A variety of production systems appearing in the literature are reviewed in order to develop a classification scheme for production systems. A number of pull production systems appearing in the classification are found to be equivalent to a tandem queue so that accurate tandem queue decomposition methods can be used to find the performance of such systems. The primary concern of this dissertation is to model and analyze non-tandem queue equivalent periodic pull production systems. In this research, an exact performance evaluation model is developed for a singleitem periodic pull production system. The processing and demand interarrival times are assumed to be Markovian. For large systems, which are difficult to evaluate exactly because of large state spaces involved, an approximate decomposition method is proposed. A typical approximate decomposition procedure takes individual stages or pairs of stages in isolation to analyze the system and then it aggregates the results to obtain an approximate performance for the whole system. An experiment is designed in order to investigate the general behavior of the decomposition. The results are worth attention. A second aspect of this study is to investigate an allocation methodology to achieve the maximum throughput rate with providing two sets of allocation parameters regarding the number of kanbans and the workload at each stage of the system. Together with some structural properties, the experimental results provide some insight into the behavior of pull production systems and also provide a basis for the proposed allocation methodology. Finally, we conclude our findings together with some directions for future research.