Stability of a cascade system with two stations and its extension for multiple stations

• Published in: Queueing systems Vol. 104; no. 3-4; pp. 155 - 174
• Main Authors: Miyazawa, Masakiyo, Morozov, Evsey
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2023; Springer Nature B.V
• Subjects: Arrivals; Business and Management; Computer Communication Networks; Control; Customers; Markov analysis; Markov processes; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Queuing theory; Stability; Supply Chain Management; Systems Theory; Multiple stations; Markov process; Cascade system; Stability; Harris positive recurrent; Renewal arrivals

We consider a two-station cascade system in which waiting or externally arriving customers at station 1 move to the station 2 if the queue size of station 1 including an arriving customer itself and a customer being served is greater than a given threshold level c 1 ≥ 1 and if station 2 is empty. As...