Regulations specify the maximum amount of waste that can be stored on site by a waste generating firm. When this regulatory threshold is reached, a polluting firm must move its on site waste to an off site recipient. In this setting, we analyse two questions in a stochastic framework from the viewpoints of a waste generator and a recipient that have received scant theoretical attention in the literature. First, given that off site storage is costlier than on site storage, we derive the long-run average cost incurred by a waste generating firm that stores waste both on and off site. Second, we compute the expected amount of time until the off site recipient's waste storage facility is full.