48 (2007), 297-314|
Multiserver queueing systems with retrials and losses
| The interest in retrial queueing systems mainly
lies in their application to telephone systems.
This paper studies multiserver retrial queueing
systems with n
servers. The arrival process is a quite general
point process. An arriving customer occupies one
of the free servers. If upon arrival all servers
are busy, then the customer waits for his service
in orbit, and after a random time retries in
order to occupy a server. The orbit has one
waiting space only, and an arriving customer, who
finds all servers busy and the waiting space
occupied, is lost from the system. Time intervals
between possible retrials are assumed to have
arbitrary distribution (the retrial scheme is
explained more precisely in the paper). The paper
provides analysis of this system. Specifically
the paper studies the optimal number of servers
to decrease the loss proportion to a given value.
The representation obtained for the loss
proportion enables us to solve the problem
numerically. The algorithm for numerical solution
includes effective simulation, which meets the
challenge of a rare events problem in simulation.
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