronecker expansion
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/7978/
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