Erlang arrivals joining the shorter queue

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We consider a system in which customers join upon arrival the shortest of two single-server queues. The interarrival times between customers are Erlang distributed and the service times of both servers are exponentially distributed. Under these assumptions, this system gives rise to a Markov chain on a multi-layered quarter plane. For this Markov chain we derive the equilibrium distribution using the compensation approach. The obtained expression for the equilibrium distribution matches and re??nes heavy-traffic approximations and tail asymptotics obtained earlier in the literature. Keywords: random walks in the quarter plane, compensation approach, join the shorter queue, tail asymptotics
Original languageEnglish
Place of PublicationEindhoven
Number of pages30
Publication statusPublished - 2011

Publication series

NameReport Eurandom
ISSN (Print)1389-2355


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