Minimization of the blocking time of the unreliable Geo/G_D/1 queueing system
Journal
Mathematical Communications
Date Issued
1999-06-20
Author(s)
Kolev, Nikolai
Abstract
In this paper we study the blocking time of an unreliable single-server queueing system Geo/GD/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 = t0 < t1 <
... < tk < tk+1; tk < X ≤ tk+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 timepoints t0, t1,... are equidistant. We determine the optimal number of
copies and the length of the corresponding interval between two consecutive copies.
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 = t0 < t1 <
... < tk < tk+1; tk < X ≤ tk+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 timepoints t0, t1,... are equidistant. We determine the optimal number of
copies and the length of the corresponding interval between two consecutive copies.
Subjects
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