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Analysis of the M/Gb/1 Queue by the Arrival Time Approach  

Chae, Kyung-Chul (Department of Industrial Engineering, KAIST)
Chang, Seok-Ho (Department of Industrial Engineering, KAIST)
Lee, Ho-Woo (School of Systems Management Engineering, Sung Kyun Kwan University)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.28, no.1, 2002 , pp. 36-43 More about this Journal
Abstract
We analyze bulk service $M/G^{b}/1$ queues using the arrival time approach of Chae et al. (2001). As a result, the decomposition property of the M/G/1 queue with generalized vacations is extended to the $M/G^{b}/1$ queue in which the batch size is exactly a constant b. We also demonstrate that the arrival time approach is useful for relating the time-average queue length PGF to that of the departure time, both for the $M/G^{b}/1$queue in which the batch size is as big as possible but up to the maximum of constant b. The case that the batch size is a random variable is also briefly mentioned.
Keywords
bulk service queue; vacation queue; decomposition property;
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