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Exact analysis for multiserver queueing systems with cross selling

Author

Listed:
  • Mor Armony

    (New York University)

  • Efrat Perel

    (Afeka College of Engineering)

  • Nir Perel

    (Shenkar - Engineering, Design and Art)

  • Uri Yechiali

    (Tel-Aviv University)

Abstract

Exact analysis of a multi-server Markovian queueing system with cross selling in steady-state is presented. Cross selling attempt is initiated at the end of a customer’s service every time the number of customers in the system is below a threshold. Both probability generating functions (PGFs) and matrix geometric methods are employed. The relation between the methods is revealed by explicitly calculating the entries of the matrix geometric rate-matrix R. Those entries are expressed in terms of the roots of a determinant of a matrix related to the set of linear equations involving the PGFs. This is a further step towards understanding of the analytical relationship between the two methods. Numerical results are presented, showing the effect of the cross selling intensity and of the threshold level on the systems performance measures. Finally, for a given set of parameters, the optimal threshold level is determined.

Suggested Citation

  • Mor Armony & Efrat Perel & Nir Perel & Uri Yechiali, 2019. "Exact analysis for multiserver queueing systems with cross selling," Annals of Operations Research, Springer, vol. 274(1), pages 75-100, March.
    • Handle: RePEc:spr:annopr:v:274:y:2019:i:1:d:10.1007_s10479-018-2924-x
    DOI: 10.1007/s10479-018-2924-x
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    References listed on IDEAS

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    1. Itay Gurvich & Mor Armony & Constantinos Maglaras, 2009. "Cross-Selling in a Call Center with a Heterogeneous Customer Population," Operations Research, INFORMS, vol. 57(2), pages 299-313, April.
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