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The paper contains recent enhancements of a formal model of agent-based computing systems. In such systems a computational task together with its data is enveloped in a shell to form a mobile agent. The shell carries the agent's logic, ie. abilities to make decisions about whether to migrate to a less loaded machine, split oneself or continue the task. The model describes an agent-based computational application as a controlled Markov chain. In this paper the operation of the agent hibernation, which is the last resort in the case of a server overload, is included in the model. This modification has an influence on the form of the state equations as well as the form of admissible control strategies.