On the integral of the workload process of the single server queue
نویسنده
چکیده
This paper is devoted to a study of the integral of the workload process of the single server queue, in particular during one busy period. Firstly, we find asymptotics of the area A swept under the workload processW (t) during the busy period when the service time distribution has a regularly varying tail. We also investigate the case of a light-tailed service time distribution. Secondly, we consider the problem of obtaining an explicit expression for the distribution of A. In the general GI|G|1 case, we use a sequential approximation to find the Laplace-Stieltjes transform of A. In the M |M |1 case, this transform is obtained explicitly in terms of Whittaker functions. Thirdly, we consider moments of A in the GI|G|1 queue. Finally, we show asymptotic normality of ∫ t 0 W (s) ds.
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