At the start of football season, the York student ticket office gets busy the da
ID: 365742 • Letter: A
Question
At the start of football season, the York student ticket office gets busy the day before the first game. Customers arrive at the rate of four every ten minutes. A ticket seller can service a customer in four minutes. Traditionally, there are two ticket sellers working. The university is considering an automated ticket machine similar to the airlines' e-ticket system. The automated ticket machine can service a customer in 2 minutes. What is the average length of the queue for the automated system model?
Explanation / Answer
Operating Characteristics of Single server constant service time queue model
Runway – 1R
Jets type - Large
Arrival rate (customers/hour)
4 every ten minutes
L = (4 x 60)/10 = 24 customers per hour
Service time
2 minutes
Service Rate ( customers/hour)
µ = (60/2) = 30 customers per hour
Average length of queue
Lq = 2/[2µ(µ - )]
Lq = 242/[2*30(30 – 24)] = 1.6
Lq = 1.6 customer per hour
Operating Characteristics of Single server constant service time queue model
Runway – 1R
Jets type - Large
Arrival rate (customers/hour)
4 every ten minutes
L = (4 x 60)/10 = 24 customers per hour
Service time
2 minutes
Service Rate ( customers/hour)
µ = (60/2) = 30 customers per hour
Average length of queue
Lq = 2/[2µ(µ - )]
Lq = 242/[2*30(30 – 24)] = 1.6
Lq = 1.6 customer per hour
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