The serverless computing model has evolved as one of the key solutions in the cloud for fast autoscaling and capacity planning. In edge computing environments, however, the serverless model is challenged by the system heterogeneity and performance variability. In this paper, we introduce BenchFaaS, an open-source edge computing network testbed which automates the deployment and benchmarking of serverless functions. Our edge computing network considers a cluster of virtual machines and Raspberry Pis, and is designed to benchmark serverless functions under different hardware and network conditions. We measure and evaluate: (i) overhead incurred by testbed, (ii) performance of compute intensive tasks, (iii) impact of application payload size, (iv) scalability, and (v) performance of chained serverless functions. We share the lessons learnt in engineering and implementing the testbed. We present the measurement results and analyze the impact of networked infrastructure on serverless performance. The measurements indicate that a properly dimensioned edge computing network can effectively serve as a serverless infrastructure.