Conolly, B. W.
Some applications of the theory of infinite capacity service systems to a single server system with linearly state dependent service.
Journal of Applied Probability,
The infinite server queue with arrivals generated by a non-homogeneous compound poisson process and heterogeneous customers.
Communications in Statistics. Stochastic Models,
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.