DNA replication in eukaryotic cells initiates from hundreds of origins along their genomes, leading to complete duplication of genetic information before cell division. The large number of potential origins, coupled with system uncertainty, dictates the need for new analytical tools to capture spatial and temporal patterns of DNA replication genome-wide. We have developed a stochastic hybrid model that reproduces DNA replication throughout a complete genome. The model can capture different modes of DNA replication and is applicable to various organisms. Using genome-wide data on the location and firing efficiencies of origins in the fission yeast, we show how the DNA replication process evolves during S-phase in the presence of stochastic origin firing. Simulations reveal small regions of the genome that extend S-phase to three times its reported duration. The low levels of late replication predicted by the model are below the detection limit of techniques used to measure S-phase length. Parameter sensitivity analysis shows that increased replication fork speeds genome-wide, or additional origins are not sufficient to reduce S-phase to its reported length. We model the redistribution of a limiting initiation factor during S-phase and show that it could shorten S-phase to the reported duration. Alternatively, S-phase may be extended, and what has traditionally been defined as G2 may be occupied by low levels of DNA synthesis with the onset of mitosis delayed by activation of the G2/M checkpoint.