I understand seasonality of a time series normally means a cyclic component with constant frequency. For example, the frequency is 24 for daily cyclic trend of hourly data. One of the basic models for a seasonal time series should be Seasonal ARIMA.
However, if the seasonality is somewhat irregular and the data about that irregularity is given, I think there is better model than Seasonal ARIMA. ARIMA model can not utilize that information about irregularity.
For example, if the business hour of a restaurant is regular (say 11am to 8pm), Seasonal ARIMA model might be able to forecast the hourly sales of the restaurant with ARIMA(p,d,q)(P,D,Q)_24.
However, if their business hour is irregular day by day (say 10:30am-9pm today and 12am-5pm tomorrow...) and the business hours for each day is given to the modeler, I guess some other model which can deal with those irregular business hours is more useful than ARIMA.
Are there some models which can deal with such kind of irregular seasonality?