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This paper describes a novel cost-driven disk scheduling algorithm for environments consisting of multipriority requests. An example application is a video-on-demand (VOD) system that provides high and low quality services, termed priority 2 and 1, respectively. Customers ordering a high quality (priority 2) service pay a higher fee and are assigned a higher priority by the underlying system. Our proposed algorithm minimizes costs by maintaining one-queue and managing requests intelligently in order to meet the deadline of as many priority 1 requests as possible while maximizing the number of priority 2 requests that meet their deadline. Our algorithm is general enough to accommodate an arbitrary number of priority levels. Prior schemes, collectively termed "multiqueue" schemes maintain a separate queue for each priority level in order to optimize the performance of the high priority requests only. When compared with our proposed scheme, in certain cases, our technique provides more than one order of magnitude improvement in total cost.