Tail asymptotics for M/G/1 type queueing processes with subexponential increments

Bivariate regenerative Markov modulated queueing processes {I _n ,L _n } are described. {I _n } is the phase process, and {L _n } is the level process. Increments in the level process have subexponential distributions. A general boundary behavior at the level 0 is allowed. The asymptotic tail of the cycle maximum, , during a regenerative cycle, , and the asymptotic tail of the stationary random variable L _∞, respectively, of the level process are given and shown to be subexponential with L _∞ having the heavier tail. This revised version was published online in June 2006 with corrections to the Cover Date.