Many service industry firms strive hard to fill free capacity in order to cover their costs for a fixed capital stock. This paper presents a time series model where the capacity constraint is an integral part. The integer-valued autoregressive model builds on a simple idea of how daily time series arise for hotels and other similar establishments. Measures that follow naturally from the time series model are the occupancy probability and the duration of stay for the visitor. Empirically, we study the effects of price changes and a large festival, on these measures.