Online real-time preemptive scheduling of jobs with deadlines on multiple machines

Abstract

SUMMARYIn this paper, we derive bounds on performance guarantees of online algorithms for real-time preemptive scheduling of jobs with deadlines on K machines when jobs are characterized in terms of their minimum stretch factor (or, equivalently, their maximum execution rate r = 1= ). We consider two well-known preemptive models that are of interest from practical applications: the hard real-time scheduling model in which a job must be completed if it was admitted for execution by the online scheduler, and the ÿrm real-time scheduling model in which the scheduler is allowed not to complete a job even if it was admitted for execution by the online scheduler. In both models, the objective is to maximize the sum of execution times of the jobs that were executed to completion, preemption is allowed, and the online scheduler must immediately decide, whenever a job arrives, whether to admit it for execution or reject it. However, migration of jobs is not allowed. We measure the competitive ratio of any online algorithm as the ratio of the value of the objective function obtained by this algorithm to that of the best possible o ine algorithm. We show that no online algorithm can have a competitive ratio greater than 1 − (1= ) + for 1 machine and 1 − (1=(K )) for K¿1 machines for hard real-time scheduling, and greater than 1 − (3=(4 )) + for ÿrm real-time scheduling on a single machine, where ¿0 may be arbitrarily small, even if the algorithm is allowed to know the value of in advance. On the other hand, we exhibit a simple online scheduler that achieves a competitive ratio of at least 1 − (1= ) in either of these models with K machines. The performance guarantee of our simple scheduler shows that it is in fact an optimal scheduler for hard real-time scheduling with 1 machine. We also describe an alternative scheduler for ÿrm real-time scheduling on a single machine in which the competitive ratio does not go to zero as approaches 1. Both of our schedulers do not know the value of in advance.

On the Competitiveness of Online Real-Time Scheduling with Rate of Progress Guarantees

“…In such an application, while it is acceptable to slow down the processing (up to some minimum "operating level"), it is nonetheless crucial that the processing progresses at a relatively uniform rate throughout the lifetime of the application. Unfortunately, the scheduling algorithms described in [8,9] as well as in [4,5,21] are prone to producing "bursty" schedules with non-uniform processing rates, and hence are not applicable to these types of applications.…”

“…For example, an application which has an execution time of 100 msec (on an unloaded system) and stretch factor 2 may be allowed to run at a slower rate, or have its execution delayed, so long as it is completed no later than 200 msec after it first becomes runnable. A number of recent papers have addressed the task scheduling problem based on this model [2,3,4,5,8,9,15,16,21]. In [4,5,21] Muthukrishnan et al presented offline and online scheduling algorithms that mimimize either the maximum stretch factor or the average stretch factor among all the tasks in the system.…”

“…In [4,5,21] Muthukrishnan et al presented offline and online scheduling algorithms that mimimize either the maximum stretch factor or the average stretch factor among all the tasks in the system. In [8,9] DasGupta and Palis considered the problem of online task scheduling with admission control, in which each arriving task specifies a maximum stretch factor that it can tolerate and the system admits a task only if it can guarantee that the task can be completed within the specified stretch factor.…”

Automated competitive analysis of real-time scheduling with graph games

“…The goal of the scheduling algorithm is to maximize the cumulated utility. Firm-deadline tasks arise in various application domains, e.g., machine scheduling (Gupta and Palis 2001), multimedia and video streaming (Abeni and Buttazzo 1998), QoS management in bounded-delay data network switches (Englert and Westermann 2007) and even networks-on-chip (Lu and Jantsch 2007), and other systems that may suffer from overload (Koren and Shasha 1995).…”

Online Scheduling Aiming to Satisfy Due Date for Flexible Flow Shops

“…Most of the researches concentrate on a single-stage system with one machine or with multiple machines systems (e.g. Akker, Hoogeveen and Vakhania (3) , Fleischer and Wahl (4) , and Gupta and Palis (5) ). For multi-stage manufacturing systems, two types of methods can be enumerated for the online scheduling.…”