Transient and Busy Period Analysis of the Gi/gi1 Queue as a Hilbert Factorization Problem
نویسندگان
چکیده
In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI/G/I queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/I, R/G/I queues, where R is the class of distributions with rational Laplace transforms. We obtain simple closed-form expressions for the Laplace transforms of the waiting time distribution and the busy period distribution. Furthermore, we find closed-form formulae for the first two moments of the distributions involved. TRANSIENT ANALYSIS; BUSY PERIOD; LINDLEY EQUATION
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