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| DOI：https://doi.org/10.1007/s11768-018-7074-9 |
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| 基金项目:This work was supported by the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2016JM6003) and partially by the Natural Sciences and Engineering Research Council (NSERC) of Canada (No. DG 480599). |
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| Queue reduction in discrete-event systems by relabeling |
| Yongmei GAN,Ting JIAO,W. M. WONHAM |
| (School of Electrical Engineering, Xi’an Jiaotong University, Xi’an Shaanxi 710049, China;Department of Automation, Shanxi University, Taiyuan Shanxi 030006, China;Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON M5S 3G4, Canada) |
| Abstract: |
| The customer population of entities potentially requesting to join a queue for service often have identical structure, i.e., the
same state set and isomorphic transitions. The state size of the automaton modeling a queue will grow rapidly with increase of
the size of this population. However, by relabeling the queue arrival events and service events to the same symbols respectively,
the automaton model of a queue will be converted to the structure of a buffer, which is proved to be independent of the total size
of the customer population, as long as the queue size is held fixed. We propose the model of a dynamic buffer to embody order
and shift of a queue. The result is applied to a manufacturing facility with a dynamic buffer to manage the repair of broken down
machines. |
| Key words: Queue, relabeling, identical structures, invariance property, discrete-event systems |
