Exact analysis for multiserver queueing systems with cross selling

Mor Armony, Efrat Perel, Nir Perel*, Uri Yechiali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)75-100
Number of pages26
JournalAnnals of Operations Research
Issue number1-2
StatePublished - 15 Mar 2019


  • Cross-selling
  • Matrix geometric
  • Probability generating functions


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