Function-as-a-Service (FaaS) is increasingly popularin the software industry due to the implied cost-savings in event-driven workloads and its synergy with DevOps. To size an on-premise FaaS platform, it is important to estimate the requiredCPU and memory capacity to serve the expected loads. Giventhe service-level agreements, it is however challenging to takethe cold start issue into account during the sizing process. Wehave investigated the similarity of this problem with the hitrate improvement problem in TTL caches and concluded thatsolutions for TTL cache, although potentially applicable, lead toover-provisioning in FaaS. Thus, we propose a novel approach,COCOA, to solve this issue. COCOA uses a queueing-basedapproach to assess the effect of cold starts on FaaS responsetimes. It also considers different memory consumption valuesdepending on whether the function is idle or in execution. Usingan event-driven FaaS simulator,FaasSim, we have developed, weshow that COCOA can reduce over-provisioning by over 70% insome workloads, while satisfying the service-level agreements.