Fischer's protocol is a well-known timed mechanism through which a set of processes can synchronize access to a critical section without relying on atomic test-and-set operations, as might occur in a distributed environment or on a low-level computing platform. The protocol is based on a deterministic waiting time that can be defined so as to guarantee that possible interference due to concurrent accesses with random bounded delays be resolved with certainty. While protocol correctness descends from firm lower and upper bounds on waiting times and random delays, performance attained in synchronization also depends on continuous distributions of delays. Performance evaluation of a correct implementation thus requires the solution of a non-Markovian model whose underlying stochastic process falls in the class of Markov regenerative processes (MRPs) with multiple concurrent delays with non-exponential duration. Numerical solution of this class of models is to a large extent still an open problem. We provide a twofold contribution. We first introduce a novel method for the steady-state analysis of MRPs where regenerations are reached in a bounded number of discrete events, which enlarges the class amenable to numerical solution by allowing multiple concurrent timers with non-exponential distributions. The proposed technique is then applied to Fischer's protocol by characterizing the latency overhead due to synchronization, which comprises the first case where performance of the protocol is quantitatively assessed by jointly accounting for firm bounds and continuous distributions of delays.