Device drivers are integral components of operating systems. The computational workloads imposed by device drivers tend to be aperiodic and unpredictable because they are triggered in response to events that occur in the device, and may arbitrarily block or preempt other time-critical tasks. This characteristic poses significant challenges in real-time systems, where schedulability analysis is essential to guarantee system-wide timing constraints. At the same time, device driver workloads cannot be ignored. Demand-based schedulability analysis is a technique that has been successful in validating the timing constraints in both single and multiprocessor systems. In this paper we present two approaches to demand-based schedulability analysis of systems that include device drivers. First, we derive load-bound functions using empirical measurement techniques. Second, we modify the scheduling of network device driver tasks in Linux to implement an algorithm for which a load-bound function can be derived analytically. We demonstrate the practicality of our approach through detailed experiments with a network device under Linux. Our results show that, even though the network device driver does not conform to conventional periodic or sporadic task models, it can be successfully modeled using hyperbolic load-bound functions that are fitted to empirical performance measurements.