The customer support hotline for a computer software company is currently staffed by a single technician. Customer service calls arrive at a rate of five calls per hour and follow a Poisson distribution. Calls are handled on a first-in-first-out basis and customers enter a waiting queue in the event the technician is busy assisting another customer. The technician currently assigned to the hotline is relatively inexperienced and can only handle service calls at an average rate of six calls per hour with the actual time required to handle a given call following an exponential distribution.
The president of the company has received numerous complaints from customers regarding the length of time that they currently have to wait on line before the technician is able to answer their call.
1. What is the average waiting time in the queue (in hours) before the technician answers a customer's call?