On The Spectrum Of The Operator Corresponding To The M/M/1 Queueing Model With Single Vacations

The M/M/1 queueing system with single vacations is useful in many fields such as bank,hospital,telecommunication,transport.So,study of the structure of the time-dependent solution of the M/M/1 queueing model with single vacations is very important and the structure of its time-dependent solution is decided by the spectral distribution of the operator which corresponds to the M/M/1 queueing model with single vacations.This thesis studies spectrum of the operator which corresponds to the M/M/1 queueing model with single vacations and proves that-min{η,μ}is not an eigenvalue of the operator if the arrival rate of customersλ,the service rate of the serverηand the vacation rate of the serverμsatisfy one of the following conditions:(1)λ<ηandη=μ(2)λ<η,μ<ηandλ≠μ(3)λ<η<(?),2λ+(?)≠2η and (?)...