Time to deplete a resource with Gamma usage

Many situations arise where a given resource is depleted according to a usage variable whose behaviour is described by a Gamma distribution function. A related issue is then deriving the distribution of the time to deplete or consume a given amount of that resource. This is important for planning some operations like in maintenance, distribution and inventory control. A few authors have addressed this point, but the present paper extends their results and suggests approximations for general practice.