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\iteman{io-port 05271311}
\itemau{Goldberg, David Alan; Whitt, Ward}
\itemti{The last departure time from an $M_t/G/\infty$ queue with a terminating arrival process.}
\itemso{Queueing Syst. 58, No. 2, 77-104 (2008).}
\itemab
In this paper, the last departure time from a $M_t/G/\infty$ queue with a terminating arrival process is considered as an appropriate approximation for a real application concerning a two-stage inspection in which finitely many items come to a first stage for screening and next go to a second stage to be examined further (e.g. inspecting shipping containers). The paper introduces the problem of evaluating the probability distribution for the last departure time from a queue with a terminating arrival process. Technically, the explicit expression for the remaining time are given, together with approximations for the transient distributions. Next, the approximations are compared with the exact values of the mean, variance and several quantiles of the distribution of the last departure time, for validation. The numerical results show that the approximations are remarkably effective for the exponential-tail case, provided that certain conditions are satisfied.
\itemrv{Marina Gorunescu (Craiova)}
\itemcc{}
\itemut{queues with terminating arrival processes; last departure time; infinite-server queues; non-stationary queues; congestion caused by inspection; two-stage inspection; extreme-value theory}
\itemli{doi:10.1007/s11134-008-9060-2}
\end