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.)

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