Abstract. In a perfectly periodic schedule, each job must be scheduled precisely every some fixed number of time units after its previous occurrence. Traditionally, motivated by centralized systems, the perfect periodicity requirement is relaxed, the main goal being to attain the requested average rate. Recently, motivated by mobile clients with limited power supply, perfect periodicity seems to be an attractive alternative that allows clients to save energy by reducing their "busy waiting" time. In this case, clients may be willing to compromise their requested service rate in order to get perfect periodicity. In this paper we study a general model of perfectly periodic schedules, where each job has a requested period and a length; we assume that m jobs can be served in parallel for some given m. Job lengths may not be truncated, but granted periods may be different than the requested periods. We present an algorithm which computes schedules such that the worst-case proportion between the requested period and the granted period is guaranteed to be close to the lower bound. This algorithm improves on previous algorithms for perfect schedules in providing a worst-case guarantee rather than an average-case guarantee, in generalizing unit length jobs to arbitrary length jobs, and in generalizing the single-server model to multiple servers.

In a perfectly-periodic schedule, time is divided into time-slots, and each client gets a time slot precisely every predefined number of time slots, called the period of that client. Periodic schedules are useful in mobile communication where they can help save power in the mobile device, and they also enjoy the best possible smoothness. In this paper we study the question of dispatching in a perfectly periodic schedule, namely how to find the next item to schedule, assuming that the schedule is already given somehow. Simple dispatching algorithms suffer from either linear time complexity per slot or from exponential space requirement. We show that if the schedule is given in a natural tree representation, then there exists a way to get the best possible running time per slot for a given space parameter, or the best possible space (up to a polynomial) for a given time parameter. We show that in many practical cases, the running time is constant and the space complexity is polynomial.

We

Abstract. In a perfectly periodic schedule, each job must be scheduled precisely every some fixed number of time units after its previous occurrence. Traditionally, motivated by centralized systems, the perfect periodicity requirement is relaxed, the main goal being to attain the requested average rate. Recently, motivated by mobile clients with limited power supply, perfect periodicity seems to be an attractive alternative that allows clients to save energy by reducing their "busy waiting" time. In this case, clients may be willing to compromise their requested service rate in order to get perfect periodicity. In this paper we study a general model of perfectly periodic schedules, where each job has a requested period and a length; we assume that m jobs can be served in parallel for some given m. Job lengths may not be truncated, but granted periods may be different than the requested periods. We present an algorithm which computes schedules such that the worst-case proportion between the requested period and the granted period is guaranteed to be close to the lower bound. This algorithm improves on previous algorithms for perfect schedules in providing a worst-case guarantee rather than an average-case guarantee, in generalizing unit length jobs to arbitrary length jobs, and in generalizing the single-server model to multiple servers.

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