Unreliable Single-Server Queueing System with Customers of Random Capacity

  • Oleg Tikhonenko
  • Marcin ZiółkowskiEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1231)


In the paper, we investigate one-server queueing system with stationary Poisson arrival process, non-homogeneous customers and unreliable server. As non-homogenity, we mean that each customer is characterized by some arbitrarily distributed random capacity that is called customer volume. Service time of a customer generally depends on his volume. The server can be broken when it is free or busy and the renewal period goes on for random time having an arbitrary distribution. During this period, customers present in the system and arriving to it are not served. Their service continues immediately after renewal period termination. For such systems, we determine the distribution of total volume of customers present in it. An analysis of some special cases and some numerical examples are attached as well.


Queueing system with non-homogeneous customers Unreliable queueing system Total volume Additional event method Laplace-Stieltjes transform 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Computer ScienceCardinal Stefan Wyszyński University in WarsawWarsawPoland
  2. 2.Institute of Information TechnologyWarsaw University of Life Sciences – SGGWWarsawPoland

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