Driving nuts for Beetles

Consumer preferences for cars need to be continually tracked to identify changing demands and specifications. However, there is one car that is quite an exception – the Volkswagen Beetle. More than 22 million of the original model were built between 1938 and 2003. Surveys have been conducted in different countries to determine the reasons why people purchased Beetles. Principal components analysis of the variables measuring the reasons for owning Beetles have consistently revealed one factor – fanatical loyalty. The company had long wished for the car’s natural death, but without any effect. The noisy and cramped ‘bug’ inspired devotion in drivers across the generations. Now old bugs are being sought across the globe. VW reintroduced the brand in 1998 as the ‘New Beetle’, which has won several distinguished automotive awards.

A repair and inspection facility consists of two stations: a repair station with two technicians, and an inspection station with I inspector. Each repair technician works at the rate 3 items per hour; the inspector can inspect 8 items per hour. Approximately 10% of all items fail inspection and are sent back to the repair station. (This percentage holds even for items that have been repaired two or more times.) If items arrive at the rate 5 per hour, what is the long-run expected delay that items experience at each of the two stations, assuming a Poisson arrival process and exponentially distributed service times? What is the maximum arrival rate that the system can handle without adding personnel?