Informatics and Applications
2017, Volume 11, Issue 4, pp 109-117
STUDY OF THE MMPP/GI/w QUEUEING SYSTEM WITH RANDOM CUSTOMERS' CAPACITIES
- E. Lisovskaya
- S. Moiseeva
- M. Pagano
- V. Potatueva
Abstract
A queueing system with an infinite number of servers is considered. Customers arrive in the system according to a Markov Modulated Poisson Process (MMPP). Each customer carries a random quantity of work (capacity of the customer). In this study, service time does not depend on the customers' capacities; the latter are used just to fix some additional features of the system's evolution. It is shown that the joint probability distribution of the customers' number and total capacities in the system is two-dimensional Gaussian under the asymptotic condition of an infinitely growing service time. Simulation results allow determining the applicability area of the asymptotic result.
[+] References (13)
- Mandjes, M. 2007. Large deviations of Gaussian queues. Chichester: Wiley. 340 p.
- Melikov, A., L. Zadiranova, and A. Moiseev 2016. Two asymptotic conditions in queue with MMPP arrivals and feedback. Comm. Com. Inf. Sc. 678:231-240. doi: 10.1007/978-3-319-51917-3_21.
- Naumov, V., K. Samouylov, E. Sopin, and S. Andreev.
2015. Two approaches to analyzing dynamic cellular networks with limited resources. 6th Congress (Interna-tional) on Ultra Modern Telecommunications and Control Systems and Workshops. St. Petersburg. 485-488. doi: 10.1109/ICUMT2014.7002149.
- Morozov, E., L. Potakhina, and O. Tikhonenko. 2016. Regenerative analysis of a system with a random volume of customers. Comm. Com. Inf. Sc. 638:261-272. doi: 10.1007/978-3-319-44615-8_23.
- Tikhonenko, O. M., and W. Kempa. 2015. Queueing sys-tems with processor sharing and limited memory under control of the AQM mechanism. Automat. Rem. Contr 76(10):1784-1796. doi: 10.1134/S0005117915100069.
- Naumov, V. A., K. E. Samuilov, and A. K. Samuilov. 2016. On the total amount of resources occupied by serviced customers. Automat. Rem. Contr. 77(8):1419-1427.
- Tikhonenko, O. M. 2010. Queueing system with processor sharing and limited resources. Automat. Rem. Contr. 71(5):803-815.
- Pankratova, E. V., and S. P Moiseeva. 2014. Queueing sys-tem MAP/M/то with n types of customers. Comm. Com. Inf. Sc. 487:356-366.
- Moiseev, A., and A. Nazarov. 2016. Tandem of infinite- server queues with Markovian arrival process. Comm. Com. Inf. Sc. 601:323-333. doi: 10.1007/978-3-319-30843- 2_34.
- Lisovskaya, E., S. Moiseeva, and M. Pagano. 2016. The total capacity of customers in the infinite-server queue with MMPP arrivals. Comm. Com. Inf. Sc. 678:110-120. doi: 10.1007/978-3-319-51917-3-11.
- Moiseev, A., and A. Nazarov. 2016. Queueing network MAP/(GI/to)k with high-rate arrivals. Eur. J. Oper. Res. 254:161-168. doi: 10.1016/j.ejor.2016.04.011.
- Moiseev, A.N., and M.V. Sinyakov. 2010. Razrabotka ob"ektno-orientirovannoy modeli sistemy imitatsionnogo modelirovaniya protsessov massovogo obsluzhivaniya [Design of object-oriented model for queueing simulation software]. Vestnik Tomskogogosudarstvennogo universiteta. Upravlenie, vychislitel'naya tekhnika i informatika [Tomsk State University. J. Control Computer Sci.] 1:89-93.
- Moiseev, A., A. Demin, V. Dorofeev, and V. Sorokin.
2016. Discrete-event approach to simulation of queueing networks. Key Eng. Mater. 685:939-942. doi: 10.4028/www.scientific.net/KEM.685.939.
[+] About this article
Title
STUDY OF THE MMPP/GI/w QUEUEING SYSTEM WITH RANDOM CUSTOMERS' CAPACITIES
Journal
Informatics and Applications
2017, Volume 11, Issue 4, pp 109-117
Cover Date
2017-12-30
DOI
10.14357/19922264170414
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
infinite-server queueing system; random capacity of customers; Markov Modulated Poisson Process
Authors
E. Lisovskaya  , S. Moiseeva ,
M. Pagano  , and V. Potatueva
Author Affiliations
Tomsk State University, 36 Lenin ave., Tomsk 634050, Russian Federation
University of Pisa, 16 Via Caruso, Pisa 56122, Italy
|