Logarithmic Asymptotics for Unserved Messages at a FIFO

K. Duffy, W.G. Sullivan

2004, v.10, Issue 1, 175-189


We consider an infinite-buffered single server First In, First Out
(FIFO) queue. Messages arrive at stochastic intervals and take
random amo\-unts of time to process. Logarithmic asymptotics are
proved for the tail of the distribution of the number of messages
awaiting service, under general large deviation and stability
assumptions, and formulae presented for the asymptotic decay rate.

Keywords: FIFO-system, logarithmic asymptotics, large deviations


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