The research project reported in this thesis considers Multiple Distributed Replications in Parallel (MDRIP), a hybrid approach to parallelisation of quantitative stochastic discrete-event simulation. Parallel Discrete-Event Simulation (PDES) generally covers distributed simulation or simulation with replicated trials. Distributed simulation requires model partitioning and synchronisation among submodels. Simulation with replicated trials can be executed on-line by applying Multiple Replications in Parallel (MRIP). MDRIP has been proposed for overcoming problems related to the large size of simulated models and their complexity, as well as with the problem of controlling the accuracy of the final simulation results. A survey of PDES investigates several primary issues which are directly related to the parallelisation of DES. A secondary issue related to implementation efficiency is also covered. Statistical analysis as a supporting issue is described. The AKAROA2 package is an implementation of making such supporting issue effortless. Existing solutions proposed for PDES have exclusively focused on collecting of output data during simulation and conducting analysis of these data when simulation is finished. Such off-line statistical analysis of output data offers no control of statistical errors of the final estimates. On-line control of statistical errors during simulation has been successfully implemented in AKAROA2, an automated controller of output data analysis during simulation executed in MRIP. However, AKAROA2 cannot be applied directly to distributed simulation. This thesis reports results of a research project aimed at employing AKAROA2 for launching multiple replications of distributed simulation models and for on-line sequential control of statistical errors associated with a distributed performance measure; i.e. with a performance measure which depends on output data being generated by a number of submodels of distributed simulation. We report changes required in the architecture of AKAROA2 to make MDRIP possible. A new MDRIP-related component of AKAROA2, a distributed simulation engine mdrip engine, is introduced. Stochastic simulation in its MDRIP version, as implemented in AKAROA2, has been tested in a number of simulation scenarios. We discuss two specific simulation models employed in our tests: (i) a model consisting of independent queues, and (ii) a queueing network consisting of tandem connection of queueing systems. In the first case, we look at the correctness of message orderings from the distributed messages. In the second case, we look at the correctness of output data analysis when the analysed performance measures require data from all submodels of a given (distributed) simulation model. Our tests confirm correctness of our mdrip engine design in the cases considered; i.e. in models in which causality errors do not occur. However, we argue that the same design principles should be applicable in the case of distributed simulation models with (potential) causality errors.