Abstract:
Methods developed in the theory of large deviations are an appropriate tool for investigation of probabilities of large fluctuations in queueing systems. In the paper, the large-deviation principle for generalized Poisson processes defined on the positive half-line $[0,\infty)$ is proved. Our approach is to find a representation of a parameter of the queueing system under investigation in terms of input flows of the system. Then the probabilities of large fluctuations of this parameter can be examined if the large-deviation principle for input processes is proved. With the help of the large-deviation principle proved here, we give a new proof for the known result on the asymptotics of the logarithm of the probability of large delay in a queueing system with a single server and Poisson input flow.