论文标题
Lorden的不平等和某些扩展的Erlang-Sevastyanov排队系统的融合率
Lorden's inequality and the polynomial rate of convergence of some extended Erlang-Sevastyanov queuing system
论文作者
论文摘要
更重要的是要估计收敛速率属于固定分布，而不仅仅是证明存在于许多应用的可靠性问题和排队理论的问题。这可以通过标准方法完成，但仅在关于服务时间的指数分布，恢复时间之间的独立间隔等的假设下进行。对于此类最简单的情况，结果才是众所周知的。这些假设的拒绝结果是无法使用标准算法研究的相当复杂的随机过程。对于此类过程，需要一种更复杂的方法。这需要更一般情况下的某些经典结果的概括和证明。其中之一是本文证明的广义洛尔登的不平等。我们建议在恢复时间之间的依赖和任意分布的间隔的情况下，提出了这种不平等的广义版本。这种概括可以找到在可靠性理论中引起的一系列复杂过程的收敛速率的上限。在本文中，通过广义的Lorden的不平等获得了两个组成过程的收敛速率。
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only under assumptions about an exponential distribution of service time, independent intervals between recovery times, etc. Results for such simplest cases are well-known. Rejection of these assumptions results to rather complex stochastic processes that cannot be studied using standard algorithms. A more sophisticated approach is needed for such processes. That requires generalizations and proofs of some classical results for a more general case. One of them is the generalized Lorden's inequality proved in this paper. We propose the generalized version of this inequality for the case of dependent and arbitrarily distributed intervals between recovery times. This generalization allows to find upper bounds for the rate of convergence for a wide class of complicated processes arising in the theory of reliability. The rate of convergence for a two-component process has been obtained via the generalized Lorden's inequality in this paper.
