STABILIZING PERFORMANCE IN NETWORKS OF QUEUES WITH TIME-VARYING ARRIVAL RATES
STABILIZING PERFORMANCE IN NETWORKS OF QUEUES WITH TIME-VARYING ARRIVAL RATES
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DOI：
10.1017/s0269964814000084
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发表时间：
2014-07
影响因子：
1.1
通讯作者：
Yunan Liu;W. Whitt
中科院分区：
文献类型：
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作者：
Yunan Liu;W. Whitt
本文研究了一种算法对前馈排队网络的扩展，该算法设置人员配备水平(服务器数量)，以在具有时变到达率的mt/gi/st+gi多服务器队列中稳定服务质量(Qos)目标的性能百分比。模型具有非齐次泊松过程(NHPP)、顾客放弃、服务和耐心的非指数分布。对于单个队列，仿真实验表明，该算法在较大范围的服务质量目标上成功地稳定了丢弃概率和预期时延。一个极限定理表明，在固定的服务质量目标下，稳定的性能是随着规模的增加而渐近实现的(通过在保持服务和耐心分布不变的情况下允许到达率增长)。在这里，我们将极限定理推广到前馈排队网络。然而，随着规模的增加，这些固定的服务质量目标提供的服务质量较低。因此，这些限制主要支持具有低服务质量目标的算法。对于高服务质量目标，有效性取决于NHPP属性，但离开过程永远不会完全是NHPP。因此，我们调查了什么时候一个离开过程可以被认为是近似的NHPP。我们表明，在这种情况下，计数的离散度指数对于确定偏离过程何时近似为NHPP是有效的。在重要的常见情况下，当所有队列都有较高的服务质量目标时，我们证明了：(I)从这个角度出发，离开过程近似为NHPP；(Ii)算法是有效的。
This paper investigates extensions to feed-forward queueing networks of an algorithm to set staffing levels (the number of servers) to stabilize performance % at Quality of Service (QoS) targets in an Mt/GI/st+GI multi-server queue with a time-varying arrival rate. The model has a non-homogeneous Poisson process (NHPP), customer abandonment, and non-exponential service and patience distributions. For a single queue, simulation experiments showed that the algorithm successfully stabilizes abandonment probabilities and expected delays over a wide range of Quality-of-Service (QoS) targets. A limit theorem showed that stable performance at fixed QoS targets is achieved asymptotically as the scale increases (by letting the arrival rate grow while holding the service and patience distributions fixed). Here we extend that limit theorem to a feed-forward queueing network. However, these fixed QoS targets provide low QoS as the scale increases. Hence, these limits primarily support the algorithm with a low QoS target. For a high QoS target, effectiveness depends on the NHPP property, but the departure process never is exactly an NHPP. Thus, we investigate when a departure process can be regarded as approximately an NHPP. We show that index of dispersion for counts is effective for determining when a departure process is approximately an NHPP in this setting. In the important common case when all queues have high QoS targets, we show that both: (i) the departure process is approximately an NHPP from this perspective and (ii) the algorithm is effective.