We introduce a new class of combinatorial markets in which agents have covering constraints over resources required and are interested in delay minimization. Our market model is applicable to several settings including scheduling and communicating over a network. This model is quite different from the traditional mod-els, to the extent that neither do the classical equilibrium existence results seem to apply to it nor do any of the efficient algorithmic techniques developed to compute equilib-ria. In particular, our model does not satisfy the condition of non-satiation, which is used critically to show the existence of equilibria in traditional market models and we observe that our set of equilibrium prices could be a connected, non-convex set. We give a proof of the existence of equilibria and a poly-nomial time algorithm for finding one, drawing heavily on techniques from LP duality and submodular minimization. Finally, we show that our model inherits many of the fair-ness properties of traditional equilibrium models as well as new models, such as CEEI.