The Arctic Flyers Minor League Hockey Team Has One Box

question 36

Essay

The Arctic Flyers minor league hockey team has one box office clerk.On average,each customer that comes to see a game can be sold a ticket at the rate of 8 per minute.For normal games,customers arrive at the rate of 5 per minute.Assume arrivals follow the Poisson distribution and service times follow the exponential distribution.
a.What is the average number of customers waiting in line?
b.What is the average time a customer spends in the waiting line?
c.What is the average number of customers in the system?
d.What is a customer's average time in the system?
e.What is the probability that someone will be buying tickets when an arrival occurs?
The Flyers are playing in the league playoffs and anticipate more fans,estimating that the arrival rate will increase to 12 per minute.Output is supplied for a two-cashier and a three-cashier system. $$\begin{array} { | l | l | l | } \hline \text { Number of Channels } & 2 & 3 \\\hline \text { Arrival Rate } & 12 & 12 \\\hline \text { Service Rate } & 8 & 8 \\\hline \text { Probability of No Units in System } & 1429 & 2105 \\\hline \text { Average Waiting Time } & 1607 & 0197 \\\hline \text { Average Time in System } & 2857 & 1447 \\\hline \text { Average Number Waiting } & 1.9286 & 2368 \\\hline \text { Average Number in System } & 3.4286 & 1.7368 \\\hline \text { Probability of Waiting } & 6429 & 2368 \\\hline \text { Probability of } 7 \text { in System } & .0381 & .0074 \\\hline\end{array}$$
The rink has space for six customers to wait indoors to buy tickets. Which system will be better?
g. Do you think it is more sensible for them to continue the one cashier system?

---

Definitions:

Marginal Utility

The change in satisfaction or usefulness obtained by consuming one additional unit of a good or service.

Price

Price is the amount of money required to purchase a good, service, or asset, determined by factors like supply, demand, production cost, and market competition.

Turkey Sandwich

A sandwich made with sliced turkey as the main ingredient, often accompanied by various other toppings and condiments.

Utility

A measure in economics of the satisfaction or benefit derived by consuming a product or service.