Customers arrive at a taxi depot according to a Poisson process with rate λ. The dispatcher sends for a taxi when there are N customers waiting at the station. It takes M units of time for a taxi to...

Customers arrive at a taxi depot according to a Poisson process with rate λ. The dispatcher sends for a taxi when there are N customers waiting at the station. It takes M units of time for a taxi to arrive at the depot. When it arrives, the taxi picks up all waiting customers. The taxi company incurs a cost at a rate of nk per unit time whenever n customers are waiting. What is the steady-state average cost that the company incurs?