Container-based Software-as-a-Service (SaaS) systems are rapidly emerging as a dominate cloud deployment paradigm, as supported via Docker, etc. This has opened new research avenues as lighter-weight containers replace heavier-weight virtual machines (VMs) as atomic cloud deployment units. Advancing such research requires sufficiently rich, container-aware cloud simulation frameworks so as to explore issues such as optimal cloud orchestration and elastic service strategies, achieving assured application-layer quality of service (QoS), etc. This work presents DockerSim, an extension and augmentation of the iCanCloud OMNet++ cloud simulator to incorporate: i) a full container deployment and behavioral layer, ii) full packet-level network and protocol behaviors, iii) full multi-layer OS process scheduling behaviors, and iv) a generic queuing network approach to modeling application-layer SaaS deployments. To our knowledge DockerSim is the first cloud simulation platform fully incorporating capabilities (i)-(iv), as required to rigorous explore a wide range of timing sensitive container-based computing cloud and SaaS-deployment issues.