Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (4): 1301-1330.doi: 10.1016/S0252-9602(14)60086-2

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FUNCTIONAL ANALYSIS METHOD FOR THE M/G/1 QUEUEING MODEL WITH OPTIONAL SECOND SERVICE

 Geni GUPUR, Ehmet KASIM   

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
  • Received:2012-04-02 Revised:2013-03-27 Online:2014-07-20 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).

Abstract:

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.

Key words: M/G/1 queueing model with optional second service, eigenvalue, resolvent set

CLC Number: 

  • 47A10
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