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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

    as
    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.
    2. Che Kim & Moon Lee & Alexander Dudin & Valentina Klimenok, 2008. "Multi-server queueing systems with cooperation of the servers," Annals of Operations Research, Springer, vol. 162(1), pages 57-68, September.
    3. Saed Alizamir & Francis de Véricourt & Peng Sun, 2013. "Diagnostic Accuracy Under Congestion," Management Science, INFORMS, vol. 59(1), pages 157-171, December.
    4. Itay Gurvich & Mor Armony & Avishai Mandelbaum, 2008. "Service-Level Differentiation in Call Centers with Fully Flexible Servers," Management Science, INFORMS, vol. 54(2), pages 279-294, February.
    5. Ying Xu & Alan Scheller-Wolf & Katia Sycara, 2015. "The Benefit of Introducing Variability in Single-Server Queues with Application to Quality-Based Service Domains," Operations Research, INFORMS, vol. 63(1), pages 233-246, February.
    6. Efrat Perel & Uri Yechiali, 2013. "On Customers Acting As Servers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-23.
    7. Xiaofang Wang & Laurens G. Debo & Alan Scheller-Wolf & Stephen F. Smith, 2010. "Design and Analysis of Diagnostic Service Centers," Management Science, INFORMS, vol. 56(11), pages 1873-1890, November.
    8. Mor Armony & Itai Gurvich, 2010. "When Promotions Meet Operations: Cross-Selling and Its Effect on Call Center Performance," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 470-488, April.
    9. Alex F. Mills & Nilay Tanık Argon & Serhan Ziya, 2013. "Resource-Based Patient Prioritization in Mass-Casualty Incidents," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 361-377, July.
    10. Ohad Perry & Ward Whitt, 2009. "Responding to Unexpected Overloads in Large-Scale Service Systems," Management Science, INFORMS, vol. 55(8), pages 1353-1367, August.
    11. Mor Armony & Constantinos Maglaras, 2004. "On Customer Contact Centers with a Call-Back Option: Customer Decisions, Routing Rules, and System Design," Operations Research, INFORMS, vol. 52(2), pages 271-292, April.
    12. Reynold E. Byers & Kut C. So, 2007. "Note--A Mathematical Model for Evaluating Cross-Sales Policies in Telephone Service Centers," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 1-8, January.
    13. Mor Armony & Constantinos Maglaras, 2004. "Contact Centers with a Call-Back Option and Real-Time Delay Information," Operations Research, INFORMS, vol. 52(4), pages 527-545, August.
    14. Krishnan S. Anand & M. Faz{i}l Paç & Senthil Veeraraghavan, 2011. "Quality-Speed Conundrum: Trade-offs in Customer-Intensive Services," Management Science, INFORMS, vol. 57(1), pages 40-56, January.
    15. Noam Paz & Uri Yechiali, 2014. "An M/M/1 Queue In Random Environment With Disasters," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-12.
    16. Noah Gans & Yong-Pin Zhou, 2003. "A Call-Routing Problem with Service-Level Constraints," Operations Research, INFORMS, vol. 51(2), pages 255-271, April.
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