Whitt's (1983) open queuing network analyzer (QNA) has been used in different application areas, such as communication system and discrete parts manufacturing system. It uses the parametric decomposition method to approximately calculate the performance measures. The core of the method involves solving two systems of linear equations to calculate the first two moments of effective arrival rate and service time. In this paper, we consider the effects of batch size on the parametric decomposition

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... procedure of QNA and modify the two sets of linear equations accordingly. The concept of relative batch size is proposed for the purpose of modeling the effects of batch size. Experimental results are shown to illustrate the effectiveness of the method. Keywords: Open queuing network, batch size, performance analysis the computational cost. Yilmaz and Boe (1988) use statistical hypothesis testing to examine the relative performance of different algorithms as well as three major factors that may affect the relative performance of different algorithms. The null hypothesis that different batch-sizing algorithms perform equally, is rejected. The effects of: (1) demand variability, (2) the ratio of setup cost to holding cost (the cost structure ratio), and (3) the length of the planning horizon, on the relative performance of different algorithms are explored and summarized. Jeunet and Jonard (2000) proposed robustness of batch-sizing algorithms as the third evaluation criteria, together with the cost effectiveness and computational time. Robustness of batch-sizing algorithms addresses evaluation needs in manufacturing environments where demand variability cannot be ignored. Six alternative measures of robustness are proposed and simulation experiments are conducted to rank different batch-sizing algorithms. Other researchers have used the performance of the overall manufacturing system to evaluate batch-sizing algorithms. Byrne and O'Grady (1990) did a case study of a manufacturing system at Rolls-Royce Ltd., which consists of 78 work centers and 487 products, each product having 46 operations on average. For each run of each batching algorithm, the product lead times, throughput rate, setup cost, WIP inventories and total cost of the manufacturing system are recorded. 104 simulation runs showed that the minimum cost batch sizing policy had a batch size that was approximately 50% of the existing batch sizes. Habchi and Labrune (1995) did a similar study of a job-shop, considering several single product/multiple product combinations with stable and variable demand. Using simulation models to design, benchmark or explore factors that affect performance of batch-sizing policies is expensive. Building simulation model of a manufacturing system and running the model for each configuration of batch-sizing policy is time consuming. Analytical models of a manufacturing system with batch-size parameters embedded in them are of research machine j