Question

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. Use the decimal places provided in the output (ie up to 4).

The Flyers are playing in the league playoffs and anticipate more fans, estimating that the arrival rate will increase to 12 per minute.

Explore using a 2-cashier model and a 3 cashier model, the operating characteristics for the future designs.

The rink has space for six customers to wait indoors to buy tickets. What are the corresponding queue lengths for each model?

2-cashier | 3-cashier | |

Queue Length |

Answer #1

Number of Channels |
2 |
3 |

Arrival Rate |
12 |
12 |

Service Rate |
8 |
8 |

Probability of No Units in System |
.1429 |
.2105 |

Average Waiting Time |
.1607 |
.0197 |

Average Time in System |
.2857 |
.1447 |

Average Number Waiting |
1.9286 |
.2368 |

Average Number in System |
3.4286 |
1.7368 |

Probability of Waiting |
.6429 |
.2368 |

Probability of 7 in System |
.0381 |
.0074 |

The three-cashier system is probably too good and not cost effective.

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