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Abstract:
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In this paper, we study a k-out-of-n system with single server
who provides service to external customers also. The system consists of
two parts:(i) a main queue consisting of customers (failed components of
the k-out-of-n system) and (ii) a pool (of finite capacity M) of external
customers together with an orbit for external customers who find the pool
full. An external customer who finds the pool full on arrival, joins the orbit
with probability
and with probability 1−
leaves the system forever. An
orbital customer, who finds the pool full, at an epoch of repeated attempt,
returns to orbit with probability (< 1) and with probability 1 − leaves
the system forever. We compute the steady state system size probability.
Several performance measures are computed, numerical illustrations are
provided. |