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AbstractA review is presented of the development over the years of the theory and practical use of Markov decision processes. To this purpose three periods are considered: before 1966, from 1966 till 1972, and after 1973. In all 3 periods there has been some contribution from the Netherlands, but particularly in the last period the research in the Netherlands on the subject has become a major stream. In this review particular emphasis is given to the work which has been done in the Netherlands, but the main line of the paper is determined by the development of the applicability of the available theory.

The M/G/∞ queue with Optimistic Concurrency Control (OCC) is a model for a special form of parallel transaction processing in a real‐time database. Transactions arrive according to a Poisson process and require some generally distributed execution time. One of the differences with ordinary multi‐ and infinite‐server queueing models is that under OCC the successful completion of one transaction may immediately cause the failure of one or more of the other transactions. This happens if the completing transaction has overwritten a data‐item that is in use by another transaction in progress. As soon as this failure is detected the failed transaction is restarted. So the total service time of a transaction consists of its final successful run and the time spent on unsuccessful runs.In this study we develop an approximation for the distribution of the total service time, and test the approximation against simulation. Although in practice the number of servers is never unlimited, this study provides valuable insight in the asymptotics with respect to the number of servers. The approximation clearly demonstrates the very limited performance gain from an increase of the number of servers.