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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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