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Arrival rate problem

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  • #47968

    chhabra
    Participant

    Hi
    How to calculate departure rate at the end of a tunnel if the arrival rate ( mean of exponential distribution)Β at the other end is known and also the time it takes to pass through the tunnel (normal distribution with known mean and sd) is known ?
    Β 
    Thanks

    0
    #160474

    BTDT
    Participant

    Amit:Use Monte Carlo simulation (Google “CrystalBall” “Decisioneering” or “@Risk”).Cheers, BTDT

    0
    #160477

    chhabra
    Participant

    Thanks BTDT….but even for simulating, I need to have a formula for creating the “forecast”. While I do have the “assumptions” (arrival rate and passthrough time distribution), I am not sure how to formulate the forecast(departure).

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    #160480

    BTDT
    Participant

    Amit:The forecast will have a particular distribution of its own. You can use the “fit distribution” option to find out what the parameters are.If you have Minitab, generate 10,000 values of the arrival times, 10,000 values of the passthrough time, add the two and see what the result looks like.Cheers, BTDT

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    #160489

    chhabra
    Participant

    BTDT, I am not sure I understand that the forecast distribution will be a summation of the interarrival distribution and the pass through time distribution…..and how to extract the departure rate from this.
    Had this problem been deterministic, say an interarrival time of 0.25 minutes ( 4 arrivals per minute), and a pass through time of 5 minutes, how will the sum (0.25+5 OR 4+1/5) help in calculating departure rate? Intutively we understand that in this case, during the first five minutes, there will be no departures. But once the 5 minutes warm up is over, we will expect the departure rate to equal the arrival rate at the other end…ie…4 per minute.

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    #160495

    Mikel
    Member

    The simulation suggested to you would look something like this -Exponential = -Mean*Log(1-Uni, 2.71828)
    Arrival Rate Arrival Time Travel Time Departure
    Time
    Random Uniform Random Exponential Last Arrival + Next
    Arrival Random Normal Arrival Time + Travel Time
    Average of 0.25 minutes Average of 5 minutes, STDEV
    of 0.3
    0.903286843 0.58400185 0.58400185 4.937225425
    5.521227276
    0.027588733 0.006994117 0.590995968 5.036314418
    5.627310386
    0.567949461 0.209803319 0.800799286 5.05426034
    5.855059626
    0.660847804 0.270326761 1.071126047 5.015371597
    6.086497645
    0.301614429 0.089746044 1.160872091 4.67920121
    5.840073301
    0.401379437 0.128281919 1.289154011 4.524678969
    5.81383298
    0.649189734 0.261877614 1.551031625 5.326508143
    6.877539768
    0.820368053 0.429211604 1.980243229 4.957991577
    6.938234806
    0.043488876 0.011115723 1.991358952 4.711776582
    6.703135533
    0.663838618 0.272541166 2.263900118 5.024019528
    7.287919646
    0.869319742 0.508750773 2.77265089 5.059822014
    7.832472904
    0.498611408 0.172593577 2.945244468 4.540214958
    7.485459426
    0.278756066 0.081694523 3.02693899 4.910914312
    7.937853302
    0.355418561 0.1097886 3.136727591 4.943778903
    8.080506494
    0.279671621 0.082012077 3.218739668 5.091318952
    8.31005862
    0.31019013 0.09283488 3.311574548 4.523060978
    7.834635526
    0.202063051 0.056431462 3.36800601 5.615810677
    8.983816687
    0.598010193 0.22783229 3.5958383 4.95769042
    8.55352872
    0.965849788 0.844247188 4.440085488 4.814989337
    9.255074826
    0.554734947 0.202271523 4.642357012 5.248208153
    9.890565164
    0.001800592 0.000450554 4.642807566 4.746747562
    9.389555128
    0.305734428 0.091225242 4.734032808 4.755649242
    9.48968205
    0.588915677 0.22223938 4.956272188 5.007907147
    9.964179335
    0.540055544 0.194162517 5.150434704 4.67378244
    9.824217145
    0.142582476 0.038457598 5.188892302 5.007516633
    10.19640893
    0.800103763 0.402489486 5.591381788 4.914839918
    10.50622171
    0.995422224 1.34663638 6.938018168 4.556600869
    11.49461904
    0.356608783 0.110250653 7.048268821 4.504638254
    11.55290707
    0.825525681 0.436494723 7.484763544 5.150776714
    12.63554026
    0.798028504 0.399907444 7.884670989 4.93221968
    12.81689067
    0.48893704 0.167815735 8.052486723 4.927668227
    12.98015495
    0.821497238 0.430788091 8.483274814 5.400096042
    13.88337086
    0.970000305 0.876642607 9.359917422 5.247530124
    14.60744755
    0.241920225 0.06924171 9.429159132 4.858859269
    14.2880184
    0.858027894 0.488031497 9.917190629 4.901030719
    14.81822135
    0.811487167 0.417147579 10.33433821 5.294550091
    15.6288883
    0.560930204 0.205774361 10.54011257 4.950864094
    15.49097666
    0.94021424 0.704247417 11.24435999 5.381753125
    16.62611311
    0.753440962 0.350038688 11.59439867 5.222692734
    16.81709141
    0.703268532 0.303732129 11.8981308 5.358940952
    17.25707175
    0.70455031 0.304814382 12.20294519 4.927006229
    17.12995141
    0.487014374 0.166876976 12.36982216 5.112031216
    17.48185338
    0.508774071 0.177712899 12.54753506 5.012384589
    17.55991965
    0.139927366 0.037684634 12.58521969 4.948490313
    17.53371001
    0.237281411 0.06771658 12.65293627 4.533104528
    17.1860408
    0.430036317 0.140545753 12.79348203 5.143375019
    17.93685705
    0.998321482 1.597462076 14.3909441 5.084013436
    19.47495754
    0.842432936 0.461976337 14.85292044 5.110531573
    19.96345201
    0.231086154 0.065694131 14.91861457 4.971488023
    19.8901026
    0.155339213 0.04220507 14.96081964 4.761549589
    19.72236923

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    #160497

    Mikel
    Member

    Yikes – send me an email address and I’ll send you the [email protected]

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    #160516

    BTDT
    Participant

    Stan:Yikes indeed!I looked more carefully and realized it is a queue management problem. I’d do this with a process simulator to keep track of the queue length, etc.If you’ve got a way of managing the queue in Excel, I’d like to see the spreadsheet too.Cheers, BTDT6Sigmaguru(at)gmail(dot)com

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    #160517

    BTDT
    Participant

    Amit:I didn’t see the problem immediately. Ignore what I posted and see what Stan comes up with.Cheers, BTDT

    0
    #160530

    Mikel
    Member

    We use a nice example that is not intuitive because of the queues.I’ll send the problem set up and a solution built in Excel later.

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    #160669

    chhabra
    Participant

    Thanks a lot Stan. Appreciate yours taking time out to help.

    0
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