The stochastic simulation of large-scale biochemical reaction networks is of great importance for systems biology since it enables the study of inherently stochastic biological mechanisms at the whole cell scale. Stochastic Simulation Algorithms (SSA) allow us to simulate the dynamic behavior of complex kinetic models, but their high computational cost makes them very slow for many realistic size problems. We present a pilot service, named WebStoch, developed in the context of our StochSoCs research project, allowing life scientists with no high-performance computing expertise to perform over the internet stochastic simulations of large-scale biological network models described in the SBML standard format. Biomodels submitted to the service are parsed automatically and then placed for parallel execution on distributed worker nodes. The workers are implemented using multi-core and many-core processors, or FPGA accelerators that can handle the simulation of thousands of stochastic repetitions of complex biomodels, with possibly thousands of reactions and interacting species. Using benchmark LCSE biomodels, whose workload can be scaled on demand, we demonstrate linear speedup and more than two orders of magnitude higher throughput than existing serial simulators.