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首页> 外文期刊>IEEE Transactions on Automatic Control >Pricing and congestion management in a network with heterogeneous users
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Pricing and congestion management in a network with heterogeneous users

机译：异构用户网络中的定价和拥塞管理

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This note presents an economic model for a communication network with utility-maximizing elastic users who adapt to congestion by adjusting their flows. Users are heterogeneous with respect to both the utility they attach to different levels of flow and their sensitivity to delay. Following Kelly et al. (1998), we introduce dynamic rate-control algorithms, based on the users' utility functions and delay sensitivities, as well as tolls charged by the system, and examine the behavior of these algorithms. We show that allowing heterogeneity with respect to delay sensitivity introduces a fundamental nonconvexity into the congestion-cost functions. As a result, there are often multiple stationary points of the aggregate net utility function. Hence, marginal-cost pricing-equating users' marginal utilities to their marginal costs-may identify a local maximum or even a saddle point, rather than a global maximum. Moreover, the dynamic rate-control algorithm may converge to a local rather than global maximum, depending on the starting point. We present examples with different user utility functions, including some in which the only interior stationary point is a saddlepoint which is dominated by all the single-user optimal allocations. We also consider variants of the dynamic algorithm and their performance in a network with heterogeneous users. Our results suggest that applying a rate-control algorithm such as TCP (Transmission Control Protocol), even when augmented by some form of implicit or explicit pricing, may have unexpected and perhaps undesirable effects on the allocation of flows among heterogeneous delay-sensitive users.
机译：本说明介绍了一种通信网络的经济模型，该网络具有效用最大化的弹性用户，这些用户通过调整流量来适应拥塞。用户在附加到不同级别的流量的实用程序以及对延迟的敏感性方面都各不相同。继凯利等。 （1998年），我们引入了基于用户的效用函数和时延敏感度以及系统收费的动态速率控制算法，并研究了这些算法的行为。我们表明，允许关于延迟敏感性的异构性将基本的非凸性引入到拥塞成本函数中。结果，聚集净效用函数通常有多个固定点。因此，边际成本定价使用户的边际效用等于他们的边际成本，可能会确定一个局部最大值甚至一个鞍点，而不是一个全局最大值。而且，取决于起始点，动态速率控制算法可以收敛到局部最大值而不是全局最大值。我们提供了具有不同用户实用程序功能的示例，包括一些其中唯一的内部固定点是鞍点的示例，该鞍点由所有单用户最佳分配控制。我们还考虑了动态算法的变体及其在异构用户网络中的性能。我们的结果表明，即使采用某种形式的隐式或显式定价进行扩展，应用诸如TCP（传输控制协议）之类的速率控制算法，也可能会对异构的延迟敏感用户之间的流量分配产生意想不到的甚至是不良的影响。

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