Diffusion Approximations for a Multiclass Markovian Service System with "Guaranteed" and "Best-Effort" Service Levels
Diffusion Approximations for a Multiclass Markovian Service System with "Guaranteed" and "Best-Effort" Service Levels
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具有“保证”和“尽力而为”服务级别的多类马尔可夫服务系统的扩散近似
DOI：
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发表时间：
2004
影响因子：
1.7
通讯作者：
A. Zeevi
中科院分区：
文献类型：
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作者：
C. Maglaras;A. Zeevi
本文考虑了由通信和信息服务促进的服务系统的马尔可夫模型。该系统具有有限的处理能力，并提供多个服务。最高优先用户会收到“保证”处理率，而优先用户根据其优先级级别的剩余容量较低，因此可能会体验服务退化（因此“最佳努力”一词）。本文着重于此类系统的性能分析。我们考虑了Halfin-Whitt繁重的人流量制度，其中到达率和系统处理能力都以交通强度接近一个的方式增长。我们首先为系统动力学得出多维扩散近似，然后基于直观的“扰动方法”获得了更可拖延的扩散极限。这种方法使我们能够计算各种封闭形式的近似值，以进行稳态以及瞬态拥塞相关的性能指标。数值示例说明了这些近似值的准确性。
This paper considers a Markovian model of a service system motivated by communication and information services. The system has finite processing capacity and offers multiple grades of service. The highest priority users receive a "guaranteed" processing rate, while lower priority usersshare residual capacity according to their priority level and therefore may experience service degradation (hence the term "best effort"). This paper focuses on performance analysis for this class of systems. We consider the Halfin-Whitt heavy-traffic regime, where the arrival rate and system processing capacity both grow large in a way that the traffic intensity approaches one. We first derive a multidimensional diffusion approximation for the system dynamics and subsequently obtain a more tractable diffusion limit based on an intuitive "perturbation approach." This method enables us to compute various closed form approximations to steady-state as well as transient congestion-related performance measures. Numerical examples illustrate the accuracy of these approximations.