Abstract
The queueing system studied in this paper is the one in which
(i)
there are an infinite number of servers,
(ii)
initially (at t = 0) all the servers are idle,
(iii)
one server serves only one customer at a time and the service times are independent and identically distributed with distribution function B(t) (t > 0) and mean β(< ∞),
(iv)
the arrivals are in batches such that a batch arrives during (t, t + δt) with probability λ(t)δt + o(δt) (λ(t) > 0) and no arrival takes place during (t, t + δt) with the probability 1 –λ(t)δt + o(δt),
(v)
the batch sizes are independent and identically distributed with mean α(< ∞), and the probability that a batch size equals r is given by a
r(r ≧ 1),
(vi)
the batch sizes, the service times and the arrivals are independent.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
15 articles.
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