Question

Cactus Baseball Stadium is trying to determine how many ticket scanners are needed to admit fans entrance. The stadium has 4 outfield bleacher sections: sections 1 and 3 in the right field and sections 2 and 4 in the left field. Fans use the backside of the stadium's entrance to get to these 4 sections. 40 people per minute show up to a game with their ticket (assume uniform distribution of location - that is each fan is equally likely to go to section 1, 2, 3, or 4). On average, it takes 5 seconds per person to process their ticket at a scanner and pass through the turnstiles. The backside stadium entrance is designed to hold up to 50 people waiting before getting to the ticket scanners.
Using the above, answer the following:
(a) Buffer Capacity (K)
(b) Customer Inflow (Arrival) Rate (Ri)
(c) Total Processing Rate (Capacity) (Rp)

Answer 1

Answer:

Explanation:

Arrival rate = 40 people per minute

Service rate   = 5 seconds per person = 12 people per minute

b)  Customer Inflow (Arrival) Rate (Ri)

Ri = Arrival Rate = 40 per minute

Inter arrival Time = 1 / Ri = 1 / 40 minutes

c) Total Processing Rate (Capacity) (Rp)

Processing Time = Tp = 5 seconds =

5/60 minutes

= 1/12 minutes

Processing Rate = Rp = 1 / Tp = 1 / (1/12) = 12 customers per minute

Server utilization = Throughput Rate R / Rp

Chi = Lambda / Miu ( must be < 1 )

Ls = Chi / (1-Chi)

Lq = Ls - Chi

Ws = Ls / Lambda

Wq = Lq / Lambda

Buffer capacity K = 50