The linear reservoir with Markovian inflows

Abstract

The purpose of the work reported here is to derive the outflow distribution from a linear reservoir fed by a discrete‐time gamma‐distributed Markovian inflow. A satisfactory continuous time solution is available for the linear reservoir when the inflow distribution has independent increments. For the case of nonindependent increments discussed in the paper the treatment is in terms of a gamma‐distributed Markov chain inflow process in discrete time, for which the Laplace transform of the outflow rate distribution is derived. This is inverted, numerically, for a set of typical parameter values.