#### Mathematical Communications, Vol. 4 No. 1, 1999.

Izvorni znanstveni članak

Minimization of the blocking time of the unreliable Geo/G_D/1 queueing system

V. Bakeva
N. Kolev

Puni tekst:

str. 1-10

preuzimanja: 430

###### Sažetak

In this paper we study the blocking time of an unreliable single-server
queueing system $Geo/G_D/1$. The service can be interrupted upon
explicit or implicit breakdowns. For the successful finish of the
service we use a special service discipline
dividing the pure service time $X$ (assumed to be a random variable
with known distribution) in subintervals with deterministically
selected time-points $0=t_0 t_{k+1},$ and making a copy at the end of each subinterval (if no
breakdowns occur during it) we derive the probability generating function of the blocking time of the server by a customer. As an application, we consider an unreliable system Geo/D/1 and the results is that the expected blocking time is minimized when the time-points t_0,t_1,... are equidistant. We determine the optimal number of copies and the length of the corresponding interval between two consecutive copies.

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