Abstract
In this paper we consider the steady state behaviour of a queueing system. The arrivals follow Poisson distribution and the service time distribution is exponential. Whenever the system size reaches a certain length, the system adds an additional space of unit size on every arrival with some probability and drops the additional space at the departure. Steady state probabilities are calculated explicitly and the average number of customers in the system is also obtained. Associating the cost with the rent of the additional space and the profit with each customer served, a criterion to obtain the optimum size of the ordinary space and the optimum number of unit size additional spaces to be hired is discussed.
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