新Copula函数的构造及其应用
Construction of New Copulas with Queueing Application
摘要：
在本文中，我们构造了一个有界copula，它可以达到Frechet的下限和上界的情况下，完美的积极和消极的依赖。由于它涵盖了广泛的依赖性和简单的计算目的，它可以是非常有用的。利用Frechet Copula的上下界上界，构造了一个新的扰动Copula，并证明了它满足Copula的所有性质.在某些情况下，利用诸如Archemedes，Guassian，$t$-copula等Copula函数很难得到分布函数和期望值的显式表达式。因此，我们可以使用这些新的copula。对于这两个Copula，我们推导出的依赖性，如斯皮尔曼的ρ，肯德尔的τ，布洛姆奎斯特的β和基尼的γ，和系数的尾部依赖性的措施的强度。作为一个应用，我们使用绑定copula分析两个服务时间之间的依赖关系，以评估平均等待时间和平均服务时间时，客户启动两个副本的每个任务在两个并行服务器上使用cancel-on-finish策略。我们假设到达间隔时间是指数的，服务时间是一般的。
英文摘要：
In this paper, we construct a bound copula, which can reach both Frechet's lower and upper bounds for perfect positive and negative dependence cases. Since it covers a wide range of dependency and simple for computational purposes, it can be very useful. We then develop a new perturbed copula using the lower and upper bounds of Frechet copula and show that it satisfies all properties of a copula. In some cases, it is very difficult to get results such as distribution functions and the expected values in explicit form by using copulas such as Archemedes, Guassian, $t$-copula. Thus, we can use these new copulas. For both copulas, we derive the strength of measures of the dependency such as Spearman's rho, Kendall's tau, Blomqvist's beta and Gini's gamma, and the coefficients of the tail dependency. As an application, we use the bound copula to analyze the dependency between two service times to evaluate the mean waiting time and the mean service time when customers launch two replicas of each task on two parallel servers using the cancel-on-finish policy. We assume that the inter-arrival time is exponential and the service time is general.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
