 
Summary: Minimizing Total Flow Time and Total Completion Time with
Immediate Dispatching
Nir Avrahami Yossi Azar y
February 5, 2003
Abstract
We consider the problem of scheduling jobs arriving over time in a multiprocessor
setting, with immediate dispatching, disallowing job migration. The goal is to minimize
both the total
ow time (total time in the system) and the total completion time.
Previous studies have shown that while preemption (interrupt a job and later continue
its execution) is inherent to make a scheduling algorithm eÆcient, migration (continue the
execution on a dierent machine) is not. Still, the current nonmigratory online algorithms
suer from a need for a central queue of unassigned jobs which is a "no option" in large
computing system, such as the Web.
We introduce a simple online nonmigratory algorithm IMD, which employs immediate
dispatching, i.e., it immediately assigns released jobs to one of the machines. We show that
the performance of this algorithm is within a logarithmic factor of the optimal migratory
oine algorithm, with respect to the total
ow time, and within a small constant factor of
the optimal migratory oine algorithm, with respect to the total completion time. This
solves an open problem suggested by Awerbuch et al [STOC99].
1 Introduction
