Most of the literature on two-sided matching markets without transfers focuses on the case where a central planner (often an algorithm) clears the market, like in the case of school assignments, or medical residents. In contrast, we focus on decentralized matching markets without transfers, where prices are regulated and thus cannot clear the market, as in the case of taxis. In these markets, time waited in line often plays the role of a numéraire. We investigate the properties of equilibrium in these markets (existence, uniqueness, and welfare). We use this analysis to study the problem of surge pricing: given beliefs on random demand and supply, how should a market designer set prices to minimize expected market inefficiency?