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Petri Net Modeling and Analysis for Periodic Job Shops with Blocking
Lee, Tae-Eog,Song, Ju-Seog 한국경영과학회 1996 한국경영과학회 학술대회논문집 Vol.- No.1
We investigate the scheduling problem for periodic job shops with blocking. We develop Petri net models for periodic job shops with finite buffers. A buffer control method would allow the jobs to enter the input buffer of the next machine in the order for which they are completed. We discuss difficulties in using such a random order buffer control method and random access buffers. We thus propose an alternative buffer control policy that restricts the jobs to enter the input buffer of the next machine in a predetermined order. The buffer control method simplifies job flows and control systems. Further, it requires only a cost-effective simple sequential buffer. We show that the periodic scheduling model with finite buffers using the buffer control policy can be transformed into an equivalent periodic scheduling model with no buffer, which is modeled as a timed marked graph. We characterize for the no buffer problem that finds a deadlock-free optimal sequence that minimizes the cycle time.
Characterizing Token Delays of Timed Event Graphs for $K$- Cyclic Schedules
Lee, Tae-Eog,Kim, Hyun-Jung,Roh, Dong-Hyun,Sreenivas, Ramavarapu S. Institute of Electrical and Electronics Engineers 2017 IEEE Transactions on Automatic Control Vol. No.
<P>A timed discrete event system, which repeats identical work cycles, has task delays due to synchronization between work cycles. Real such systems tend to operate mostly in a K-cyclic timing regime, where a sequence of identical timing patterns is repeated for every K cycles. Therefore, the task delays fluctuate and repeat a sequence of K different values, and hence have higher risk of violating an upper limit. Task delays correspond to token delays at the system's timed event graph model. We therefore examine token delays in K-cyclic schedules of a timed event graph, an essential class of Petri nets. We first identify all possible K-cyclic schedules and define their initial phases. We then develop a closed-formula on the token delays on a path for a K-cyclic schedule, which can be computed by the longest path lengths between the nodes in an associated directed graph. We also present a formula for 1-cyclic schedules. The formulae can be used for computing statistics on K-different token delays, maximizing or minimizing the token delays with regard to all possible initial phases, and verifying task delay constraints, if any.</P>