You\'re the ticket manager for the Houston Astros and are using queuing theory t

Question

You're the ticket manager for the Houston Astros and are using queuing theory to determine how many ticket windows should be open for the first home game of the 2018 baseball season. Because of the World Series victory, you anticipate that customers will arrive at a rate of 144 fans per hour and each fan will take 1 minute to serve. The fans are still ecstatic over the World Series victory so they won't mind waiting in line too much but you estimate that it still costs approximately $45 per hour for each customer. Your ticket takers are paid $25 per hour per person.

Determine the continuum number of ticket takers that minimize your total cost of providing this service.

Explanation / Answer

Arrival rate, = 144 fans per hour
Service rate, = 60/1 = 60 per hour per ticket window
This is M/M/s queue model.
Calculation of total cost for number of ticket takers is given below.


EXCEL Formula:
B12 =($B$4/$B$5)^A12/FACT(A12)
C14 =SUM(B$11:$B13)
D14 =+B14/(1-$B$4/(A14*$B$5))
E14 =1/(C14+D14)
F14 =$B$4/($B$5*A14)
G14 =+E14*B14*F14/(1-F14)^2
H14 =A14*$B$6+G14*$B$7
All the above formulas are copied till the end of table (row 18)
Total hourly cost is lowest for 4 ticket takers.
Number of ticket takers Total cost per hour
3 191.49
4 119.38
5 129.71
6 151.20
7 175.29

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