IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3232-d1200373.html
   My bibliography  Save this article

The Delay Time Profile of Multistage Networks with Synchronization

Author

Listed:
  • Yonit Barron

    (Industrial Engineering and Management, Ariel University, Ariel 40700, Israel)

Abstract

The interaction between projects and servers has grown significantly in complexity; thus, applying parallel calculations increases dramatically. However, it should not be ignored that parallel processing gives rise to synchronization constraints and delays, generating penalty costs that may overshadow the savings obtained from parallel processing. Motivated by this trade-off, this study investigates two special and symmetric systems of split–join structures: (i) parallel structure and (ii) serial structure. In a parallel structure, the project arrives, splits into m parallel groups (subprojects), each comprising n subsequent stages, and ends after all groups are completed. In the serial structure, the project requires synchronization after each stage. Employing a numerical study, we investigates the time profile of the project by focusing on two types of delays: delay due to synchronization overhead (occurring due to the parallel structure), and delay due to overloaded servers (occurring due to the serial structure). In particular, the author studies the effect of the number of stages, the number of groups, and the utilization of the servers on the time profile and performance of the system. Further, this study shows the efficiency of lower and upper bounds for the mean sojourn time. The results show that the added time grows logarithmically with m (parallelism) and linearly with n (seriality) in both structures. However, comparing the two types of split–join structures shows that the synchronization overhead grows logarithmically undr both parallelism and seriality; this yields an unexpected duality property of the added time to the serial system.

Suggested Citation

  • Yonit Barron, 2023. "The Delay Time Profile of Multistage Networks with Synchronization," Mathematics, MDPI, vol. 11(14), pages 1-30, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3232-:d:1200373
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3232/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/14/3232/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Roy, Debjit & van Ommeren, Jan-Kees & de Koster, René & Gharehgozli, Amir, 2022. "Modeling landside container terminal queues: Exact analysis and approximations," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 73-102.
    2. Matta, Andrea & Dallery, Yves & Di Mascolo, Maria, 2005. "Analysis of assembly systems controlled with kanbans," European Journal of Operational Research, Elsevier, vol. 166(2), pages 310-336, October.
    3. Sung‐Seok Ko & Richard F. Serfozo, 2008. "Sojourn times in G/M/1 fork‐join networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(5), pages 432-443, August.
    4. Sabry Shaaban & Rodrigo Romero-Silva, 2021. "Performance of merging lines with uneven buffer capacity allocation: the effects of unreliability under different inventory-related costs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(4), pages 1253-1288, December.
    5. Charles Knessl, 1999. "A diffusion model for two parallel queues with processor sharing: transient behavior and asymptotics," International Journal of Stochastic Analysis, Hindawi, vol. 12, pages 1-28, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dieter Fiems, 2024. "Performance of a Synchronisation Station with Abandonment," Mathematics, MDPI, vol. 12(5), pages 1-12, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Engin Topan & Zeynep Avṣar, 2011. "An approximation for kanban controlled assembly systems," Annals of Operations Research, Springer, vol. 182(1), pages 133-162, January.
    2. Battaïa, Olga & Dolgui, Alexandre, 2022. "Hybridizations in line balancing problems: A comprehensive review on new trends and formulations," International Journal of Production Economics, Elsevier, vol. 250(C).
    3. Lage Junior, Muris & Godinho Filho, Moacir, 2010. "Variations of the kanban system: Literature review and classification," International Journal of Production Economics, Elsevier, vol. 125(1), pages 13-21, May.
    4. Legros, Benjamin & Fransoo, Jan & Jouini, Oualid, 2024. "How to optimize container withholding decisions for reuse in the hinterland?," European Journal of Operational Research, Elsevier, vol. 316(3), pages 930-941.
    5. Iwase, Masaharu & Ohno, Katsuhisa, 2011. "The performance evaluation of a multi-stage JIT production system with stochastic demand and production capacities," European Journal of Operational Research, Elsevier, vol. 214(2), pages 216-222, October.
    6. Zhang, Xiaoju & Jia, Nan & Song, Dongping & Liu, Baoli, 2024. "Modelling and analyzing the stacking strategies in automated container terminals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 187(C).
    7. Hongyuan Lu & Guodong Pang, 2016. "Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 560-595, May.
    8. De Boeck, Liesje & Vandaele, Nico, 2011. "Analytical analysis of a generic assembly system," International Journal of Production Economics, Elsevier, vol. 131(1), pages 107-114, May.
    9. Asefeh Hasani Goodarzi & Seyed Hessameddin Zegordi, 2020. "Vehicle routing problem in a kanban controlled supply chain system considering cross-docking strategy," Operational Research, Springer, vol. 20(4), pages 2397-2425, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3232-:d:1200373. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.