Exact time-dependent solutions for the queue

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• 作者：Jung Woo Baek^a ; ^{jwbaek@chosun.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Ho Woo Lee^b ; ^{hwlee@skku.edu" class="auth_mail" title="E-mail the corresponding author} ; Soohan Ahn^c ; ^{sahn@uos.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Yun Han Bae^d ; ^{yhbae@smu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：M/D/1M/D/1 queue ; Time-dependent queue length probability ; Time-dependent waiting time distribution ; Closed-form solution
• 刊名：Operations Research Letters
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：44
• 期：5
• 页码：692-695
• 全文大小：378 K

文摘

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/1$M/D/1$ 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.