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Sharp Bounds and Simple Approximations for the Erlang Delay and Loss Formulas

Author

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  • Arie Harel

    (Graduate School of Management, Rutgers University, Newark, New Jersey 07102)

Abstract

Some sharp bounds and simple approximations are obtained for the Erlang delay formula and for the Erlang loss formula. One of the results is then used to get a simple analytical solution for the Server Allocation Problem.

Suggested Citation

  • Arie Harel, 1988. "Sharp Bounds and Simple Approximations for the Erlang Delay and Loss Formulas," Management Science, INFORMS, vol. 34(8), pages 959-972, August.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:8:p:959-972
    DOI: 10.1287/mnsc.34.8.959
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    Citations

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    Cited by:

    1. Ramandeep S. Randhawa, 2016. "Optimality gap of asymptotically derived prescriptions in queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 131-155, June.
    2. Saif Benjaafar & Shining Wu & Hanlin Liu & Einar Bjarki Gunnarsson, 2022. "Dimensioning On-Demand Vehicle Sharing Systems," Management Science, INFORMS, vol. 68(2), pages 1218-1232, February.
    3. Zhang, Xuelu & Wang, Jinting & Do, Tien Van, 2015. "Threshold properties of the M/M/1 queue under T-policy with applications," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 284-301.
    4. Vincent W. Slaugh & Bahar Biller & Sridhar R. Tayur, 2016. "Managing Rentals with Usage-Based Loss," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 429-444, July.
    5. Linda V. Green & Peter J. Kolesar, 1998. "A Note on Approximating Peak Congestion in Mt/G/\infty Queues with Sinusoidal Arrivals," Management Science, INFORMS, vol. 44(11-Part-2), pages 137-144, November.
    6. Cavada, Juan P. & Cortés, Cristián E. & Goic, Marcel & Weintraub, Andrés & Zambrano, Juan I., 2020. "Accounting for cost heterogeneity on the demand in the context of a technician dispatching problem," European Journal of Operational Research, Elsevier, vol. 287(3), pages 820-831.
    7. Arie Harel, 2011. "Convexity Results for the Erlang Delay and Loss Formulae When the Server Utilization Is Held Constant," Operations Research, INFORMS, vol. 59(6), pages 1420-1426, December.
    8. Daniel Adelman, 2007. "Price-Directed Control of a Closed Logistics Queueing Network," Operations Research, INFORMS, vol. 55(6), pages 1022-1038, December.

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