Growth of performance sensitive applications, such as voice and multimedia, has led to widespread adoption of resource virtualization by a variety of service providers (xSPs). For instance, Internet Service Providers (ISPs) increasingly differentiate their offerings by means of customized services, such as virtual private networks (VPN) with Quality of Service (QoS) guarantees or QVPNs. Similarly Storage Service Providers (SSPs) use storage area networks (SAN)/network attached storage (NAS) technology to provision virtual disks with QoS guarantees or QVDs. The key challenge faced by these xSPs is to maximize the number of virtual resource units they can support by exploiting the statistical multiplexing nature of the customers' input request load.While a number of measurement-based admission control algorithms utilize statistical multiplexing along the bandwidth dimension, they do not satisfactorily exploit statistical multiplexing along the delay dimension to guarantee distinct per-virtual-unit delay bounds. This article presents Delay Distribution Measurement (DDM) based admission control algorithm, the first measurement-based approach that effectively exploits statistical multiplexing along the delay dimension. In other words, DDM exploits the well-known fact that the actual delay experienced by most service requests (packets or disk I/O requests) for a virtual unit is usually far smaller than its worst-case delay bound requirement because multiple virtual units rarely send request bursts at the same time. Additionally, DDM supports virtual units with distinct probabilistic delay guarantees---virtual units that can tolerate more delay violations can reserve fewer resources than those that tolerate less, even though they require the same delay bound. Comprehensive trace-driven performance evaluation of QVPNs (using Voice over IP traces) and QVDs (using video stream, TPC-C, and Web search I/O traces) shows that, when compared to deterministic admission control, DDM can potentially increase the number of admitted virtual units (and resource utilization) by up to a factor of 3.