At the start of football season, the York student ticket office gets busy the da

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. A ticket agency offers to take over the ticket distribution at a cost of $15/hour. The university will only accept an outside agency if (i) the cost is lower than providing the services internally (either in-person or using an automated ticket machine) and (ii) if the average queue length is lower than providing the services internally. The ticket agency promises an average service rate of 36 per hour. What standard deviation on SERVICE TIME does the agency have to achieve in order for the university to be willing to hire them?

Explanation / Answer

Lambda = average number of customers arriving per unit of time= 4 for 10 minutes= 24 customers arrive in one hour
Mu = average number of customers that can be served per unit of time= 1 customer in 2 minutes= 30 customers in 1 hour
L = lambda / lambda - mu = 24 / 30 - 24= 4
P=Average utilisation=24/30 = 0.8
1. Lq=P*L= 0.8*4 = 3.2. Hence no. of customers in the queue is 3.2
2. Average time waiting in the system = 1/mu -lambda = 1/ 30-24 = 1/6= 0.16
3. Proportion that the system is busy:
W= 1/Mu –Lambda= 1/30-24= 0.16
L=Lambda*W= 24*0.16= 3.84

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.