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Consider a multipriority batch computer system which users from several different classes may join, with toll, service, and waiting charges. Such a system is formulated here as a semi- Markov decision process, In which the aim of arriving users Is to minimize their expected loss. The optimal joining policy of arriving users who may join the system at some of its queues is a control limit policy, with a single control number for any possible queue and the user's class; a newly arriving user will join a queue that is not filled up to the control number corresponding to this queue and the user's class. In this paper control numbers, as well as lower and upper bounds for the control numbers and the capacities of the system's queues, are derived. [ABSTRACT FROM AUTHOR]