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《Journal of Jiangxi Normal University(Natural Science Edition)》 2018-03
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The Spectral Properties of the Operator Corresponding to the M/G/1/1 Feedback Queue with Regular and Optional Services

ALIM Mijit;Xinjiang Radio and TV University;  
Under a certain condition,by studying the spectral properties of the underlying operator which corresponding to the M/G/1/1 feedback queue with regular and optional service,the asymptotic behavior of the time dependent solution of this queueing model has been obtained. First,it is proved that zero is an eigenvalue of the underlying operator with geometric multiplicity one. Next,by studying the expression of the adjoint operator of the underlying operator,it is proved that zero is an eigenvalue of the adjoint operator with geometric multiplicity one. Then,under a certain condition,it has been deduced that all points on the imaginary axis except zero belong to the resolvent set of the underlying operator corresponding to the system model. Thus,under the same condition,by combining the above results,it is obtained that the time-dependent solution of the system model converges strongly to its steady state solution.
【Fund】: 新疆少数民族科技人才特殊培养计划科研(2016D0211);; 国家自然科学基金(11601464)资助项目
【CateGory Index】: O226
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