A finite-source M/G/1 retrial queue with outgoing calls

  • Velika I. Dragieva
  • Tuan Phung-DucEmail author
S.I.: Queueing Theory and Network Applications II


In this paper we deal with a single-server, finite-source retrial queue where the server not only accepts incoming calls but after some exponentially distributed idle time makes outgoing calls. The service times of incoming and outgoing calls follow two distinct arbitrary distributions. The outgoing calls are directed not to the customers in the system but outside it, which implies that the model can be considered as a model with vacations or with customers of two types. Along with the standard retrial queue where all customers are allowed to join the orbit we consider also the corresponding queue with restriction on the orbit size. We derive formulas for computing the stationary system state distribution and investigate the influence of the system input parameters on the main macro characteristics of the system performance.


Finite queues Retrials Outgoing calls Restriction on the orbit size 



T. Phung-Duc was supported in part by JSPS KAKENHI Grant Number 18K18006.


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Authors and Affiliations

  1. 1.University of ForestrySofiaBulgaria
  2. 2.University of TsukubaTsukubaJapan

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