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Ymorist [56]
2 years ago
12

The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests, and then load passengers. Cabs

arrive at the hotel every 8 minutes; if a taxi drives by the hotel and the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. It takes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel(exponentially distributed).
1. What is the average time a cab must wait for a fare?
2. What is the probability that the line will be full when a cab drives by, causing it to drive on?
Mathematics
1 answer:
maksim [4K]2 years ago
6 0

Answer:

The appropriate solution is:

(1) 22.81 minutes

(2) 0.171

Step-by-step explanation:

According to the question, the values will be:

The service rate of guess will be:

= 5+3.5

= 8.5 \ minutes

The mean arrival rate will be:

\lambda =\frac{60}{5}

  =7.5 \ cabs/hr

The mean service rate will be:

\mu= 7.05 \ cabs/hr

(1)

The average time a cab must wait will be:

⇒ W_q=22.95-\frac{1}{7.05}

⇒       =\frac{161.798-1}{7.05}

⇒       =\frac{160.798}{7.05}

⇒       =22.81 \ minutes

(2)

The required probability will be:

⇒ P(X\geq 6)=\frac{1-2.115}{1-7.5}

⇒                  =\frac{-1.1115}{-6.5}

⇒                  =0.171

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