Analytical performance models have been leveraged extensively to analyze and improve the performance and cost of various cloud computing services. However, in the case of serverless computing, which is projected to be the dominant form of cloud computing, we have not seen analytical performance models to help with the analysis and optimization of such platforms. In this work, we propose an analytical performance model that captures the unique details of serverless platforms. The model can be leveraged to improve the quality of service and resource utilization and reduce the operational cost of serverless platforms. Also, the proposed performance model provides a framework that enables serverless platforms to become workload-aware and operate differently for different workloads to provide a better trade-off between the cost and performance depending on the user’s preferences. We validate the applicability and accuracy of the proposed model by extensive experimentation on AWS Lambda. We show that the proposed model can calculate essential performance metrics like average response time, probability of cold start, and the average number of function instances in steady-state. Also, the performance model can be used to tune the platform for each workload resulting in better performance or lower cost without scarifying the other.