论文标题
与霍克斯到达的霍克斯过程和队列的完美采样
Perfect Sampling of Hawkes Processes and Queues with Hawkes Arrivals
论文作者
论文摘要
在本文中，我们开发了第一个使用Hawkes输入的队列的完美采样算法，即带有Hawkes Arrivals和I.I.D.的单人队列。一般分配的服务时间。除了稳定条件外，我们还假设霍克斯工艺的激发功能具有轻尾部，并且服务时间在原点附近具有有限的力矩生成功能。在此过程中，与现有算法相比，我们还为霍克斯工艺提出了一种新的完美抽样算法，其计算效率提高。还包括有关算法正确性和效率的理论分析和数值测试。
In this paper we develop the first perfect sampling algorithm for queues with Hawkes input, i.e. single-server queues with Hawkes arrivals and i.i.d. service times of general distribution. In addition to the stability condition, we also assume the excitation function of the Hawkes process has a light tail and the service time has finite moment generating function in the neighborhood of the origin. In this procedure, we also propose a new perfect sampling algorithm for Hawkes process with improved computational efficiency compared to the existing algorithm. Theoretical analysis and numerical tests on the algorithms' correctness and efficiency are also included.
