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As computer and Internet technology continue to advance, real-time online services are emerging. Different from traditional real-time applications for which the scheduling objective is to meet task deadlines, the optimization goal for online service systems is to maximize profit obtained through providing timely services. For this class of applications, there are two distinctive characteristics. First, tasks are associated with a pair of time dependent functions representing accrued profit when completed before their deadlines and accrued penalty otherwise, respectively. Second, the service requests or tasks arrive aperiodically with execution time varying in a wide range. This paper presents a novel scheduling method and related analysis for such applications. Two scheduling algorithms, i.e., the nonpreemptive and preemptive Profit and Penalty aware (PP-aware) scheduling algorithms, are proposed with an objective to maximize system's total accrued profit. Our simulation results clearly demonstrate the advantages of the proposed algorithms, with respect to the system total accrued profit, over other commonly used scheduling algorithms, such as Earliest Deadline First (EDF) and Utility Accrual (UA) algorithms.