DNA replication, the basis of genetic information maintenance, is a remarkably robust yet highly stochastic process. We present a computational model that incorporates experimental genome structures and protein mobility dynamics to mechanistically describe the stochastic foundations of DNA replication. Analysis of about 300,000 in silico profiles for fission yeast indicates that the number of firing factors is rate-limiting and dominates completion time. Incorporating probabilistic activation and binding, a full-genome duplication was achieved with at least 300 firing factors, with the only assumption that factors get recycled upon replication fork collision. Spatial patterns of replication timing were reproduced only when firing factors were explicitly activated proximally to the spindle pole body. Independent in vivo experiments corroborate that the spindle pole body acts as a replication activator, driving origin firing. Our model provides a framework to realistically simulate full-genome DNA replication and investigate the effects of nuclear architecture.