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Published online by Cambridge University Press: 14 July 2016
The system provides each customer with a service made up of a random number of stages in sequence. Arrivals are Poisson, and the stage times are independent exponential random variables. The number of stages of a particular service depends on the customer's random demand and on the arrival process, in a way which is aimed at preventing the queue from growing fast while matching the customer's demand as well as possible.
This work was carried out while the author was a visitor in the Department of Mathematics, Chelsea College, University of London, with financial support from NATO-CNR.