Single-Server Queuing Analysis The Gabe Center for the Arts has one single ticke
ID: 455232 • Letter: S
Question
Single-Server Queuing Analysis
The Gabe Center for the Arts has one single ticket station open in person throughout the day. It takes a customer service representative 5 minutes to start and finish a ticket order. Patrons arrive to purchase tickets at a rate of 6 people per hour.
A) Determine the average number of people that will stack up waiting in line.
B)Find the average time a person must wait before they can be helped.
C) Calculate the average time a customer spends in the queue waiting to be helped.
D) The Gabe Center for the Arts has a rule that, on average, a customer service representative can spend a maximum of 5 minutes helping out every customers. There must be 5 minutes of idle time available to relieve tension. Will the ticket office have to schedule an extra person?
Explanation / Answer
We have Arrival rate = 6 per hour
Service rate µ = 60 minutes/ 5 minutes per customer = 12 customer per hour
A) Determine the average number of people that will stack up waiting in line.
= ^2 /µ * (µ - ) = 6^2 / 12 * (12 -6) = 36/ 12 * 6 = 36 /72 = ½ or 0.5 people
B)Find the average time a person must wait before they can be helped.
= 1 / µ - = 1 / (12 -6) = 1/6 = 0.167 hours = 10 minutes
C) Calculate the average time a customer spends in the queue waiting to be helped.
= /µ * (µ - ) = 6 / 12 * (12 -6) = 6 / 72 = 0.083 hours = 5 minutes
D) The Gabe Center for the Arts has a rule that, on average, a customer service representative can spend a maximum of 5 minutes helping out every customers. There must be 5 minutes of idle time available to relieve tension. Will the ticket office have to schedule an extra person?
Utilization of centre = /µ = 6 /12 = 0.5 or 50 %
Here the utilization of the center in only 50 % with the service time of 5 minutes and there is 5 minutes ideal time is available after servicing each costomer so no need to hire one extra person