Studies on queues interacting with their underlying processes

2015 Fiscal Year Final Research Report

• Project/Area Number: 25330027
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical informatics
• Research Institution: Osaka University
• Principal Investigator: Takine Tetsuya 大阪大学, 工学(系)研究科(研究院), 教授 (00216821)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 待ち行列 / 背後過程 / 相互作用 / working vacation / 途中退去

Outline of Final Research Achievements

We studied queues interacting with the underlying processes. In particular, we consider queues with working vacations and queues with impatient customers. In queues with working vacations, the underlying process is reset when the system becomes empty, and queues with impatient customers are equivalent to queues with workload-dependent arrivals. As for the former, we established a matrix-analytic method for the workload process corresponding to the case that the underlying Markov chain is reset when the system becomes empty. As for the latter, we accomplished the analysis of MAP/M/c+D and M/PH/c+D queues and revealed various properties of the loss probability in the M/G/1+G queue.

Free Research Field

待ち行列理論