A Feasibility Decision Algorithm for Rate Monotonic Scheduling of Periodic Real-Time Tasks Yoshifumi Manabe Shigemi Aoyagi NTT Basic Research Laboratories zyxw 3- 1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-01 Japan Abstract zyxwvuts The rate monotonic scheduling algorithm is a com- monly used task scheduling algorithm for periodic real- time task systems. This paper discusses feasibility de- cision for a given real-time task system by the rate monotonic scheduling algorithm. It presents a new necessary and suficient condition for a given task sys- tem to be feasible, and a new feasibility decision algo- rithm based on that condition. The time complexity of this algorithm depends solely on the number of tasks. This algorithm can be applied to the inverse-deadline scheduling algorithm, which is an extension of the rate monotonic scheduling algorithm. 1 Introduction In real-time systems, there is a time constraint on computation, which is just as important as the correctness of computation. In an attempt to sat- isfy this constraint, many scheduling algorithms have been discussed [3]. The rate monotonic scheduling algorithm [lo] is one of commonly used scheduling algorithms for periodic real-time task systems be- cause it is optimal among fixed-priority preemptive scheduling algorithm. Furthermore, various exten- sions have been discussed, for example, scheduling aperiodic tasks while still meeting the deadlines of periodic tasks [ll], scheduling when a task is added or deleted or a task period is modified [4][5][12], and scheduling when some tasks share resources [l] [13]. A necessary and sufficient condition for a given pe- riodic real-time task system to be feasible by the rate monotonic scheduling algorithm has been shown [lo]. Two feasibility decision algorithms, the scheduling point test algorithm [6] and the completion-time test algorithm [14], have been shown. The time complexi- ties of these two algorithms depend on both the num- ber of tasks and the task periods. This paper presents a new necessary and sufficient condition for feasibility along with a new feasibility de- cision algorithm, a reduced scheduling point test algo- rithm. The time complexity of this algorithm depends solely on the number of tasks. Thus it is a constant if the number of tasks is a constant. This algorithm can also be applied to determine the feasibility by the inverse-deadline scheduling algorithm [9] [7], which is an extension of the rate monotonic scheduling algo- rithm. In this paper, section 2 defines real-time task scheduling. Section 3 summarizes previous results for feasibility decision algorithms. Section zyx 4 gives the necessary and sufficient condition to be feasible, and shows the feasibility decision algorithm based on this condition. Section 5 discusses an extension for the inverse-deadline scheduling algorithm. Section 6 sum- marizes the paper. zyxw 2 Scheduling periodic real-time tasks This section gives the formulation of the real-time scheduling. Definition 1 (Periodic real-time task system) [lo1 Perzodzc real-tzme task system zyx X zyxw = {q,r2, . . . ,rn} is a set of tasks. These tasks are zndependent an that job requests for a certazn task do not depend on the completzon of requests for other tasks. Each task r, zs perzodzc, wzth a constant znterval zy p, between job requests. a Each task r, has an znztzahzataon tzme I%(> 0) Assume that minl<,<,I, = 0 r, are znztzated at I, + kp,(k = 0,1, The jobs for task - ) zyx 2 12 1080-1812/95 $04.00 0 1995 IEEE