Original scientific paper

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

V. Bakeva

N. Kolev

###### Abstract

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.

###### Keywords

blocking time, breakdowns, discrete-time single-server unreliable queueing system, geometric distribution, minimization, service discipline

###### Hrčak ID:

1730

###### URI

Visits: 785 *