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Queueing Models Involving Buffers

1978; Wiley; Volume: 46; Issue: 1 Linguagem: Inglês

10.2307/1402518

1751-5823

J. Gani, F. Göbel, F. Göbel,

Flexible and Reconfigurable Manufacturing Systems

LEMMA 2.1.(2.6) ~+1 = max(O,w +x -Y ), 71 71 --n z +l = max(O,w +x -Y, z +s -y ).71 71 71 --n 71 71 --n PROOF.For then-th customer (or load), we define following epochs (n ~ 1). a arrival time, 71 b start of filling, 71 C start of emptying, 71 d end of filling, 71 e end of emptying. 71From the definition of~ we haveThe (n+1)-st customer starts to fill as soon as possible, that is: on his arrival, or else when then-th customer has completed his filling operation. Hence Likewise we haveOnce a customer has started to fill the buffer, there are no restrictions on this operation, and we have simply