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This paper surveys applications of queueing theory for semiconductor manufacturing systems (SMSs). Due to sophisticated tool specifications and process flows in semiconductor manufacturing, queueing models can be very complicated. Research efforts have been on the improvement of model assumptions and model input, mainly in the first moment (averages) and the second moment (variations). However, practices show that implementation of classical queueing theory in semiconductor industry has been unsatisfactory. In this paper, open problems on queueing modeling of SMS are discussed. A potential solution is also proposed by relaxing the independent assumptions in the classical queueing theory. Cycle time reduction has constantly been a key focus of semiconductor manufacturing. Compared with simulation, queueing theory-based analytical modeling is much faster in estimating manufacturing system performance and providing more insights for performance improvement. Therefore, queueing modeling attracts generous semiconductor research grants. Unfortunately, existing queueing models focus on simple extensions of the classical queueing theory and fail to question its applicability to the complicated SMS. Hence, related researches have not been employed widely in the semiconductor industry. In this paper, we conduct a survey on the important works and also present some open problems. We also propose a novel solution by relaxing a key assumption in the classical queueing theory. We are currently funded by Intel to explore this potential solution, and we hope it can foster an interesting research field for the years to come.