Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1142042 | Operations Research Letters | 2016 | 4 Pages |
Abstract
Time-dependent solutions to queuing models are very useful for evaluating the performance of real-world systems. However, because of their mathematical complexity, few available results exist. In this paper, we derive the time-dependent performance measures for an M/D/1M/D/1 queue starting with a positive number of initial customers. Using the limiting property of an Erlang distribution, we obtain closed-form time-dependent formulas for the queue length and the waiting time. Furthermore, the time-dependent queue length probability in a busy period is derived.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jung Woo Baek, Ho Woo Lee, Soohan Ahn, Yun Han Bae,