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A new formula for the transient solution of the Erlang queueing model

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  • Leonenko, G.M.

Abstract

This paper studies the transient solution of the Markovian queue, namely M/Ek/1 model. A new approach is introduced for finding exact solution for this queueing system. The transient probabilities are expressed recurrently.

Suggested Citation

  • Leonenko, G.M., 2009. "A new formula for the transient solution of the Erlang queueing model," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 400-406, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:3:p:400-406
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    References listed on IDEAS

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    1. Amedeo R. Odoni & Emily Roth, 1983. "An Empirical Investigation of the Transient Behavior of Stationary Queueing Systems," Operations Research, INFORMS, vol. 31(3), pages 432-455, June.
    2. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    3. George Luchak, 1956. "The Solution of the Single-Channel Queuing Equations Characterized by a Time-Dependent Poisson-Distributed Arrival Rate and a General Class of Holding Times," Operations Research, INFORMS, vol. 4(6), pages 711-732, December.
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    Cited by:

    1. Baek, Jung Woo & Moon, Seung Ki & Lee, Ho Woo, 2014. "A time-dependent busy period queue length formula for the M/Ek/1 queue," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 98-104.
    2. Jung Woo Baek & Yun Han Bae, 2019. "Exact Time-Dependent Queue-Length Solution to a Discrete-Time Geo / D /1 Queue," Mathematics, MDPI, vol. 7(8), pages 1-8, August.
    3. Xiaoyuan Liu & Brian Fralix, 2019. "On Lattice Path Counting and the Random Product Representation, with Applications to the Er/M/1 Queue and the M/Er/1 Queue," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1119-1149, December.
    4. B. H. Margolius, 2023. "The periodic steady-state solution for queues with Erlang arrivals and service and time-varying periodic transition rates," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 45-94, February.
    5. Jain, Madhu & Bhagat, Amita & Shekhar, Chandra, 2015. "Double orbit finite retrial queues with priority customers and service interruptions," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 324-344.

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