DNA replication is an important process in the life of a cell. It has to be completed with extreme accuracy in a specific phase of the cell cycle, known as the S phase. Eukaryotic DNA replication is a rather complex and uncertain process. Several mathematical models have been recently proposed in the literature to interpret experimental data from various organisms. A common concern of many of these models is the so-called random gap problem, the observation that eukaryotic DNA replication should last longer than experimental evidence suggests due to its stochastic nature. One of the biological hypotheses proposed for resolving the random gap problem postulates the presence of a limiting factor regulating the rate with which DNA replication initiates. We show how this hypothesis can be captured in the Piecewise Deterministic Markov Process modeling framework. Monte Carlo simulations allow us to analyze the proposed model and compare model predictions with independent experimental data. (C) 2011 Elsevier Ltd. All rights reserved.