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 ar(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
Reference4 articles.
1. On a problem of servicing a Poisson flow of demands;Shanbhag;Ann. Math. Statist.,1964
2. Congestion system with incomplete service;Downton;J. R. Statist. Soc.,1962
3. Letter to the Editor—The Output of anM/G/∞ Queuing System is Poisson
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