Acta mathematica scientia, Series B >
FUNCTIONAL ANALYSIS METHOD FOR THE M/G/1 QUEUEING MODEL WITH OPTIONAL SECOND SERVICE
Received date: 2012-04-02
Revised date: 2013-03-27
Online published: 2014-07-20
Supported by
This work was supported by the National Natural Science Foundation of China (11371303) and Natural Science Foundation of Xinjiang (2012211A023), and Science Foundation of Xinjiang University (XY110101).
By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-
state queueing size at the departure point.
Geni GUPUR , Ehmet KASIM . FUNCTIONAL ANALYSIS METHOD FOR THE M/G/1 QUEUEING MODEL WITH OPTIONAL SECOND SERVICE[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1301 -1330 . DOI: 10.1016/S0252-9602(14)60086-2
[1] Adams R A. Sobolev Spaces. New York: Academic Press, 1975
[2] Arendt W, Batty C J K. Tauberian theorems and stability of one-parameter semigroups. Tran Amer Math Soc, 1998, 306: 837–852
[3] Cheng Z S, Gupur G. Other eigenvalues of the exhaustive-service M/M/1 queueing model with single vacations. Int J Pure Appl Math, 2007, 41: 1171–1186
[4] Choudhury G. Some aspects of an M/G/1 queueing system with optional second service. Top, 2003, 11: 141–150
[5] Greiner G. Perturbing the boundary conditions of a generator. Houston J Math, 1987, 13: 213–229
[6] Gupur G. Functional Analysis Methods for Reliability Models, Pseudo-Differential Operators, Theory and Applications, Vol 6. Basel: Birkh¨auser, 2011
[7] Gupur G, Cao J. Asymptotic properties of the four indices for the M/M/1 queueing system. Mathematics in Practice and Theory, 2003 33: 45–48
[8] Gupur G, Li X Z, Zhu G T. Functional Analysis Method in Queueing Theory. Hertfordshire: Research Information Ltd, 2001
[9] Haji A, Radl A. A semigroup approach to queueing systems. Semigroup Forum, 2007, 75: 610–624
[10] Haji A, Radl A. Asymptotic stability of the solution of the M/MB/1 queueing model. Comp Math Appl, 2007, 53: 1411–1420
[11] Ke J C, Chu Y K. Optimization on bicriterion policies for M/G/1 system with second optional service. Journal of Zhejiang University-Science A, 2008, 9: 1437–1445
[12] Ke J C. An M [x]/G/1 system with startup server and J additional options for service. Appl Math Modell, 32: 443–458
[13] Kasim E, Gupur G. Other eigenvavlues of the M/M/1 operator. Acta Anal Funct Appl, 2011, 13(1): 45–64
[14] Madan K C. An M/G/1 queue with second optional service. Queueing Systems: Theory and Applications, 2000, 34: 37–46
[15] Nagel R. One-parameter semigroups of positive operators//LNM 1184. Berlin: Springer, 1986
[16] Zhao C H. Well-Posedness of the M/G/1 Queueing Model with Optional Second Service [D]. Urumqi: Xinjiang
University, 2009
[17] Zhao C H, Gupur G. Well-posedness of the M/G/1 queueing model with optional second service. Acta Anal Funct Appl, 2011, 13(2): 124–135
/
| 〈 |
|
〉 |