A small company maintains a fleet of four cars to be driven by its workers on business trips. Requests to use cars are a Poisson process with rate 1.5 per day. A car is used for an exponentially...

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A small company maintains a fleet of four cars to be driven by its workers on business trips. Requests to use cars are a Poisson process with rate 1.5 per day. A car is used for an exponentially distributed time with mean 2 days. Forgetting about weekends, we arrive at the following Markov chain for the number of cars in service:

Answered Same DayDec 26, 2021

Answer To: A small company maintains a fleet of four cars to be driven by its workers on business trips....

David answered on Dec 26 2021

125 Votes

Solution:
(a) The stationary distribution is computed using ?? = 0 and we get,
? =
8
131
,
24
131
,
36
131
,
36
131
,
27
131

(b) unfulfilled request is,
As per the statement in long run, all four cars on business trip using fraction of time is
27
131

hence the rate...

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A small company maintains a fleet of four cars to be driven by its workers on business trips. Requests to use cars are a Poisson process with rate 1.5 per day. A car is used for an exponentially...

Answer To: A small company maintains a fleet of four cars to be driven by its workers on business trips....

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