Weak convergence in multiphase queues (Q1113217)

A K-phase queueing system with renewal input and a renewal process of service at each single-channel phase is considered. Let \(w_ n^{(i)}\) be the waiting time of the n-th arrival at the j-th phase \((j=1,...,k\); \(n=1,2,...)\) and [x] be the integer part of x. Conditions of weak convergence of the sequence of stochastic processes \((w^{(1)}_{[nt]}/(\sqrt{n}),...,w^{(k)}_{[nt]}/(\sqrt{n}))\) to a K-dimensional diffusion process with reflection are given.