  The Grid technology is evolving into a global, service-orientated
architecture, a universal platform for delivering future high demand
computational services. Strong adoption of the Grid and the utility computing
concept is leading to an increasing number of Grid installations running a wide
range of applications of different size and complexity. In this paper we
address the problem of elivering deadline/economy based scheduling in a
heterogeneous application environment using statistical properties of job
historical executions and its associated meta-data. This approach is motivated
by a study of six-month computational load generated by Grid applications in a
multi-purpose Grid cluster serving a community of twenty e-Science projects.
The observed job statistics, resource utilisation and user behaviour is
discussed in the context of management approaches and models most suitable for
supporting a probabilistic and autonomous scheduling architecture.
