Large deviation analysis of the single server queue

The paper establishes the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/G/1 queue. The rate functions are found explicitly. As an application, the paper obtains the logarithmic asymptotics of the probabilities that the virutal waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of ‘unconditional’ LDPs for ‘conditional ones’. The present approach applies in large deviations ideas and methods of weak convergence theory.