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Thread: probability (queuing question)

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    probability (queuing question)

    An air freight terminal has five loading docks on the main concourse. Any aircraft which arrives when all docks are full is diverted to docks on the back concourse with slightly slower service time. The average aircraft arrival rate is 4 aircrafts per hour. The average service time (in the main concourse) per aircraft is 2.5 hours. The probability (to 4 decimal places) that an arriving aircraft has to be diverted to the back concourse is?

    For this question the
    ρ i gotten was 2.

    letting x(t) be the number of total aircraft, is it right to say that po + p1 + p2 + p3 + p4 + p5 = 1 since the 6th aircraft will be diverted to docks on the back concourse and so p6 and thereafter is zero?

    If not, how do i go about doing this question?
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    Re: probability (queuing question)

    "For this question the p I gotten was 2."

    Wait, stop right there! If you know anything about probability then you should know that a "probability" must be between 0 and 1. p= 2 is impossible.
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    Re: probability (queuing question)

    opps i was referring to the traffic intensity rho = 2. sorry for the confusion lol... even tho i think i typed the lowercase symbol for rho~
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    Re: probability (queuing question)

    Quote Originally Posted by noobpronoobpro View Post
    opps i was referring to the traffic intensity rho = 2. sorry for the confusion lol... even tho i think i typed the lowercase symbol for rho~
    $\rho$ is not a universal symbol for traffic intensity. If you do not tell us what it means, it is just a Greek letter. Here are some other ways that it can be used: Uses of $\rho$.

    Unfortunately, I do not know enough about queuing theory to be able to help. I am not understanding your question. What are $p_0$ through $p_5$? Is that the probability that planes 0 through 5 make it to the main concourse? Note: If these are probabilities of planes being serviced in the main concourse, then $p_6$ would be the 7th plane since you used a zero index.

    I do not see why the sum of the probabilities would be 1. These are not discrete events. If all five loading docks happen to be empty at the exact same time, then the probability of the next five arrivals getting serviced at the main concourse will be 1 for each. If only one could possibly be serviced at a time, this would be a completely different problem.
    Last edited by SlipEternal; Oct 1st 2018 at 05:07 AM.
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    Re: probability (queuing question)

    Quote Originally Posted by SlipEternal View Post
    $\rho$ is not a universal symbol for traffic intensity. If you do not tell us what it means, it is just a Greek letter. Here are some other ways that it can be used: Uses of $\rho$.

    Unfortunately, I do not know enough about queuing theory to be able to help. I am not understanding your question. What are $p_0$ through $p_5$? Is that the probability that planes 0 through 5 make it to the main concourse? Note: If these are probabilities of planes being serviced in the main concourse, then $p_6$ would be the 7th plane since you used a zero index.

    I do not see why the sum of the probabilities would be 1. These are not discrete events. If all five loading docks happen to be empty at the exact same time, then the probability of the next five arrivals getting serviced at the main concourse will be 1 for each. If only one could possibly be serviced at a time, this would be a completely different problem.
    Pi is the probability that there will be i number of airplanes in the system

    P0 in this case would mean that there are 0 airplane in the system

    Since the system can only service 5 airplanes in the main concourse, is it correct to infer that Pi > 5 =0, since any airplanes that enter the system after P​5 will be all directed to back concourse(which is another separate system).
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    Re: probability (queuing question)

    Quote Originally Posted by noobpronoobpro View Post
    Pi is the probability that there will be i number of airplanes in the system

    P0 in this case would mean that there are 0 airplane in the system

    Since the system can only service 5 airplanes in the main concourse, is it correct to infer that Pi > 5 =0, since any airplanes that enter the system after P​5 will be all directed to back concourse(which is another separate system).
    That is a question for how you are supposed to model it. Suppose there are 5 planes already being serviced. If $p_6=0$, does that means that there is a zero percent chance that a 6th plane arrives, or does that mean that there is a zero percent chance that a sixth plane will be serviced by the main concourse? Is the sixth plane "in the system" for an instant while you are deciding whether or not to send it to the back concourse? If it is, then the sum would be:

    $$\sum_{n \ge 0}p_n = 1$$
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