Controlled jump Markov processes with local transitions and their fluid approximation
Controlled jump Markov processes with local transitions and their fluid approximation
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发表时间：
2009-08
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通讯作者：
A. Piunovskiy
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作者：
A. Piunovskiy
随机跳过程，特别是生灭过程，在排队论、计算机网络和信息传输中有着广泛的应用。这种过程的状态描述了队列的瞬时长度（通过网络传输的不同边缘的数据包数量）。如果出生率和死亡率很大，这种过程的轨迹接近于确定性动力系统的轨迹。因此，如果我们考虑相关的最优控制问题，我们期望确定性（“流体”）模型中的最优控制策略将在潜在的随机模型中接近最优。在目前的文件中，一种新的技术，用于计算这种近似的精度。简而言之，而不是研究的轨迹，我们调查相应的动态规划方程。应该强调的是，我们也处理多维格，使结果适用于复杂的通信系统的队列。其他应用领域是人口动力学，数学流行病学和库存系统。
Stochastic jump processes, especially birth-and-death processes, are widely used in the queuing theory, computer networks and information transmission. The state of such process describes the instant length of the queues (numbers of packets at different edges to be transmitted through the net). If the birth and death rates are big, trajectories of such processes are close to the trajectories of deterministic dynamic systems. Therefore, if we consider the related optimal control problems, we expect that the optimal control strategy in the deterministic ('fluid') model will be nearly optimal in the underlying stochastic model. In the current paper, a new technique for calculating the accuracy of this approximation is described. In a nutshell, instead of the study of trajectories, we investigate the corresponding dynamic programming equations. It should be emphasized that we deal also with multiple-dimensional lattices, so that the results are applicable to complex communicating systems of queues. Other areas of application are population dynamics, mathematical epidemiology, and inventory systems.