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This paper examines a stochastic model to determine optimal pricing, waiting time, output, and sizing decisions for service firms which compete on time in an uncertain environment. Sizing decisions concern optimal service capacity and maximum physical waiting room (with a given probability). Customers are sensitive to money price and expected waiting time. The firm, modeled as an M/M/1 queue, is assumed to be a full price taker as a result of the stochastic version of the perfect competitiondoi:10.1007/s13209-009-0005-8 fatcat:olo6a2756zb4vldqz6cl6vranm