  In this paper we study the multiple-processor multitask scheduling problem in
both deterministic and stochastic models, where each job have several tasks and
is complete only when all its tasks are finished. We consider and analyze
Modified Shortest Remaining Processing Time (M-SRPT) scheduling algorithm, a
simple modification of SRPT, which always schedules jobs according to SRPT
whenever possible, while processes tasks in an arbitrary order. The M-SRPT
algorithm is proved to achieve a competitive ratio of $\Theta(\log \alpha
+\beta)$ for minimizing response time, where $\alpha$ denotes the ratio between
maximum job workload and minimum job workload, $\beta$ represents the ratio
between maximum non-preemptive task workload and minimum job workload. In
addition, the competitive ratio achieved 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
(\ie, M/GI/$N$ system), and show that M-SRPT achieves asymptotic optimal mean
response time when the traffic intensity $\rho$ approaches $1$, if job size
distribution has finite support. Beyond finite job workload, the asymptotic
optimality of M-SRPT also holds for infinite job size distributions with
certain probabilistic assumptions, for example, M/M/$N$ system with finite task
workload. As a special case, we show that M-SRPT is asymptotic optimal in
M/M/$1$ model, in which the task size distribution is allowed to have infinite
support.
