Analysis of a Crowdsourcing Markovian Queue with Phase-Type and Imperfect Service, Working Vacations, Breakdown, and Repair

N. Arulmozhi, Aliakbar Montazer Haghighi (), G. Ayyappan and G. Archana @ Gurulakshmi
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N. Arulmozhi: Sri Venkateshwaraa College of Engineering and Technology, Puducherry 605102, India
Aliakbar Montazer Haghighi: Prairie View A&M University, Prairie View, TX 77446, USA
G. Ayyappan: Puducherry Technological University, Puducherry 605014, India
G. Archana @ Gurulakshmi: Vel Tech Rangarajan Dr.Sagunthala R&D Institution of Science and Technology, Avadi, Chennai 600062, India

Mathematics, 2025, vol. 13, issue 23, 1-28

Abstract: Analysis of a crowdsourcing Markovian queue with phase-type service is considered in this paper. In this model, a customer not only receives service but also assists in delivery. In other words, in a retail environment, while some customers shop in-store, others place orders online or by phone and require home delivery. Store management can utilize online customers as couriers to complete these deliveries. However, because not every customer may agree to take part, a probabilistic element is included to capture the chances of their participation. The model also incorporates imperfect service, reflecting cases where deliveries may fail or require rework, and working breakdowns, representing partial disruptions in service capacity rather than complete stoppages. To analyze the system under steady-state conditions, matrix-analytic methods are applied. Numerical examples illustrate the significant benefits of incorporating these dynamics into traditional queueing models.

Keywords: crowdsourcing; working vacation policy; imperfect service (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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