Steady-state and first passage time distributions for waiting times in the MAP/M/s+G queueing model with generally distributed patience times

buir.contributor.authorGürsoy, Ömer
buir.contributor.authorAkar, Nail
buir.contributor.orcidAkar, Nail|0000-0001-8143-1379
dc.contributor.authorGürsoy, Ömer
dc.contributor.authorMehr, Kamal Adli
dc.contributor.authorAkar, Nail
dc.date.accessioned2022-04-29T06:39:59Z
dc.date.available2022-04-29T06:39:59Z
dc.date.issued2022-11-30
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractWe study the MAP/M/s+G queueing model that arises in various multi-server engineering problems including telephone call centers, under the assumption of MAP (Markovian Arrival Process) arrivals, exponentially distributed service times, infinite waiting room, and generally distributed patience times. Using sample-path arguments, we propose to obtain the steady-state distribution of the virtual waiting time and subsequently the other relevant performance metrics of interest via the steady-state solution of a certain Continuous Feedback Fluid Queue (CFFQ). The proposed method is exact when the patience time is a discrete random variable and is asymptotically exact when it is continuous/hybrid, for which case discretization of the patience time distribution is required giving rise to a computational complexity depending linearly on the number of discretization levels. Additionally, a novel method is proposed to accurately obtain the first passage time distributions for the virtual and actual waiting times again using CFFQs while approximating the deterministic time horizons by Erlang distributions or more efficient Concentrated Matrix Exponential (CME) distributions. Numerical results are presented to validate the effectiveness of the proposed numerical method.en_US
dc.description.provenanceSubmitted by Cem Çağatay Akgün (cem.akgun@bilkent.edu.tr) on 2022-04-29T06:39:59Z No. of bitstreams: 1 Steady_state_and_first_passage_time_distributions_for_waiting_times_in_the_MAPMs+G_queueing_model_with_generally_distributed_patience_times.pdf: 424339 bytes, checksum: 3826e25ec9e1ca0f41fed3714cd3c040 (MD5)en
dc.description.provenanceMade available in DSpace on 2022-04-29T06:39:59Z (GMT). No. of bitstreams: 1 Steady_state_and_first_passage_time_distributions_for_waiting_times_in_the_MAPMs+G_queueing_model_with_generally_distributed_patience_times.pdf: 424339 bytes, checksum: 3826e25ec9e1ca0f41fed3714cd3c040 (MD5) Previous issue date: 2021en
dc.identifier.doi10.3934/jimo.2021078en_US
dc.identifier.eissn1553-166X
dc.identifier.issn1547-5816
dc.identifier.urihttp://hdl.handle.net/11693/78181
dc.language.isoEnglishen_US
dc.publisherAIMS Pressen_US
dc.relation.isversionofhttps://dx.doi.org/10.3934/jimo.2021078en_US
dc.source.titleJournal of Industrial and Management Optimizationen_US
dc.subjectCall center modelsen_US
dc.subjectGenerally distributed patience timesen_US
dc.subjectMarkov fluid queuesen_US
dc.subjectSteady-state solutionen_US
dc.subjectFirst passage time distributionen_US
dc.titleSteady-state and first passage time distributions for waiting times in the MAP/M/s+G queueing model with generally distributed patience timesen_US
dc.typeArticleen_US

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