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Overflow in systems with two servers: the negative consequences

Author

Listed:
  • Yanting Chen

    (University of Shanghai for Science and Technology)

  • Jingui Xie

    (Technical University of Munich)

  • Taozeng Zhu

    (Dongbei University of Finance and Economics)

Abstract

We investigate a system with two types of customers wherein each customer type has a dedicated server. When the corresponding dedicated server is busy, we allow customer overflow to the non-dedicated server, and the service time of each server is customer-dependent. The objective of this study is to assess the negative consequences of overflow. On the basis of the analytical stationary distribution of the proposed two-server model, we first identify the conditions under which overflow leads to improvement of throughputs. Second, we obtain customers’ overflow rates and ratios. For a symmetric system under heavy traffic, the wrong assignment ratio comes close to 50%. Third, we analyze the probability that a customer is served by a non-dedicated server. The probability that both servers are serving non-dedicated customers approaches 25% in a symmetric system under heavy traffic. Finally, we determine various overflow conditions while including the overflow costs.

Suggested Citation

  • Yanting Chen & Jingui Xie & Taozeng Zhu, 2023. "Overflow in systems with two servers: the negative consequences," Flexible Services and Manufacturing Journal, Springer, vol. 35(3), pages 838-863, September.
    • Handle: RePEc:spr:flsman:v:35:y:2023:i:3:d:10.1007_s10696-022-09455-w
    DOI: 10.1007/s10696-022-09455-w
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    References listed on IDEAS

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    1. Ward Whitt, 1999. "Partitioning Customers into Service Groups," Management Science, INFORMS, vol. 45(11), pages 1579-1592, November.
    2. Md Asaduzzaman & Thierry Chaussalet & Nicola Robertson, 2010. "A loss network model with overflow for capacity planning of a neonatal unit," Annals of Operations Research, Springer, vol. 178(1), pages 67-76, July.
    3. J. G. Dai & Pengyi Shi, 2019. "Inpatient Overflow: An Approximate Dynamic Programming Approach," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 894-911, October.
    4. Nadra Abdalla & Richard Boucherie, 2002. "Blocking Probabilities in Mobile Communications Networks with Time-Varying Rates and Redialing Subscribers," Annals of Operations Research, Springer, vol. 112(1), pages 15-34, April.
    5. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    6. Litvak, Nelly & van Rijsbergen, Marleen & Boucherie, Richard J. & van Houdenhoven, Mark, 2008. "Managing the overflow of intensive care patients," European Journal of Operational Research, Elsevier, vol. 185(3), pages 998-1010, March.
    7. Avishai Mandelbaum & Martin I. Reiman, 1998. "On Pooling in Queueing Networks," Management Science, INFORMS, vol. 44(7), pages 971-981, July.
    8. William C. Jordan & Stephen C. Graves, 1995. "Principles on the Benefits of Manufacturing Process Flexibility," Management Science, INFORMS, vol. 41(4), pages 577-594, April.
    9. Ward Whitt, 1992. "Understanding the Efficiency of Multi-Server Service Systems," Management Science, INFORMS, vol. 38(5), pages 708-723, May.
    10. Hummy Song & Anita L. Tucker & Ryan Graue & Sarah Moravick & Julius J. Yang, 2020. "Capacity Pooling in Hospitals: The Hidden Consequences of Off-Service Placement," Management Science, INFORMS, vol. 66(9), pages 3825-3842, September.
    11. Thomas J. Best & Burhaneddin Sandıkçı & Donald D. Eisenstein & David O. Meltzer, 2015. "Managing Hospital Inpatient Bed Capacity Through Partitioning Care into Focused Wings," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 157-176, May.
    12. Asaduzzaman, Md & Chaussalet, Thierry J., 2014. "Capacity planning of a perinatal network with generalised loss network model with overflow," European Journal of Operational Research, Elsevier, vol. 232(1), pages 178-185.
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