Question

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Voters arrive at a polling station at an average of 4 per minute (Poisson) where the service rate is 50 per hour (Poisson).

a. What is the average number of voters in the system with 5 voter booths? (10 pts)

b. What is the minimum number of voting booths needed to keep the average time in the system under three minutes? (10 pts)

**PLEASE SHOW ALL WORK IN EXCEL!!!!!!!**

**SHOW CALCULATIONS / FORMULAS IN
EXCEL!!!!!!!!**

Answer #1

The Excel model is following:

FORMULAS:

Cell | Formula | Copy to |

B12 | =($B$4/$B$5)^A12/FACT(A12) | B12:B17 |

C16 | =SUM(B$11:$B15) | C16:C17 |

D16 | =+B16/(1-$B$4/(A16*$B$5)) | D16:D17 |

E16 | =1/(C16+D16) | E16:E17 |

F16 | =$B$4/($B$5*A16) | F16:F17 |

G16 | =+E16*B16*F16/(1-F16)^2 | G16:G17 |

H16 | =G16+$B$4/$B$5 | H16:H17 |

I16 | =G16/$B$4 | I16:I17 |

J16 | =I16+1/$B$5 | J16:J17 |

Arrival rate = 4 per minute = 4*60 per hour = 240 per hour

a) Average number of voters in the system with 5 voter booths
(L) = **26.44 ***(refer cell
H16)*

b) Target average time in system (W) = 3 minutes = 3/60 hour = 0.05 hour

For s = 6, W = 0.0286, which is less than target W of 0.05

Therefore, minimum number of voting booths needed to keep the
average time in system under three minutes = **6**
voting booths

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