Mathematical study on the effect of flexibility in complex queueing systems

2015 Fiscal Year Final Research Report

• Project/Area Number: 26540008
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical informatics
• Research Institution: Tokyo University of Science
• Principal Investigator: Miyazawa Masakiyo 東京理科大学, 理工学部, 教授 (80110948)
• Project Period (FY): 2014-04-01 – 2016-03-31
• Keywords: 複合待ち行列 / 柔軟性の効果 / 定常分布の裾の漸近特性 / 重負荷近似 / マルチンゲール / 大偏差値理論 / 複数種類の客をもつ待ち行列ネットワーク / 一般化最小行列選択待ち行列

Outline of Final Research Achievements

We study a new method for mathematical study on the effect of flexibility in complex queueing systems including networks. This method describes those systems, which may have generally distributed inter-arrival and service times, by a piewise deterministic Markov process, PDMP for short, and uses a martingale decomposition of the PDMP by exponential type of test functions. It differs from our original plan, which uses a reflecting random walk assuming that inter-arrival and service times are exponentially distributed. We apply this method to study the stationary queue length distributions of various systems through their tail asymptotics and their limits in heavy traffic. Those results are used to study flexibility in multiclass queueing networks with static buffer priority service and parallel queues with dedicated and join shortest queue arrivals.

Free Research Field

待ち行列理論