Testing processes and workflows in information and Internet of Things systems is a major part of the typical software testing effort. Consistent and efficient path-based test cases are desired to support these tests. Because certain parts of software system workflows have a higher business priority than others, this fact has to be involved in the generation of test cases. In this paper, we propose a Prioritized Process Test (PPT), which is a model-based test case generation algorithm that represents an alternative to currently established algorithms that use directed graphs and test requirements to model the system under test. The PPT accepts a directed multigraph as a model to express priorities, and edge weights are used instead of test requirements. To determine the test-coverage level of test cases, a test-depth-level concept is used. We compared the presented PPT with five alternatives (i.e., the Process Cycle Test, a naive reduction of test set created by the Process Cycle Test, Brute Force algorithm, Set-covering Based Solution and Matching-based Prefix Graph Solution) for edge coverage and edge-pair coverage. To assess the optimality of the path-based test cases produced by these strategies, we used fourteen metrics based on the properties of these test cases and 59 models that were created for three real-world systems. For all edge coverage, the PPT produced more optimal test cases than the alternatives in terms of the majority of the metrics. For edge-pair coverage, the PPT strategy yielded similar results to those of the alternatives. Thus, the PPT strategy is an applicable alternative, as it reflects both the required test coverage level and the business priority in parallel.