Some Properties of Throughput in a Queueing Network with Changing-Speed Servers and Blocking
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A class of queueing networks, called the Jackson networks, is well known to have a convenient property for queue length distributions, namely, the so-called product form (see, e.g.,Walrand ). This property enables us to calculate the queue length distributions for large-scale queueing networks, and hence Jackson networks have been used extensively in the design or performance evaluation of communication systems. On the other hand, these queueing networks have not been used so often for manufacturing systems. Of course, there are exceptions, e.g., an attempt has been made to apply the networks to flexible manufacturing systems (FMSs; for details, see ). Why haven’t these networks been used so often for manufacturing systems? We think there are two main reasons. One is the structure of Jackson networks. Each node (or station) in a manufacturing system usually has only a finite buffer capacity, so a blocking phenomenon may occur. In this case, it is very important to evaluate how the performance parameters such as the production rate (throughput) are affected by blocking. In Jackson networks, however, there is no blocking. The other reason is the service time distribution of jobs at each station. In Jackson networks, this distribution is exponential—an unacceptable situation for practitioners working on manufacturing systems. Of course, there are exceptions in this context, e.g., symmetric queueing networks by Kelly . For these reasons, tandem queues with blocking and general service time distribution at each station have been used in the design or performance evaluation of manufacturing systems such as flow lines, transfer lines, and flexible assembly lines (see, e.g.,  and ).
KeywordsService Time Flexible Manufacturing System Single Server Service Time Distribution Service Discipline
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- Ohi, K. On Tandem Queues with State-Dependent-Service Rate (in Japanese). Master Thesis, Tokyo Metropolitan Institute of Technology, 1995.Google Scholar