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Kanban control systems bear a great potential to significantly improve operations. A company may reap the full benefits of kanban control only after determining an optimal or near-optimal system configuration. To do that, methods are needed to evaluate the performance and operating costs of individual system configurations. We propose an innovative construction-kit approach that enables us to build stochastic analytical models of a large class of single- and multi-product kanban systems. The presented construction-kit approach may be extended and augmented in various directions