Problem
Nail spa is a small shop on campus that provides manicures and pedicures. Customer arrival follows a poisson process, at an average rate of 2 customers per hour. 60% of the customers want only a manicure, 40% of the customers want only a pedicure. No customer wants both a manicure and pedicure. Due to different requirements from different customers, the service time varies. The service time of a manicure follows an exponential distribution, and it takes 40 minutes, on average, to do manicure. The service time of a pedicure follows an exponential distribution, and it takes 40 minutes, on average, to do pedicure. The shop hires two employees. Manicure customers are served by employee A, following the first-come-first-served service rule. Pedicure customers are served by employee B, following the first-come-first-served rule. If a customer arrives and cannot be served immediately, the customer will wait in the waiting area.
What is the average time that a customer spends at Nail Spa (including waiting and in service)?