How pre-emptive priority affects completion rate in an M/M/1 queue with Poisson reneging

• Published in: European journal of operational research Vol. 193; no. 1; pp. 317 - 320
• Main Author: Nasrallah, Walid F.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.02.2009; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Customer services; Exact sciences and technology; Firm modelling; Formal organization; Operational research and scientific management; Operational research. Management science; OR in business process analysis; Poisson distribution; Priority; Queueing; Queueing OR in business process analysis Reneging Priority; Queuing theory; Queuing theory. Traffic theory; Reneging; Studies; Queueing; OR in business process analysis; Priority; Reneging; Probabilistic approach; Integrated management; Modeling; Poisson process; Exact solution; Business process; M M 1 queue; Completion; User service; Completeness; Firm management; Queue
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2007.11.055

Queuing problems in which customers leave the queue without obtaining service (i.e. renege) have many applications. This paper looks at a queue where arrival, service and reneging events are all generated by independent Poisson processes, and customers are selected for service according to priority. A closed-form expression is derived for the probability of completing service for each priority class if high-priority customers always pre-empt low-priority ones. This result has applications in modeling the value of communications between members of an interacting population, such as a formal organization or an online community.