Complete Question
A waiting line problem has an average of 250 arrivals per eight hour day. Suppose there are several servers, and each has an average service time of 8 minutes. (Assume Poisson arrivals and exponential service times.)
What is the average service rate of a server per hour?
Answer:
7½ arrivals per hour
Explanation:
Given
Arrivals = 250 arrivals per 8 hour day
Service Time of Servers = 8 minutes
The service time of Servers is given as 8 minutes.
This means that; on average, a server will attend to 1 arrival in every 8 minutes.
Calculating this per hour;
Average service rate of a server per hour = Service Rate * 1 hour per hour
Average service rate of a server per hour = 1 arrival per 8 minutes * 1 hour per hour
(1 hour = 60 minutes);
So, we have.
Average service rate of a server per hour = 1/8minutes * 60minutes/hour
= ⅛ * 60 arrivals/hour
= 60/8 arrivals/hour
= 7½ arrivals per hour
