We develop a model for the competitive interactions in service industries where firms cater to multiple customer classes or market segments with the help of shared service facilities or processes so as to exploit pooling benefits. Different customer classes typically have distinct sensitivities to the price of service as well as the delays encountered. In such settings firms need to determine (i) the prices charged to all customer classes; (ii) the waiting time standards, i.e., expected steady state waiting time promised to all classes; (iii) the capacity level; and (iv) a priority discipline enabling the firm to meet the promised waiting time standards under the chosen capacity level, all in an integrated planning model that accounts for the impact of the strategic choices of all competing firms. We distinguish between three types of competition: depending on whether firms compete on the basis of their prices only, waiting time standards only, or on the basis of prices and waiting time standards. We establish in each of the three competition models that a Nash equilibrium exists under minor conditions regarding the demand volumes. We systematically compare the equilibria with those achieved when the firms service each market segment with a dedicated service process.