Spectral Analysis of the Underlying Operator of the M[X]/M/1 Queueing Model with Service Failure State as Absorbent State and Constant Rate of Repeated Attempts
We study spectra of the underlying operator of the M[X]/M/1 queueing model with service failure state as absorbent state and constant rate of repeated attempts on the left half complex plane.When the arrival rate of customers A,the service rate of the server v,the repeated rate of customers α and the service completion rate of the server b satisfy a certain condition,we prove that all complex numbers whose real part-(λ+v+b)are not eigenvalue of the underlying operator.When λ,v,α,b satisfy some conditions,we prove that infinitely many numbers in the interval(-(λ+v+b),0)are eigenvalues of the underlying operator with geometric multiplicity one.
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