Exact time-dependent solutions for the $M / D / 1$ queue

DOI10.1016/j.orl.2016.08.003zbMath1408.60082OpenAlexW2509229767MaRDI QIDQ1755849

Soohan Ahn, Jung Woo Baek, Yun Han Bae, Ho Woo Lee

Publication date: 11 January 2019

Published in: Operations Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.orl.2016.08.003

zbMATH Keywords

closed-form solution$M / D / 1$ queuetime-dependent queue length probabilitytime-dependent waiting time distribution

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Cites Work

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• An application of Riordan arrays to the transient analysis of \(M/M/1\) queues
• Transient solution of the \(M/M/c\) queue with balking and reneging
• A new formula for the transient solution of the Erlang queueing model
• Transient behaviour of an M/M/1/N queue
• The transient solution to a class of Markovian queues
• The busy period of an \(\mathrm{M}/\mathrm{M}/1\) queue with balking and reneging
• A new formula for the transient behaviour of a non-empty M/M/1/\(\infty\) queue.
• A time-dependent busy period queue length formula for the \(\mathrm{M}/\mathrm{E}_k/1\) queue
• The transient solution to \(M/E_{k}/1\) queue
• Transient analytical solution of M/D/1/N queues
• A derivation of the Borel distribution

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