Corrected phase-type approximations of heavy-tailed queueing models in a   Markovian environment
  We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap- ture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase-type approximations as a sum of the delay in an MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples. 
Eleni Vatamidou, Ivo J.B.F. Adan, Maria Vlasiou, Bert Zwart
math.PR