On the asymptotic expression of the time-dependent solution of an M/G/1 queueing model

Geni Gupur ()
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Geni Gupur: Xinjiang University

Partial Differential Equations and Applications, 2022, vol. 3, issue 2, 1-16

Abstract: Abstract We study asymptotic expression of the time-dependent solution of the M/G/1 queueing model with additional optional service and no waiting capacity, which is described by finite partial differential equations with integral boundary conditions. We prove that the underlying operator, which corresponds to the M/G/1 queueing model with additional optional service and no waiting capacity, has finitely many eigenvalues at most in a strip region on the left half complex plane, all eigenvalues are real, algebraic multiplicity of each eigenvalue is one and 0 is its strictly dominant eigenvalue, thus we give asymptotic expression of the time-dependent solution of the M/G/1 queueing model with additional optional service and no waiting capacity.

Keywords: M/G/1 queueing model with additional optional service and no waiting capacity; Eigenvalue; Adjoint operator; Geometric multiplicity; 35C20; 47A10; 47D03; 60K25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00157-4

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