Strong Approximations for a Kumar-Seidman Network under a Priority Service Discipline

• Published in: Acta Mathematicae Applicatae Sinica Vol. 26; no. 4; pp. 587 - 596
• Main Authors: Wu, Lin, Zhu, Chuan-xi, Wu, Yun-jiang
• Format: Journal Article
• Language: English
• Published: Heildeberg Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.01.2010
• Subjects: Applications of Mathematics; Math Applications in Computer Science; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Theoretical; 作业服务; 先入先出; 大肠杆菌; 强逼近; 排队网络; 服务机制; 起飞过程; 输出数据; Strong approximation; 90B10; 90B22; diffusion approximation; priority service discipline; 60J70; Kumar-Seidman network; 60K25; 60G17; 60F17
• ISSN: 0168-9673; 1618-3932
• DOI: 10.1007/s10255-010-0026-x

In this paper,we derive the strong approximations for a four-class two station multi-class queuing network（Kumar-Seidman network） under a priority service discipline.Within a group,jobs are served in the order of arrival,that is,a first-in-first-out disciple,and among groups,jobs are served under a pre-emptiveresume priority disciple.We show that if the input data（i.e.,the arrival and service processe） satisfy an approximation（such as the functional law-of-iterated logarithm approximation or the strong approximation）,the output data（the departure processes） and the performance measures（such as the queue length,the work load and the sojourn time process） satisfy a similar approximation.