An Approximate Solution for M/G/1 Queues with Pure Mixture Service Time Distributions

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dc.contributor.authorKoyuncu, Melik
dc.contributor.authorUncu, Nusin
dc.date.accessioned2026-02-27T07:33:04Z
dc.date.available2026-02-27T07:33:04Z
dc.date.issued2025
dc.description.abstractThis study introduces an approximate solution for the M/G/1 queueing model in scenarios where the service time distribution follows a pure mixture distribution. The derivation of the proposed approximation leverages the analytical tractability of the variance for certain mixture distributions. By incorporating this variance into the Pollaczek-Khinchine equation, an approximate closed-form expression for the M/G/1 queue is obtained. The formulation is extended to service-time distributions composed of two or more components, specifically Gamma, Gaussian, and Beta mixtures. To assess the accuracy of the proposed approach, a discrete-event simulation of an M/G/1 system was conducted using random variates generated from these mixture distributions. The comparative analysis reveals that the approximation yields results in close agreement with simulation outputs, with particularly high accuracy observed for Gaussian mixture cases.
dc.identifier.doi10.3390/sym17101753
dc.identifier.issn2073-8994
dc.identifier.issue10
dc.identifier.urihttp://dx.doi.org/10.3390/sym17101753
dc.identifier.urihttps://hdl.handle.net/20.500.14669/4440
dc.identifier.volume17
dc.identifier.wosWOS:001602318800001
dc.indekslendigikaynakWeb of Science
dc.language.isoen
dc.publisherMDPI
dc.relation.ispartofSymmetry-Basel
dc.relation.publicationcategoryMakale - Uluslararas� Hakemli Dergi - Kurum ��retim Eleman�
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20260302
dc.subjectM/G/1 queueing model
dc.subjectmixture distributions
dc.subjectsimulation
dc.titleAn Approximate Solution for M/G/1 Queues with Pure Mixture Service Time Distributions
dc.typeArticle

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