论文标题
霍克斯到达和霍克斯服务的无限服务器系统
Infinite-server System with Hawkes Arrivals and Hawkes Services
论文作者
论文摘要
本文致力于研究由霍克斯流程驱动的无限服务器系统中的客户数量。在这些系统中，假定自我激发的到达过程由霍克斯过程和由州依赖的霍克斯过程（SDHAWKES流程）表示。在某些适当的条件下，对于Hawkes/Sdhawkes/Infty系统，该系统的Markov属性被得出。系统中客户数量的联合时间相关分布，到达强度和服务器强度的特征是微分方程的系统。然后，还针对M/sdhawkes/\ Infty系统推导了时间依赖性结果。
This paper is devoted to the study of the number of customers in infinite-server systems driven by Hawkes processes. In these systems, the self-exciting arrival process is assumed to be represented by a Hawkes process and the self-exciting service process by a state-dependent Hawkes process (sdHawkes process). Under some suitable conditions, for the Hawkes/sdHawkes/infty system, the Markov property of the system is derived. The joint time-dependent distribution of the number of customers in the system, the arrival intensity and the server intensity is characterised by a system of differential equations. Then, the time-dependent results are also deduced for the M/sdHawkes/\infty system.
