This paper presents a new schedulability analysis methodology for distributed hard real-time systems with bursty job arrivals. The schedulability is analyzed by comparing worst-case response times of jobs with their timing constraints. We compute response times with a new method, which uses the amount of received service time to determine the response time of instances of a job. We illustrate how this method can be applied to exactly determine worstcase response times for processors with preemptive staticpriority schedulers, and how it gives a good approximation on the response times for processors with non-preemptive static-priorityscheduling or first-come-first-served scheduling. Our schedulability analysis method is the first to support systems with arbitrary job arrival patterns. Nevertheless, it performs better than other known approaches used for systems with periodic job arrivals.