Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy Traffic
Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy Traffic
复制标题
使用非线性漂移扩散近似 GI/GI/1 GI 队列：交通繁忙时的危险率缩放
DOI：
10.1287/moor.1070.0303
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Amy R. Ward
中科院分区：
文献类型：
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作者：
Josh E. Reed;Amy R. Ward
我们研究一个单一服务队的队列，在第一届（FIFO）服务纪律下运行，如果他的服务尚未在一般分布的时间内开始，则每个客户都独立放弃了队列。在某些轻度的放弃分配条件下，我们确定了一个有限的重型交通状态，在该制度中，所提供的等待时间过程的结果扩散近似（跟踪无限患者到达客户的时间的时间）和队列长度的过程包含整个放弃分布。要使用连续的映射方法来建立我们的弱收敛结果，我们还会为具有独立关注的非线性广义调节器映射而发展出存在，独特性和连续性结果。我们进一步进行了一项仿真研究，以评估稳态平均队列长度的拟议近似值以及限制扩散过程所建议的放弃的稳态概率。
We study a single-server queue, operating under the first-in-first-out (FIFO) service discipline, in which each customer independently abandons the queue if his service has not begun within a generally distributed amount of time. Under some mild conditions on the abandonment distribution, we identify a limiting heavy-traffic regime in which the resulting diffusion approximation for both the offered waiting time process (the process that tracks the amount of time an infinitely patient arriving customer would wait for service) and the queue-length process contain the entire abandonment distribution. To use a continuous mapping approach to establish our weak convergence results, we additionally develop existence, uniqueness, and continuity results for nonlinear generalized regulator mappings that are of independent interest. We further perform a simulation study to evaluate the quality of the proposed approximations for the steady-state mean queue length and the steady-state probability of abandonment suggested by the limiting diffusion process.