Spectral Analysis Of The Underlying Operator Of The M/M/1 Retrial Queueing Model With Special Retrial Times

Retrial queueing systems are widely used in communication,e-commerce,etc.Therefore,it is important to study the structures of the time-dependent solutions of retrial queueing models.And,the structures of the time-dependent solutions of the models are decided by the spectral distributions of the underlying operators which correspond to retrial queueing models.In this thesis,we study spectrum of the operator,which corresponds to the M/M/1 retrial queueing model with special retrial times,on the left real axis and prove that if the arrival rate of customer ? > 0,retrial rate of customers ? > 0,service rate of the server ? > 0 satisfy ?? ?,then-(? + ?),-(? + ?)and all points on the line between them are not eigenvalue of the underlying operator.