  Heterogeneous multi-cores utilize the strength of different architectures for
executing particular types of workload, and usually offer higher performance
and energy efficiency. In this paper, we study the worst-case response time
(WCRT) analysis of \emph{typed} scheduling of parallel DAG tasks on
heterogeneous multi-cores, where the workload of each vertex in the DAG is only
allowed to execute on a particular type of cores. The only known WCRT bound for
this problem is grossly pessimistic and suffers the
\emph{non-self-sustainability} problem. In this paper, we propose two new WCRT
bounds. The first new bound has the same time complexity as the existing bound,
but is more precise and solves its \emph{non-self-sustainability} problem. The
second new bound explores more detailed task graph structure information to
greatly improve the precision, but is computationally more expensive. We prove
that the problem of computing the second bound is strongly NP-hard if the
number of types in the system is a variable, and develop an efficient algorithm
which has polynomial time complexity if the number of types is a constant.
Experiments with randomly generated workload show that our proposed new methods
are significantly more precise than the existing bound while having good
scalability.
