Jessie manages a call center. There are two types of callers: new callers and members. Phone calls
Question:
Jessie manages a call center. There are two types of callers: new callers and members. Phone calls from new callers arrive at a rate of 15 callers per hour, while calls from members arrive at a rate of 10 callers per hour. For each caller type, the inter-arrival times are exponentially distributed.
Currently, there are two waiting lines: one waiting line for new callers and a different line for members. Each line has one dedicated staff member to provide service to callers in that line, and the staff member only provides service to their assigned line. Each staff member has the same average service rate of 20 callers per hour, and the service times are exponentially distributed.
Question: Of the callers that phone into the call center, 75% are new callers and 25% are members.
On average, how long does a caller have to wait in line? (Answer in minutes)