Mobile crowdsensing (MCS) has been intensively explored recently due to its flexible and pervasive sensing ability. Although many incentive mechanisms have been built to attract extensive user participation, Most of these mechanisms focus only on independent task scenarios, where the sensing tasks are independent of each other. On the contrary, we focus on a periodical task scenario, where each user participates in the same type of sensing tasks periodically. In this paper, we consider the long-term user participation incentive in a general periodical MCS system from a frugality payment perspective. We explore the issue under both semi-online (the intra-period interactive process is synchronous while the inter-period interactive process is sequential and asynchronous during each period) and online user arrival models (the previous two interactive processes are sequential and asynchronous). In particular, we first propose a semi-online frugal incentive mechanism by introducing a Lyapunov method. Moreover, we also extend it to an online frugal incentive mechanism, which satisfies the constant frugality. Besides, the two mechanisms can also satisfy computational efficiency, asymptotical optimality, individual rationality and truthfulness. Through extensive simulations, we evaluate the performance and validate the theoretical properties of our online mechanisms.
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