The emerging high-speed storage technologies increasingly use Nonvolatile Memory Express (NVMe) protocol to meet their high throughput and low latency needs. In a datacenter environment, applications accessing multiple such devices over the fabric (i.e. the network) tend to have Quality of Service (QoS) requirements pertaining to offered throughput and experienced latency. In this paper we describe a networked storage system simulator called NeSt that supports end-to-end (E2E) QoS differentiation across multiple classes of service. This is done by conveying the class designation end to end and using it to consistently but independently apply the differentiation in each segment of the path. We demonstrate the ability of NeSt to provide end-to-end QoS differentiation under a variety of situations. To the best of our knowledge, NeSt is the first simulator of networked storage (consisting of multiple NVMe SSDs) that supports E2E QoS differentiation.