New Resource Augmentation Analysis of the Total Stretch of SRPT and SJF in Multiprocessor Scheduling

Abstract

This paper studies online job scheduling on multiprocessors and, in particular, investigates the algorithms SRPT and SJF for minimizing total stretch, where the stretch of a job is its flow time (response time) divided by its processing time. SRPT is perhaps the most well-studied algorithm for minimizing total flow time or stretch. This paper gives the first resource augmentation analysis of the total stretch of SRPT, showing that it is indeed O(1)-speed 1-competitive. This paper also gives a simple lower bound result showing that SRPT is not s-speed 1-competitive for any s < 1.5. This paper also makes contribution to the analysis of SJF. Extending the work of [4], we are able to show that SJF is O(1)-speed 1-competitive for minimizing total stretch. More interestingly, we find that the competitiveness of SJF can be reduced arbitrarily by increasing the processor speed (precisely, SJF is O(s)-speed (1/s)-competitive for any s ≥ 1). We conjecture that SRPT also admits a similar result.

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“…Recently, alternative performance measures have been considered and among them, the stretch measure has received a lot of attention (Chan et al, 2006). The stretch of a job formally is defined as the ratio of its flow time to its required processing time (Bender et al, 2004).…”