Probabilistic Decomposition Method on the ServerIndices of an M^𝜉/G/1 Vacation Queue

Table 1

The effects of batch order rate 𝜆 on production facility indices (𝑝=0.8, 𝜃=0.5, 𝜇=2, 𝛼=0.1, and 𝛽=0.8).

𝜆	𝜌	lim𝑡→∞𝐴𝑖(𝑡)	lim𝑡→∞Φ𝑖(𝑡)	lim𝑡→∞𝑀𝑖(𝑡)/𝑡
0.10	0.4320	0.3783	0.0280	0.0350
0.15	0.6480	0.5956	0.0441	0.0551
0.20	0.8640	0.8356	0.0619	0.0774
0.25	1.0800	1	0.0741	0.0926
0.30	1.2960	1	0.0741	0.0926
0.35	1.5120	1	0.0741	0.0926