For a sequence of tasks, each with a positive integer period, the pinwheel scheduling problem involves finding a valid schedule in the sense that the schedule performs one task per day and each task is performed at least once every consecutive days of its period. It had been conjectured by Chan and Chin in 1993 that there exists a valid schedule for any sequence of tasks with density, the sum of the reciprocals of each period, at most $\frac{5}{6}$. Recently, Kawamura settled this conjecture affirmatively. In this paper we consider an extended version with real periods proposed by Kawamura, in which a valid schedule must perform each task $i$ having a real period~$a_{i}$ at least $l$ times in any consecutive $\lceil l a_{i} \rceil$ days for all positive integer $l$. We show that any sequence of tasks such that the periods take three distinct real values and the density is at most $\frac{5}{6}$ admits a valid schedule. We hereby conjecture that the conjecture of Chan and Chin is true also for real periods.

翻译：对于一系列任务，每个任务具有一个正整数周期，风车调度问题旨在寻找一个有效的调度方案，使得该调度每天执行一个任务，并且每个任务在其周期的任意连续天数内至少被执行一次。Chan 和 Chin 于 1993 年曾提出猜想：对于任何任务序列，只要其密度（即各周期倒数之和）不超过 $\frac{5}{6}$，则存在有效的调度方案。最近，Kawamura 肯定地解决了这一猜想。本文考虑由 Kawamura 提出的具有实数周期的扩展版本，其中对于具有实数周期 $a_{i}$ 的每个任务 $i$，有效的调度方案必须满足：对于所有正整数 $l$，在任意连续的 $\lceil l a_{i} \rceil$ 天内至少执行该任务 $l$ 次。我们证明，对于任何任务序列，若其周期取三个不同的实数值且密度不超过 $\frac{5}{6}$，则存在有效的调度方案。基于此，我们提出猜想：Chan 和 Chin 的猜想对于实数周期同样成立。