Abstract

Poisson flow of arrivals is considered in a case when flow intensity is an inconstant value. It is supposed that a random environment exists in which the flow operates. The environment is described as alternating Markov chain. The sojourn times in the alternating two states are independent random variables having the exponential distributions with known parameters. The intensity of the flow equals λ_i, i = 1, 2, if the i-th state of the random environment takes place. The following indices of the flow are considered: the distribution, the expectation and the variance of the number of arrivals on a given interval; the correlation of the numbers of arrivals for two adjacent intervals, etc.

中文翻译：

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交替强度的泊松流及其应用

摘要

在流量强度为非恒定值的情况下考虑泊松到达流。假定存在一个随机的环境，在该环境中流将运行。环境被描述为交替的马尔可夫链。在交替的两种状态下的停留时间是具有已知参数的指数分布的独立随机变量。流的强度等于λ_我，我= 1，2，如果我的随机环境个状态发生。考虑以下流量指标：给定时间间隔内到达数量的分布，期望和方差；两个相邻间隔的到达次数的相关性等