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Layered queues are a canonical form of extended queueing network for systems with nested multiple resource possession, in which successive depths of nesting define the layers. The model has been applied to most modern distributed systems, which use different kinds of client-server and master-slave relationships, and scales up well. The layered queueing network (LQN) model is described here in a unified fashion, including its many more extensions to match the semantics of sophisticated practical distributed and parallel systems. These include efficient representation of replicated services, parallel and quorum execution, and dependability analysis under failure and reconfiguration. The full LQN model is defined here and its solver is described. A substantial case study to an air traffic control system shows errors (compared to simulation) of a few percent. The LQN model is compared to other models and solutions, and is shown to cover all their features.