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

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

doi:10.1016/j.orl.2016.08.003

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

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

Department of Statistics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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/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.

Original language	English
Pages (from-to)	692-695
Number of pages	4
Journal	Operations Research Letters
Volume	44
Issue number	5
DOIs	https://doi.org/10.1016/j.orl.2016.08.003
State	Published - 1 Sep 2016

Keywords

Closed-form solution
M/D/1 queue
Time-dependent queue length probability
Time-dependent waiting time distribution

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10.1016/j.orl.2016.08.003

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title = "Exact time-dependent solutions for the M/D/1 queue",

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/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.",

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AU - Baek, Jung Woo

AU - Lee, Ho Woo

AU - Ahn, Soohan

AU - Bae, Yun Han

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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 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.

AB - 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 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.

KW - Closed-form solution

KW - M/D/1 queue

KW - Time-dependent queue length probability

KW - Time-dependent waiting time distribution

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SP - 692

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JO - Operations Research Letters

JF - Operations Research Letters

IS - 5

ER -

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

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Keywords

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