Research Article
Tail equivalence for some time-shared systems
@INPROCEEDINGS{10.1145/1190095.1190142, author={Smruti Padhy and Arzad Kherani}, title={Tail equivalence for some time-shared systems}, proceedings={1st International ICST Conference on Performance Evaluation Methodologies and Tools}, publisher={ACM}, proceedings_a={VALUETOOLS}, year={2012}, month={4}, keywords={Sojourn Time Aysmptotic study RPT based scheduling Aged based scheduling}, doi={10.1145/1190095.1190142} }- Smruti Padhy
Arzad Kherani
Year: 2012
Tail equivalence for some time-shared systems
VALUETOOLS
ACM
DOI: 10.1145/1190095.1190142
Abstract
Many of recent studies have proved the tail equivalence result for Egalitarian Processor Sharing system: [EQUATION], where B (resp. V) is service requirement (resp. sojourn time) of a customer; for PS, g = 1 - ρ. In this paper, we consider time-shared systems in which the server capacity is shared by existing customers in proportion to (dynamic) weights assigned to customers. We consider two systems, 1) in which the weight of a customer depends on it Age (attained service), and 2) in which the weight depends on the residual processing time (RPT). We allow for a parameterized family of weight functions such that the weight associated with a customer that has received a service (or, has a RPT) of x units is ω(x) = xα for some -∞ < α < ∞. We then study the sojourn time of a customer under such scheduling discipline and provide conditions on α for tail equivalence to hold true, and also give the value of g as a function of α.