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\iteman{io-port 03930091}
\itemau{Kibkalo, A.A.}
\itemti{Quasi-stationary condition in a queueing system of type M(t)/D/1/$\infty$.}
\itemso{Vestn. Mosk. Univ., Ser. I 1985, No.5, 41-44 (1985).}
\itemab
The author considers a queue M(t)/D/1/$\infty$ in which the arrival rate function $\lambda$ ($\cdot)$ is periodic and the service-time is constant, equal to b. He assumes that $\rho =b\int\sp{1}\sb{0}\lambda (u)du<1$ and investigates the quasi-stationary probability distribution $H(t,x)=\lim\sb{n\to \infty}P\{W(n+t)\le x\},$ $t\in [0,1)$, $x\in [0,\infty)$, where $\{$ W(t),t$\ge 0\}$ is the virtual waiting-time process. It is known that if $\rho <1$ then H(t,x) exists [see {\it J. M. Harrison} and {\it A. J. Lemoine}, J. Appl. Probab. 14, 566-576 (1977; Zbl 0372.60127)]. The Laplace-Stieltjes transform $H\sp*(t,v)=\int\sp{\infty}\sb{0}e\sp{-vx}dH(t,x)$ can be expressed by H(t,0). The author gives the form of H(t,0) in the case of b rational.
\itemrv{M.Jankiewicz}
\itemcc{}
\itemut{quasi-stationary probability distribution; virtual waiting-time process}
\itemli{}
\end