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The performance of transaction processing systems is determined by the contention for hardware as well as software resources (database locks), due to the concurrency control mechanism of the database being accessed by transactions. We consider a transaction processing system with a set of dominant transcation classes. Each class needs to acquire a certain subset of the locks in the database before it can be processed, i.e., predeclared lock requests with static locking. Straightforward application of the decomposition method requires the numerical solution of a two-dimensional Markov chain. Equivalently, a hierarchical simulation method, where the computer system is represented by a composite queue with exponential service rates, can be used to analyze the system. We propose an inexpensive analytic solution method, also based on hierarchical decomposition, such that the throughput of the computer system ic characterized by the number of active transactions (regardless of class). Numerical results are provided to show that the new method is adequately accurate compared to the other two rather costly methods. It can be used to determine the effect of granularity of locking on system performance. The solution method is also applicable to multiresource queueing systems with multiple contention points.