Consider an airport where taxis and customers arrive (exponential interarrival times) with respec-tive rates of 1 and 2 per minu
te. No matter how many other taxis are present, a taxi will wait. Ifan arriving customer does not find a taxi, the customer immediately leaves the airport by takingshuttles.
1. Model this system as a birth-and-death process (hint: determine what the state of thesystem is at any given time). In particular, draw the transition rate diagram of this CTMC.
2. In the long run, what is the average time a taxi spends at the airport before it carries acustomer and leaves?
1. Model this system as a birth-and-death process (hint: determine what the state of thesystem is at any given time). In particular, draw the transition rate diagram of this CTMC.
2. In the long run, what is the average time a taxi spends at the airport before it carries acustomer and leaves?
1 answer:
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Answer:
- First, you want to divide the numerator and denominator by the cosine(x), and afterwards, it looks like this...
- Include 45 as one of the parameters and correlate with <em>tan</em>.
- Next, you want to multiply the numerator and denominator by the conjugate of the denominator, in this case, <em>tan x + tan 45.</em>
- Lastly, simplify, and you have the answer as <em>tan(45 + x)</em>