1. A grocery store checkout counter has a service rate of 45 per hour, exponentially distributed, with Poisson arrivals at the rate of 30 per hour. Find the operating characteristics of this system.

2. Suppose students arrive during the office hours of a college professor according to a Poisson process with mean arrival rate l. The professor, who deals with his students one by one, has an exponentially distributed service time of ten per hour. Analyze how the average waiting time is expected to change as the arrival rate l varies from five to eight students per hour.