taxicab

Consider a taxicab stop where a taxi arrives in every fifteen minutes. The number of customers who arrive to the stop during a fifteen-minute time interval is a Poisson random variable with mean 4. The number of arrivals during each 15-minute period is independent and identically distributed. The stop can accommodate at most 3 customers. If an arriving customer finds that there are already 3 people waiting at the stop, she or he goes to another stop and never comes back. An arriving taxi picks up a customer from the stop with probability 0.7, and does not pick up anyone with probability 0.3. Let X_n denote the number of customers waiting at the stop after the taxi departs.