Taxis and customers arrive at a taxi rank in accordance with two independent homogeneous Poisson processes with intensities λ 1 = 4 an hour and λ 2 = 3 an hour, respectively. Potential customers who...

Taxis and customers arrive at a taxi rank in accordance with two independent homogeneous Poisson processes with intensities λ₁
= 4 an hour and λ₂
= 3 an hour, respectively. Potential customers who find two waiting customers do not wait for service, but leave the rank immediately. (Groups of customers who will use the same taxi are considered to be one customer.) On the other hand, arriving taxis who find two taxis waiting leave the rank as well.

What is the average number of customers waiting at the rank?