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erlang problem

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  • #58292

    A new toll road is being constructed.You are doing the traffic engineering for north to south direction.Due to lack of width of right of way ,there is room for only 10 booths plus by pass lanes to another group ofupto 10 toll is estimated tat traffic during rush hour in the Direction of interest will reach 2500 vehicles.due to high percentage of out of state travelers on this toll road, toll tags will not be used.Each booth will be manned by a toll taker.when a car enters the toll road , the driver receives a card showing the entry point.the driver hands the card to the toll taker in te booth , along with a payment and the toll taker gives him his change based on the entry point.( there is no automatic toll machines).Red and green lights indicate to drivers thich booths are occupied and which are availlable.assume that the average time a vehicle occupies a booth is 20 seconds.

    all vehicles approach the 1st group of booths and enter a booth if available.if all of the lights are red, they move over to a bypass lane and go to the second group of booths.if all of the booths in he second group are occupied, they queue up until they receive their change, again at an average of 20 seconds.vehicles processed in the first group of booths take special exit lanes which by pass the second group of booths

    A.)how many erlangs of traffic are there in all during the busy hour?

    B.)what percentage of total vehicles actually go to the second group of toll booth?

    C.)what percentage of vehicles have to wait in line at the second group of tol booths?

    D.)if there were sufficient right of way width and all 2500 vehicles actually arrived at the beginning of rush hour, how many toll booths would be needed in 1st group to assure no blockage


    the A part solution some 1 tell is it right

    2500 vehicles
    20 seconds i.e .33 mins

    2500*.33/60=13.75 i.e 14 erlangs

    is this right and please tell the remaing ones

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