For service providers, uncertain demand for capacity and expansion lead time may create unavoidable capacity shortages, which may be allowed to accumulate before initiating an expansion. For the demand following a geometric Brownian motion process, we assume a stationary expansion policy where the timing and size of expansion are determined as fixed proportions of the capacity position. We define the service level in terms of the capacity shortages, which can be evaluated by applying pricing formulae for barrier options in finance. We observe the relationship between the two policy parameters at different specified service levels and for other model parameters.