Informatics and Applications
2020, Volume 14, Issue 2, pp 66-71
STATIONARY CHARACTERISTICS OF M/G/2/infinity QUEUE WITH IDENTICAL SERVERS, LIFO SERVICE, AND RESAMPLING POLICY
- L. A. Meykhanadzhyan
- R. V. Razumchik
Abstract
Consideration is given to the M/G/2/infinity queue with identical servers, LIFO (last in, first out) service
discipline and one special case of the generalized probabilistic priority policy called resampling. The latter implies
that a customer arriving to the nonidle system assigns independently new remaining service time to each customer
currently in service. The new customer itself either enters a free server, if there is any, or occupies a place in
the queue. Remaining service times are assumed to be independent identically distributed random variables with
the known general absolute continuous distribution. Under the assumption that the stationary regime exists, the
main performance characteristics of the system, including the joint stationary distribution of the total number of
customers in the system and the remaining service times of customers in service, are derived.
[+] References (9)
- Horvath I., R. Razumchik, and M. Telek. 2019. The resampling M/G/l non-preemptive LIFO queue and its
application to systems with uncertain service time. Perform.
Evaluation 134:102000.
- Meykhanadzhyan, L. A., T. A. Milovanova, A. V. Pechinkin,
and R. V. Razumchik. 2014. Statsionarnye veroyatnosti sostoyaniy v sisteme obsluzhivaniya s inversionnym poryadkom obsluzhivaniya i obobshchennym veroyatnostnym prioritetom [Stationary distribution in a queueing system with
inverse service order and generalized probabilistic priority].
Informatika i ee Primeneniya - Inform. Appl. 8(3):28-38.
- Meykhanadzhyan, L., and R. Razumchik. 2016. New
scheduling policy for estimation of stationary performance
characteristics in single server queues with inaccurate job
size information. 30th European Conference on Modelling
and Simulation Proceedings. Dudweiler, Germany: Digital-
druck Pirrot GmbH. 710-716.
- Milovanova, T.A., L.A. Meykhanadzhyan, and
R. V. Razumchik. 2018. Bounding moments of sojourn time in M/G/l FCFS queue with inaccurate job size information and additive error: Some observations from numerical experiments. CEUR Workshop Proceedings 2236:24-30.
- Meykhanadzhyan, L. A., and R. V. Razumchik. 2019. Sistema massovogo obsluzhivaniya Geo/G/l/infinity s inversionnym poryadkom obsluzhivaniya i resamplingom v diskretnom vremeni [Discrete-time Geo/G/l/æ LIFO queue with resampling policy]. Informatika i ee Primeneniya - Inform. Appl. 13(4):60-67.
- Hokstad, P. 1979. On the steady-state solution of the M/G/2 queue. Adv. Appl. Probab. 11(1):240-255.
- Wiens, D. P. 1989. On the busy period distribution of the M/G/2 queueing system. J. Appl. Probab. 26(4):858-865.
- Knessl, C., B. J. Matkowsky, Z. Schuss, and C. Tier. 1990. An integral equation approach to the M/G/2 queue. Oper. Res. 38(3):506-518.
- Pechinkin, A.V. 1983. Ob odnoy invariantnoy sisteme massovogo obsluzhivaniya [On an invariant queuing system]. Math. Operationsforsch. Statist. Ser. Optimization 14(3):433-444. doi: 10.1080/02331938308842876.
[+] About this article
Title
STATIONARY CHARACTERISTICS OF M/G/2/infinity QUEUE WITH IDENTICAL SERVERS, LIFO SERVICE, AND RESAMPLING POLICY
Journal
Informatics and Applications
2020, Volume 14, Issue 2, pp 66-71
Cover Date
2020-06-30
DOI
10.14357/19922264200209
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
multiserver system; inverse service order; probabilistic priority; resampling
Authors
L. A. Meykhanadzhyan  and R. V. Razumchik 
Author Affiliations
Financial University under the Government of the Russian Federation, 49 Leningradsky Prospekt, Moscow
125993, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
|