This paper considers single server retrial queues with setup time. In the basic model, if the server completes a service and there are no customers in the orbit, the server is turned off immediately. Arriving customers that see the server occupied join the orbit and repeat their attempt after some random time. The new feature of our models is that an arriving customer that sees the server off waits at the server and the server is turned on. The server needs some setup time to be active so as to serve the waiting customer. If the server completes a service and the orbit is not empty, it stays idle waiting for either a new customer or a customer from the orbit. For this model, we obtain explicit expressions for the generating functions of the joint queue length. We then consider an extended model where the server stays idle for a while before being turned off for which explicit solution is also obtained.


M/M/1/1 retrial queue Setup time Power-saving 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyMeguro-ku, TokyoJapan

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