The price-anticipating Kelly mechanism (PAKM) is one of the most extensively used strategies to allocate divisible resources for strategic users in communication networks and computing systems. The users are deemed as selfish and also benign, each of which maximizes his individual utility of the allocated resources minus his payment to the network operator. However, in many applications a user can use his payment to reduce the utilities of his opponents, thus playing a misbehaving role. It remains mysterious to what extent the misbehaving user can damage or influence the performance of benign users and the network operator. In this work, we formulate a non-cooperative game consisting of a finite amount of benign users and one misbehaving user. The maliciousness of this misbehaving user is captured by his willingness to pay to trade for unit degradation in the utilities of benign users. The network operator allocates resources to all the users via the price-anticipating Kelly mechanism. We present six important performance metrics with regard to the total utility and the total net utility of benign users, and the revenue of network operator under three different scenarios: with and without the misbehaving user, and the maximum. We quantify the robustness of PAKM against the misbehaving actions by deriving the upper and lower bounds of these metrics. With new approaches, all the theoretical bounds are applicable to an arbitrary population of benign users. Our study reveals two important insights: i) the performance bounds are very sensitive to the misbehaving user's willingness to pay at certain ranges; ii) the network operator acquires more revenues in the presence of the misbehaving user which might disincentivize his countermeasures against the misbehaving actions.
翻译:Kelly(PAKM)机制(PAKM)是用来为通信网络和计算系统中的战略用户分配可分散资源的最广泛使用的战略之一。用户被认为是自私的,也是良性的。用户被视为自私的,也是良性的。每个用户都被视为自私的,也是良性的用户,这使他们对分配的资源的个别效用最大化,减去对网络运营商的付款,但在许多应用中,用户可以使用他的付款来减少对手的水电费,从而扮演错误行为的作用。对于用户行为不当的用户在多大程度上会损害或影响良性用户和网络运营商的效能,仍然很神秘。在这项工作中,我们设计了一个不合作的游戏,由数量有限的良性用户和一个行为不端的用户组成。这个错误的用户的恶意性能体现在他愿意为良性用户的公用事业进行单位性交易。网络运营商通过价格定型的Kelly机制向所有用户分配资源。我们对良性用户的总体效用和总的净效用以及网络运营商的收入提出了六种重要的业绩衡量标准。我们用三种不同的情况是:用错误的用户收入,而不用和没有多少的用户的任意性地支付,而没有固定的用户的利润,我们用量地将所有这些的操作者的行为是用来量化的上所有的。