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Jobs associated with messages arriving to a communication processing system (CPS) can be described as ordered sets of prioritized tasks, where each task represents the execution of some part of the system's software. The service system of the CPS consists of a collection of queues, one for each distinct priority, serviced by a single server under a preemptive resume discipline. The routing of the job through this collection of queues is defined by a job's priority vector which specifies the priority at which each task in the job is to execute. For example, if a two-task job's priority vector is (3, 2), then the job first joins the priority 3 queue, obtains service for the first task, then joins the priority 2 queue. In a previous paper, the author and a colleague described a method through which average delays in such task-oriented processing systems could be computed for the special case in which all jobs have identical structure. This paper presents a substantially simplified version of the analysis methodology presented previously and extends that work to the case of a finite number of job classes, each job class having a finite number of tasks.