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?

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Definitions:

Positive Cost Variance

Occurs when the actual cost of a project is less than the budgeted amount, indicating under-spending or efficiency.

Under Budget

A situation in which the actual spending is less than what was originally planned or allocated for a project or activity.

Management Reserves

Funds set aside by management for unforeseen changes in the scope or cost of a project.

Contingency Reserves

Allocated resources, time, or funds kept in reserve to address potential unforeseen obstacles or costs in a project.