Queueing Systems

, Volume 89, Issue 3–4, pp 213–241 | Cite as

Heavy traffic limit for a tandem queue with identical service times

  • H. Christian Gromoll
  • Bryce Terwilliger
  • Bert ZwartEmail author


We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate the amount of work in the second queue at certain embedded arrival time points, namely when the upstream queue has just emptied. We focus on the case of infinite-variance service times and obtain a heavy traffic process limit for the embedded Markov chain.


Tandem queue Infinite variance Feller process Process limit 

Mathematics Subject Classification

60K25 90B22 



Funding was provided by NWO grant number 639.033.413.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  2. 2.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands

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