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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