Subexponential Asymptotics of a Network Multiplexer

For a Markov-modulated random walk with negative drift and long-tailed right tail we prove that the ascending ladder height matrix distribution is asymptotically proportional to a long-tailed distribution. This result enable us to generalize a recent result on subexponential asymptotics of a Markov-modulated M/G/1 queue to subexponential asymptotics of a Markov-modulated G/G/1 queue. For a class of processes constructed by embedding a Markov chain into a subexponential renewal process we prove that the autocorrelation function has a subexponential tail. Furthermore, we prove that when a fluid flow queue is fed by these processes the queue length distribution is asymptotically proportional to its autocorrelation function.