Fluid limits of many-server queues with abandonments, general service and continuous patience time distributions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Zuniga, Alexander Walsh

关键词: Many-server queues;    Fluid limits;    Measure-valued processes;    L-1-valued-processes;    Reneging;    Abandonment;   

DOI  :  10.1016/j.spa.2013.11.008

来源: Elsevier

【 摘 要 】

This paper extends the works of Kang and Ramanan (2010) and Kaspi and Ramanan (2011), removing the hypothesis of absolute continuity of the service requirement and patience time distributions. We consider a many-server queueing system in which customers enter service in the order of arrival in a non-idling manner and where reneging is considerate. Similarly to Kang and Ramanan (2010), the dynamics of the system are represented in terms of a process that describes the total number of customers in the system as well as two measure-valued processes that record the age in service of each of the customers being served and the potential waiting times. When the number of servers goes to infinity, fluid limit is established for this triple of processes. The convergence is in the sense of probability and the limit is characterized by an integral equation. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free