A queueing system with on-demand servers: local stability of fluid limits
A queueing system with on-demand servers: local stability of fluid limits
复制标题
具有按需服务器的排队系统：流量限制的局部稳定性
DOI：
10.1007/s11134-017-9564-8
复制
发表时间：
2016
期刊：
影响因子：
1.2
通讯作者：
A. Stolyar
中科院分区：
文献类型：
--
作者：
Lam M. Nguyen;A. Stolyar
我们研究了这样一个系统，其中随机的客户流由按需邀请的服务器(称为代理)提供服务。每个被邀请的代理在随机时间后进入系统；在每次服务完成后，代理返回系统或以一定的固定概率离开系统。客户和/或代理可能不耐烦，即在排队等待时，他们以一定的速率(可能为零)离开系统。我们考虑基于队列长度的反馈方案，该方案根据客户和代理队列长度及其变化来控制待决代理邀请的数量。基本目标是最大限度地减少客户和代理的等待时间。在顾客到达率趋于无穷大的渐近状态下，我们建立了系统过程的流体极限。我们使用切换线性系统的机制和常见的二次Lyapunov函数来逼近流体极限在期望平衡点的稳定性，并推导出各种充分的局部稳定性条件。对于我们的模型，我们猜想，对于流体极限的全局稳定性，局部稳定性实际上是充分的；数值和模拟实验支持了这一猜想的正确性。当局部稳定条件成立时，仿真结果表明该方案具有良好的整体性能。
We study a system where a random flow of customers is served by servers (called agents) invited on-demand. Each invited agent arrives into the system after a random time; after each service completion, an agent returns to the system or leaves it with some fixed probabilities. Customers and/or agents may be impatient, that is, while waiting in queue, they leave the system at a certain rate (which may be zero). We consider the queue-length-based feedback scheme, which controls the number of pending agent invitations, depending on the customer and agent queue lengths and their changes. The basic objective is to minimize both customer and agent waiting times. We establish the system process fluid limits in the asymptotic regime where the customer arrival rate goes to infinity. We use the machinery of switched linear systems and common quadratic Lyapunov functions to approach the stability of fluid limits at the desired equilibrium point and derive a variety of sufficient local stability conditions. For our model, we conjecture that local stability is in fact sufficient for global stability of fluid limits; the validity of this conjecture is supported by numerical and simulation experiments. When local stability conditions do hold, simulations show good overall performance of the scheme.