Operational Research

, Volume 12, Issue 2, pp 189–207

An explicit solution for a tandem queue with retrials and losses

Original Paper

DOI: 10.1007/s12351-011-0113-7

Cite this article as:
Phung-Duc, T. Oper Res Int J (2012) 12: 189. doi:10.1007/s12351-011-0113-7


We consider a retrial tandem queueing system with two servers whose service times follow two exponential distributions. There are two types of customers: type one and type two. Customers of type one arrive at the first server according to a Poisson process. An arriving customer of type one that finds the first server busy joins an orbit and retries to enter the server after some time. We assume that the arrival rate of customers from the orbit is a linear function of the number of retrial customers. After being served at the first server, a customer of type one moves to the second server. Customers of type two directly arrive at the second server according to another Poisson process. Customers of both types one and two are lost if the second server is busy upon arrival. For this model, we derive explicit expressions of the joint stationary distribution between the number of customers in the orbit and the states of the servers. We prove that the stationary distribution is computed by a numerically stable algorithm. Numerical examples are provided to show the influence of parameters on the performance of the system.


Tandem queue Retrial queue Hypergeometric function Linear retrial rate Call centers 

Mathematics Subject Classification (2000)

68M20 90B22 60K25 

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Graduate School of InformaticsKyoto UniversityYoshida-HonmachiJapan

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