Informatics and Applications
2023, Volume 17, Issue 4, pp 57-63
BOUNDS OF THE WORKLOAD IN A MULTICLASS RETRIAL QUEUE WITH EXPONENTIAL SERVICES
Abstract
A multiclass retrial queue with Poisson input and M classes of customers is investigated. For the given retrial system with exponential service times, the lower and upper bounds of the workload are derived. It is shown that the workload in the classical system M/Hm /1 with hyperexponential service times is the lower bound for the workload of the given retrial system. The upper bound is the workload in the classical M/G/l system where each customer occupies the server for the given service time and additional time corresponding to the inter-retrial time from the "slowest" orbit. The presented simulation results confirm the theoretical conclusions.
[+] References (18)
- Artalejo, J. R. 1999. Accessible bibliography on retrial queues. Math. Comput. Model. 30(3-4):1-6. doi: 10.1016/S0895-7177(99)00128-4.
- Artalejo, J., and A. Gomez-Corral. 2008. Retrial queueing systems: A computational approach. Springer. 318 p. doi: 10.1007/978-3-540-78725-9.
- Fayolle, G. 1986. A simple telephone exchange with delayed feedbacks. Seminar (International) on Teletraffic Analysis and Computer Performance Evaluation Proceedings. Elseiver Science. 245-253.
- Choi, B.D., Y.W. Shin, and W.C. Ahn. 1992. Retrial queues with collision arising from unslotted CSMA/CD protocol. Queueing Syst. 11:335-356. doi: 10.1007/ BF01163860.
- Choi, B.D., K.H. Rhee, and K.K. Park. 1993. The M/G/1 retrial queue with retrial rate control policy Probab. Eng. Inform. Sc. 7(1):29-46. doi: 10.1017/ S0269964800002771.
- Bertsekas, D., and R. Gallager. 2021. Data networks. Athena Scientific. 570 p.
- Avrachenkov, K., and U. Yechiali. 2008. Retrial networks with finite buffers and their application to Internet data traffic. Probab. Eng. Inform. Sc. 22(4):519-536. doi: 10.1017/S0269964808000314.
- Avrachenkov, K., andU. Yechiali. 2010. On tandem blocking queues with a common retrial queue. Comput. Oper. Res. 37(7): 1174- 1180. doi: 10.1016/j.cor.2009.10.004.
- Yao, S., F Xue, B. Mukherjee, S. J. B. Yoo, and S. Dixit. 2002. Electrical ingress buffering and traffic aggregation for optical packet switching and their effect on TCP-level performance in optical mesh networks. IEEE Commun. Mag. 40(9):66-72. doi: 10.1109/MC0M.2002.1031831.
- Wong, E.W.M., L.L.H. Andrew, T. Cui, B. Moran, A. Zalesky, R. S. Tucker, and M. Zukerman. 2009. To
wards a bufferless optical internet. J. Lightwave Technol. 27(14):2817-2833. doi: 10.1109/JLT.2009.2017211.
- Morozov, E.V., I.V Peshkova, and A. S. Rumyantsev. 2023. Bounds and maxima for the workload in a multi-class orbit queue. Mathematics 11(3):564. doi: 10.3390/ math11030564.
- Peshkova, I., and E. Morozov. 2022. On comparison of multiserver systems with multicomponent mixture distributions. J. Math. Sci. 267(2):260-272. doi: 10.1007/ s10958-022-06132-z.
- Peshkova, I.V. 2022. Granitsy ekstremal'nogo indeksa vremeni ozhidaniya v sisteme M/G/1 s raspredeleniem vremeni obsluzhivaniya v vide konechnoy smesi [On bounds of the stationary waiting time extremal index in M/G/1 system with mixture service times]. Informati- ka i ee Primeneniya - Inform. Appl. 16(4):26-33. doi: 10.14357/19922264220405. EDN: VFKRKT.
- Rego, V. 1988. Some explicit formulas for mixed exponential service systems. Comput. Oper. Res. 15(6):509-520. doi: 10.1016/0305-0548(88)90047-0.
- Morozov, E. V., A. S. Rumyantsev, S. Dey, and T. G. Deepak. 2019. Performance analysis and stability of multiclass orbit queue with constant retrial rates and balking. Perform. Evaluation 134:102005. doi: 10.1016/ J.PEVA.2019.102005.
- Asmussen, S. 2003. Applied probability and queues. Stochastic modelling and applied probability. New York, NY: Springer. 438 p.
- Ross, S., J. Shanthikumar, and Z. Zhu. 2005. On increasing-failure-rate random variables. J. Appl. Probab. 42(3):797-809. doi: 10.1239/jap/1127322028.
- Haji, R., and G. F Newell. 1971. A relation between stationary queue and waiting time distributions. J. Appl. Probab. 8(3):617-620. doi: 10.2307/3212186.
[+] About this article
Title
BOUNDS OF THE WORKLOAD IN A MULTICLASS RETRIAL QUEUE WITH EXPONENTIAL SERVICES
Journal
Informatics and Applications
2023, Volume 17, Issue 4, pp 57-63
Cover Date
2023-12-10
DOI
10.14357/19922264230408
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
retrial queue; workload; stochastic ordering
Authors
I. V. Peshkova  , 
Author Affiliations
Petrozavodsk State University, 33 Lenina Pr., Petrozavodsk 185910, Russian Federation
Karelian Research Center of the Russian Academy of Sciences, 11 Pushkinskaya Str., Petrozavodsk 185910, Russian Federation
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