MULTI-SERVER RERTIAL QUEUEING SYSTEM AS A MODEL OF A MOBILE NETWORK CELL
Abstract
A multi-server queueing system with two types of customers as a model of a cell of mobile network is considered. Part of the servers is reserved for service of first type customers only. The customers who do not receive service can make repeated attempts. All the system parameters including the total number of servers and the number of reserved servers are influenced by a random environment. The process of the system states is constructed, the ergodicity condition is derived, the stationary distribution of the system states is computed. The formulas for the main performance measures of the system are presented.
About the Authors
S. A. Dudin
Белорусский государственный университет
Belarus
Belarus
O. S. Dudina
Белорусский государственный университет
Belarus
Belarus
References
1. Tran-Gia, P. Modeling of customer retrial phenomenon in cellular mobile networks / P. Tran-Gia, M. Mandjes // IEEE Journal on Selected Areas in Communications. – 1997. – Vol. 15. – P. 1406–1414.
2. Choi, B.D. A simple numerical approximation of joint probabilities of calls in service and calls in the retrial group in a picocell / B.D. Choi, A. Melikov, A. Velibekov // Applied Computational Mathematics. – 2008. – Vol. 7. – P. 21–30.
3. Do, T.V. Solution for a retrial queueing problem in cellular networks with the Fractional Guard Channel policy / T.V. Do // Mathematical and Computer Modelling. – 2011. – Vol. 53. – P. 2059–2066.
4. Zhou, Z. Optimization of the (MAP1,MAP2 ) / (PH1,PH2 ) / N retrial queue model of wireless cellular networks with channel allocation / Z. Zhou, Y. Zhu // Computers and Electrical Engineering. – 2013. – Vol. 39. – P. 1637–1649.
5. Kim, C.S. Optimization of Guard Channel Policy in Cellular Mobile Networks with Account of Retrials / C.S. Kim, V.I. Klimenok, A.N. Dudin // Computers and Operation Research. – 2014. – Vol. 43. – P. 181–190.
6. Erlang loss queueing system with batch arrivals operating in a random environment / C.S. Kim [et al.] // Computers and Operations Research. – 2009. – Vol. 36. – P. 674–967.
7. The BMAP/PH/N retrial queueing system operating in Markovian random environment / C.S. Kim [et al.] // Computers and Operations Research. – 2010. – Vol. 37. – P. 1228–1237.
8. Wu, J. Analysis of the finite source MAP / PH / N retrial G-queue operating in a random environment / J. Wu, Z. Liu, G. Yang // Applied Mathematical Modelling. – 2001. – Vol. 35. – P. 1184–1193.
9. Cordeiro, J.D. The unreliable M/M/1 retrial queue in a random environment / J.D. Cordeiro, J.P. Kharoufeh // Stochastic Models. – 2012. – Vol. 28. – P. 29–48.
10. Dudin, A.N. Analysis of multiserver retrial queueing system with varying capacity and parameters / A.N. Dudin, O.S. Dudina // Mathematical Problems in Engineering. – 2015. – Vol. 2015. – P. 1–12.
11. Klimenok, V.I. Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory / V.I. Klimenok, A.N. Dudin // Queueing Systems. – 2006. – Vol. 54. – P. 245–259.
Review
For citations:
Dudin S.A., Dudina O.S. MULTI-SERVER RERTIAL QUEUEING SYSTEM AS A MODEL OF A MOBILE NETWORK CELL. Informatics. 2016;(2):19-29. (In Russ.)
Views: 694
Email this article 