Simple Correlated Flow and Its Application

摘要

A correlated flow of arrivals is considered in a case, where interarrival times {X_n } correspond to the Markov process with the continuous state space R+ = (0, ∞). The conditional probability density function of Xn+i given {Xn = z} is determined by means of q(x|z) = q(x|X_n = z) = (Σ)p_i{z)h_i(x), z,x ∈ R_+, where {p_i(z), ...,p_k(z)} is a probability distribution, p_1(z)+...+pk(z) = 1 for all zi=l R_+; {hi(x),..., hk(x)} is a family of probability density functions on R_+. This flow is investigated with respect to stationary case. One is considered as the Semi-Markov process J(t) on the state set {1,..., k}. Main characteristics are considered: stationary distribution of J and interarrival times X, correlation and Kendall tau (r) for adjacent intervals, and so on. Further one is considered a Markovian system on which the described flow arrives. Numerical results show that the dependence between interarrival times of the flow exercises greatly influences the efficiency characteristics of considered systems.