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Transient analysis of some queueing/inventory/healthcare models using homotopy perturbation method

Author

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  • Narayanan C. Viswanath

    (Government Engineering College)

Abstract

Homotopy perturbation method (HPM) is applied in this paper for the transient study of some queueing/inventory/healthcare models. Semi-analytic approximate transient probabilities are obtained as power series in the time variable. The numerical implementation of the method using a programming language like MATLAB, is easy. However, the number of terms that is required in the above power series, to get an accurate approximation, grows with time. This obstacle is overcame by adopting a step-by-step HPM method. Implementation of the method is discussed in the case of the classic M/M/1 queue, the (s, S) inventory model with random replenishment time but without backlogs, the (s, S) inventory model with positive service and replenishment times, allowing infinite backlogs, and the Markov chain model for the patient handoff process in emergency departments. Numerical experimentation has been carried out to evaluate the efficiency of the method and to understand the challenges involved in its implementation.

Suggested Citation

  • Narayanan C. Viswanath, 2023. "Transient analysis of some queueing/inventory/healthcare models using homotopy perturbation method," Operational Research, Springer, vol. 23(4), pages 1-21, December.
    • Handle: RePEc:spr:operea:v:23:y:2023:i:4:d:10.1007_s12351-023-00805-6
    DOI: 10.1007/s12351-023-00805-6
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