In this paper we study the multiple-processor multitask scheduling problem in the deterministic and stochastic models. We consider and analyze M-SRPT, a simple modification of the shortest remaining processing time algorithm, which always schedules jobs according to SRPT whenever possible, while processes tasks in an arbitrary order. The modified SRPT algorithm is shown to achieve an competitive ratio of \Theta(\log \alpha +\beta) for minimizing  flow time, where \alpha denotes the ratio of maximum job workload and minimum job workload, \beta represents the ratio between maximum non-preemptive task workload and minimum job workload. The algorithm is shown to be optimal (up to a constant factor) when there are constant number of machines. We further consider the problem under poisson arrival and general workload distribution,  M-SRPT is proved to be asymptotic optimal when the traffic intensity \rho approaches 1, if the task size is upper bound by the derived upper bound \eta{1-\rho}, if the job size distribution has bounded support, which generalizes the result in }[ .
In this paper we study the multiple-processor multitask scheduling problem in deterministic and stochastic models. We consider and analyze M-SRPT, a simple modification of the shortest remaining processing time algorithm, which always schedules jobs according to SRPT whenever possible, while processes tasks in an arbitrary order. The modified SRPT algorithm is shown to achieve a competitive ratio of \Theta(\log \alpha +\beta) for minimizing the flow time, where \alpha denotes the ratio of maximum job workload and minimum job workload, \beta represents the ratio between maximum non-preemptive task workload and minimum job workload. The algorithm is shown to be optimal (up to a constant factor) when there are constant number of machines. We further consider the problem under Poisson arrival and general workload distribution, and show that M-SRPT is asymptotic optimal when the traffic intensity \rho approaches 1, if the job size distribution has bounded support. In addition, we also present a characterization of the heavy traffic behavior of work-conserving algorithms in single-task job scheduling, and prove that the average flow time in GI/GI/1 system scales with \frac{1{1-\rho}, if the job size distribution has bounded support, which generalizes the result in }[Lin, Wierman and Zwart, 2011 .
D
the
R
an
a
A
the
R
poisson
Poisson
A
and show that
D
proved to be
R
task size is upper bound by the derived upper bound \eta
job size distribution has bounded support. In addition, we also present a characterization of the heavy traffic behavior of work-conserving algorithms in single-task job scheduling, and prove that the average flow time in GI/GI/1 system scales with \frac{1
A
Lin, Wierman and Zwart, 2011