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 expression for the equilibrium distribution matches and refines tail asymptotics obtained earlier in the literature.
Original languageEnglish
Pages (from-to)273-302
JournalQueueing Systems: Theory and Applications
Issue number2-3
Publication statusPublished - 2013


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