Large Deviations for Random Processes with Independent Increments on Infinite Intervals

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.