In this paper, a new count model with gamma interarrival time distribution is introduced and its properties are studied. The Erlang model is developed as a special case and studied in detail. Various characteristics like mean function, variance function, probability generating function, hazard rate function, etc. are derived. The model is applied to a real data set on interarrival times of customers arrived in a bank counter at Muvattupuzha, Kerala, India.

count model, gamma count model, Erlang count model.