Analysis of the M/G/1 retrial queueing model with server breakdowns

作者：Gupur Geni^*

来源：Journal of Pseudo-Differential Operators and Applications, 2010, 1(3): 313-340.

DOI：10.1007/s11868-010-0015-0

• The M/G/1 retrial queueing model with server breakdowns
• C-0-semigroup
• Dispersive operator
• Resolvent set
• Eigenvalue

By using the Hille-Yosida theorem and the Phillips theorem in functional analysis we prove that the M/G/1 retrial queueing model with server breakdowns has a unique nonnegative time-dependent solution. Next, when the service completion rate is a constant, by studying spectral properties of the operator corresponding to the model we study asymptotic behavior of its time-dependent solution. First of all, through considering the resolvent set of the adjoint operator of the operator we obtain that all points on the imaginary axis except zero belong to the resolvent set of the operator. In addition, we prove that zero is not an eigenvalue of the operator. Our results show that the time-dependent solution of the model strongly converges to zero.

• 出版日期2010-9
• 单位新疆大学