Or Data & SApplication of Simulation Technique in Queuing Model for reducing waiting time in ...

7/28/2019 Or Data & SApplication of Simulation Technique in Queuing Model for reducing waiting time in ATMimulation

1/55

CustomerTime Between

Arrivals

Arrival Time Start Service Service Time End Service Wait Time for

customer Queue LengthTime available for

Service

1 0 0 30 30 0 0 25

2 25 25 30 60 90 5 1 15

3 20 45 90 65 155 45 1 -30

4 15 60 155 40 195 95 2 -65

5 30 90 195 50 245 105 2 -80

6 25 115 245 60 305 130 3 -115

7 15 130 305 35 340 175 4 -155

8 20 150 340 30 370 190 5 -165

9 25 175 370 60 430 195 5 -170

10 25 200 430 30 460 230 5 -205

11 25 225 460 40 500 235 6 -21512 20 245 500 45 545 255 6 -230

13 25 270 545 55 600 275 7 -245

14 30 300 600 45 645 300 8 -275

15 25 325 645 40 685 320 8 -295

16 25 350 685 45 730 335 8 -305

17 30 380 730 30 760 350 8 -325

18 25 405 760 45 805 355 9 -325

19 30 435 805 50 855 370 9 -345

20 25 460 855 35 890 395 9

SBI (Weekdays Busy)


2/55

ATM Idle Time

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0


3/55

Customer Time Between

Arrivals


customer

Queue Length Time available

for Service

ATM Idle

Time

1 0 0 30 30 0 0 30 0

2 30 30 30 25 55 0 0 35 10

3 35 65 65 50 115 0 0 25 0

4 25 90 115 60 175 25 1 -10 05 15 105 175 35 210 70 2 -45 0

6 25 130 210 45 255 80 2 -60 0

7 20 150 255 40 295 105 3 -70 0

8 35 185 295 45 340 110 3 -85 0

9 25 210 340 50 390 130 3 -95 0

10 35 245 390 40 430 145 4 -120 0

11 25 270 430 50 480 160 4 -125 0

12 35 305 480 45 525 175 4 -145 0

13 30 335 525 35 560 190 5 -155 0

14 35 370 560 45 605 190 5 -155 0

15 35 405 605 45 650 200 5 -175 0

16 25 430 650 45 695 220 5 -185 0

17 35 465 695 35 730 230 6 -190 0

18 40 505 730 45 775 225 6 -200 0

19 25 530 775 40 815 245 6 -215 0

20 30 560 815 35 850 255 6

ICICI (Weekdays Busy)


4/55


Arrivals


customer

Queue

Length

Time available

for Service

ATM Idle

Time

1 0 0 50 15 0 0 45 0

2 45 45 45 45 90 0 0 35 0

3 35 80 80 45 125 0 0 65 20

4 30 110 110 65 175 0 0 70 5

5 40 150 150 45 195 0 0 75 30

6 35 185 185 45 230 0 0 70 25

7 35 220 220 50 270 0 0 65 15

8 30 250 250 65 315 0 0 75 10

9 45 295 295 55 350 0 0 85 30

10 40 335 335 55 390 0 0 80 25

11 40 375 375 65 440 0 0 85 20

12 45 420 420 65 485 0 0 80 15

13 35 455 455 55 510 0 0 65 10

14 30 485 485 50 535 0 0 55 515 25 510 510 55 565 0 0 65 10

16 40 550 550 55 605 0 0 70 15

17 30 580 580 60 640 0 0 75 15

18 45 625 625 55 680 0 0 65 10

19 20 645 645 65 710 0 0 70 5

20 50 695 695 45 740 0 0

SBI (Weekdays Free)


5/55


Arrivals


customer

Queue

Length

Time

available for

ATM Idle

Time

1 0 0 45 15 0 0 45 0

2 45 45 45 50 95 0 0 50 0

3 50 95 95 45 140 0 0 115 70

4 65 160 160 55 215 0 0 75 20

5 75 235 235 65 300 0 0 60 0

6 60 295 295 35 330 0 0 110 75

7 50 345 345 45 390 0 0 55 10

8 55 400 400 50 450 0 0 50 0

9 50 450 450 55 505 0 0 110 55

10 60 510 510 45 555 0 0 50 5

11 50 560 560 45 605 0 0 35 0

12 35 595 595 55 650 0 0 90 35

13 55 650 650 45 695 0 0 100 55

14 45 695 695 55 750 0 0 95 4015 50 745 745 55 800 0 0 85 30

16 35 780 780 50 830 0 0 85 35

17 50 830 830 45 875 0 0 95 50

18 45 875 875 45 920 0 0 75 30

19 30 905 905 50 955 0 0 75 25

20 45 950 950 35 985 0 0

ICICI (Weekdays Free)


6/55


Arrivals


customer

Queue

Length

Time available

for Service

ATM Idle

Time

1 0 0 45 45 0 0 35 0

2 35 35 45 55 100 10 1 20 0

3 30 65 100 45 145 35 1 -10 0

4 25 90 145 40 185 55 2 -25 0

5 30 120 185 45 230 65 2 -40 0

6 25 145 230 55 285 85 2 -55 0

7 30 175 285 45 330 110 3 -85 0

8 25 200 330 55 385 130 3 -105 0

9 25 225 385 45 430 160 4 -130 0

10 30 255 430 50 480 175 4 -150 0

11 25 280 480 45 525 200 5 -170 0

12 30 310 525 55 580 215 5 -180 0

13 35 345 580 50 630 235 5 -200 0

14 35 380 630 35 665 250 6 -215 015 35 415 665 50 715 250 6 -220 0

16 30 445 715 55 770 270 6 -235 0

17 35 480 770 45 815 290 6 -260 0

18 30 510 815 55 870 305 7 -275 0

19 30 540 870 45 915 330 7 -305 0

20 25 565 915 55 970 350 8 0

SBI (Weekend Busy)


7/55


Arrivals

Arrival Time Start Service Service

Time

End Service Wait Time for

customer

Queue

Length

Time available for

Service

ATM Idle Time

1 0 0 45 45 0 0 40 0

2 40 40 45 55 100 5 1 30 0

3 35 75 100 50 150 25 1 25 0

4 50 125 150 45 195 25 1 20 0

5 45 170 195 40 235 25 1 15 0

6 40 210 235 40 275 25 1 15 0

7 40 250 275 35 310 25 1 0 0

8 25 275 310 45 355 35 1 0 0

9 35 310 355 50 405 45 1 0 0

10 45 355 405 40 445 50 1 -15 0

11 35 390 445 45 490 55 2 -20 0

12 35 425 490 45 535 65 2 -15 0

13 50 475 535 45 580 60 2 -25 0

14 35 510 580 40 620 70 2 -65 015 5 515 620 40 660 105 3 -65 0

16 40 555 660 45 705 105 3 -70 0

17 35 590 705 35 740 115 3 -75 0

18 40 630 740 40 780 110 3 -70 0

19 40 670 780 40 820 110 3 -65 0

20 45 715 820 30 850 105 3

ICICI (Weekend Busy)


8/55


Arrivals

Arrival Time Start

Service

Service Time End Service Wait Time for

customer

Queue Length Time available

for Service

ATM Idle

Time

1 0 0 30 15 0 0 55 25

2 55 55 55 65 120 0 0 55 0

3 55 110 110 45 155 0 0 105 60

4 50 160 160 50 210 0 0 45 0

5 45 205 205 45 250 0 0 90 45

6 45 250 250 50 300 0 0 95 45

7 50 300 300 50 350 0 0 95 45

8 45 345 345 55 400 0 0 90 35

9 45 390 390 45 435 0 0 75 30

10 30 420 420 50 470 0 0 80 30

11 50 470 470 60 530 0 0 95 35

12 45 515 515 50 565 0 0 75 25

13 30 545 545 45 590 0 0 85 4014 55 600 600 55 655 0 0 35 0

15 35 635 635 55 690 0 0 90 35

16 55 690 690 50 740 0 0 90 40

17 35 725 725 60 785 0 0 65 5

18 30 755 755 50 805 0 0 85 35

19 55 810 810 45 855 0 0 50 5

20 50 860 860 60 920 0 0

SBI (Weekend Free)


9/55


Arrivals


customer

Queue Length Time available for

Service

ATM Idle

Time

1 0 0 45 15 0 0 70 25

2 70 70 70 35 105 0 0 60 25

3 60 130 130 45 175 0 0 80 35

4 80 210 210 40 250 0 0 70 30

5 70 280 280 55 335 0 0 65 10

6 65 345 345 45 390 0 0 60 15

7 60 405 405 55 460 0 0 55 0

8 55 460 460 45 505 0 0 115 70

9 60 520 520 45 565 0 0 55 10

10 55 575 575 65 640 0 0 40 0

11 40 615 615 50 665 0 0 100 50

12 60 675 675 70 745 0 0 55 0

13 55 730 730 55 785 0 0 105 50

14 50 780 780 50 830 0 0 90 4015 40 820 820 65 885 0 0 95 30

16 55 875 875 45 920 0 0 120 75

17 65 940 940 55 995 0 0 55 0

18 55 995 995 45 1040 0 0 115 70

19 60 1055 1055 70 1125 0 0 45 0

20 45 1100 1100 50 1150 0 0

ICICI(Weekend Free)


10/55

SBI(Weekdays Busy)

Waiting Lines M/M/s

Data Results

Arrival rate (l) 156.52 Average server utilization(r) 0.96737Service rate (m) 80.9 Average number of customers in the queue(Lq) 28.2009

Number of servers(s) 2 Average number of customers in the system(L) 30.1356

Server cost $/time) 12 Average waiting time in the queue(Wq) 0.18017

Waiting cost ($/time) 10 Average time in the system(W) 0.19254

Probability (% of time) system is empty (P0) 0.01659

Cost - based on waiting 306.009

Cost - based on system 325.356

Probabilities

Number Probability Cumulative Probability

0 0.016587 0.016587

1 0.032092 0.048679

2 0.031044 0.079723

3 0.030031 0.109754

4 0.029051 0.138806

5 0.028103 0.166909

6 0.027186 0.194095

7 0.026299 0.220394

8 0.025441 0.245835

9 0.024611 0.27044510 0.023807 0.294253

11 0.023031 0.317283

12 0.022279 0.339562

13 0.021552 0.361114

14 0.020849 0.381963

15 0.020168 0.402131

16 0.019510 0.421642

17 0.018874 0.440515

18 0.018258 0.458773

19 0.017662 0.476434

20 0.017085 0.493520 term2 P0(s)

0 1.000000

1 1.93473424 1 -2.069822798 -0.9347

2 1.87159829 2.9347342 57.35314455 0.01659

3 1.2070151 4.8063325 3.399194294 0.12187

4 0.58381336 6.0133476 1.130727814 0.13998

5 0.22590474 6.597161 0.368491278 0.14356

6 0.07284427 6.8230657 0.107512192 0.14429


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7 0.02013347 6.89591 0.027823675 0.14443

8 0.00486911 6.9160435 0.006422294 0.14446

9 0.00104672 6.9209126 0.001333346 0.14446

10 0.00020251 6.9219593 0.000251091 0.14446

11 3.5619E-05 6.9221618 4.32206E-05 0.14446

12 5.7427E-06 6.9221974 6.8466E-06 0.14446

13 8.5467E-07 6.9222032 1.0041E-06 0.1444614 1.1811E-07 6.922204 1.37051E-07 0.14446

15 1.5234E-08 6.9222041 1.74901E-08 0.14446

16 1.8421E-09 6.9222042 2.09553E-09 0.14446

17 2.0965E-10 6.9222042 2.36573E-10 0.14446

18 2.2534E-11 6.9222042 2.5248E-11 0.14446

19 2.2946E-12 6.9222042 2.55477E-12 0.14446

20 2.2197E-13 6.9222042 2.45747E-13 0.14446

21 2.045E-14 6.9222042 2.25258E-14 0.14446

22 1.7985E-15 6.9222042 1.97188E-15 0.14446

23

24

25

26

27

28

29

30


12/55

Rho(s) Lq(s) L(s) Wq(s) W(S)

1.934734 -4.00456 -2.06982 -0.02558 -0.01322

0.967367 28.20091 30.13565 0.180174 0.192535

0.644911 0.752372 2.687107 0.004807 0.017168

0.483684 0.148271 2.083006 0.000947 0.013308

0.386947 0.03339 1.968124 0.000213 0.012574

0.322456 0.007383 1.942117 4.72E-05 0.012408


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0.276391 0.001535 1.936269 9.81E-06 0.012371

0.241842 0.000296 1.93503 1.89E-06 0.012363

0.21497 5.27E-05 1.934787 3.37E-07 0.012361

0.193473 8.7E-06 1.934743 5.56E-08 0.012361

0.175885 1.33E-06 1.934736 8.51E-09 0.012361

0.161228 1.9E-07 1.934734 1.21E-09 0.012361

0.148826 2.54E-08 1.934734 1.62E-10 0.0123610.138195 3.17E-09 1.934734 2.03E-11 0.012361

0.128982 3.74E-10 1.934734 2.39E-12 0.012361

0.120921 4.16E-11 1.934734 2.66E-13 0.012361

0.113808 4.39E-12 1.934734 2.8E-14 0.012361

0.107485 4.39E-13 1.934734 2.81E-15 0.012361

0.101828 4.18E-14 1.934734 2.67E-16 0.012361

0.096737 3.8E-15 1.934734 2.43E-17 0.012361

0.09213 3.3E-16 1.934734 2.11E-18 0.012361

0.087942 2.75E-17 1.934734 1.75E-19 0.012361


14/55

Waiting Lines M/M/s

Data Results

Arrival rate (l) 128.57 Average server utilization(r) 0.75003Service rate (m) 85.71 Average number of customers in the queue(Lq) 1.92899

Number of servers(s) 2 Average number of customers in the system(L) 3.42905

Server cost $/time) 12 Average waiting time in the queue(Wq) 0.015

Waiting cost ($/time) 10 Average time in the system(W) 0.02667




Probabilities

Number Probability Cumulative Probability

0 0.142838 0.142838

1 0.214265 0.357104

2 0.160705 0.517809

3 0.120534 0.638343

4 0.090404 0.728746

5 0.067805 0.796552

6 0.050856 0.847408

7 0.038144 0.885552

8 0.028609 0.9141609 0.021457 0.935618

10 0.016094 0.951711

11 0.012071 0.963782

12 0.009053 0.972836

13 0.006790 0.979626

14 0.005093 0.984719

15 0.003820 0.988539

16 0.002865 0.991404

17 0.002149 0.993552

18 0.001612 0.995164

19 0.001209 0.996373

20 0.000907 0.997280 term2 P0(s)

0 1.000000

1 1.50005834 1 -2.999766682 -0.5001

2 1.12508751 2.5000583 4.500875153 0.14284

3 0.56256563 3.6251458 1.125175021 0.21051

4 0.21097032 4.1877115 0.337560382 0.22098

5 0.06329356 4.3986818 0.090420873 0.22276

ICICI (Weekdays Busy)


15/55

6 0.015824 4.4619753 0.021098946 0.22306

7 0.00339099 4.4777993 0.004315851 0.22311

8 0.00063584 4.4811903 0.000782574 0.22312

9 0.00010598 4.4818262 0.000127173 0.22312

10 1.5897E-05 4.4819322 1.87026E-05 0.22312

11 2.1679E-06 4.481948 2.51018E-06 0.22312

12 2.7099E-07 4.4819502 3.0971E-07 0.2231213 3.127E-08 4.4819505 3.53487E-08 0.22312

14 3.3505E-09 4.4819505 3.75254E-09 0.22312

15 3.3506E-10 4.4819505 3.72291E-10 0.22312

16 3.1413E-11 4.4819505 3.46629E-11 0.22312

17 2.7719E-12 4.4819505 3.04011E-12 0.22312

18 2.31E-13 4.4819505 2.51997E-13 0.22312

19 1.8237E-14 4.4819505 1.98005E-14 0.22312

20 1.3678E-15 4.4819505 1.47876E-15 0.22312

21 9.7707E-17 4.4819505 1.05224E-16 0.22312

22 6.6621E-18 4.4819505 7.14962E-18 0.22312

23

24

25

26

27

28

29

30


16/55

Rho(s) Lq(s) L(s) Wq(s) W(S)

1.500058 -4.49983 -2.99977 -0.035 -0.02333

0.750029 1.928989 3.429048 0.015003 0.026671

0.500019 0.236881 1.73694 0.001842 0.01351

0.375015 0.044759 1.544818 0.000348 0.012015

0.300012 0.008633 1.508691 6.71E-05 0.011734


17/55


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19/55


20/55

Results

Average server utilization(r) 0.78425Average number of customers in the queue(Lq) 2.50612

Average number of customers in the system(L) 4.07463

Average waiting time in the queue(Wq) 0.02419

Average time in the system(W) 0.03933




robability

term2 P0(s) Rho(s) Lq(s) L(s) Wq(s)

-2.758988016 -0.5685 1.568509 -4.3275 -2.75899 -0.04177

5.701666733 0.12092 0.784254 2.506121 4.07463 0.02419

1.347851646 0.19431 0.522836 0.286966 1.855475 0.00277

0.414881208 0.2059 0.392127 0.055106 1.623615 0.000532

0.115276432 0.20793 0.313702 0.010956 1.579465 0.000106

0.02800209 0.20829 0.261418 0.002064 1.570573 1.99E-05

0.005972511 0.20835 0.224073 0.000359 1.568868 3.47E-06


21/55

0.001130195 0.20835 0.196064 5.74E-05 1.568566 5.54E-07

0.000191772 0.20836 0.174279 8.43E-06 1.568517 8.14E-08

2.94579E-05 0.20836 0.156851 1.14E-06 1.56851 1.1E-08

4.1306E-06 0.20836 0.142592 1.43E-07 1.568509 1.38E-09

5.32526E-07 0.20836 0.130709 1.67E-08 1.568509 1.61E-10

6.3517E-08 0.20836 0.120655 1.82E-09 1.568509 1.75E-11

7.04715E-09 0.20836 0.112036 1.85E-10 1.568509 1.79E-127.30754E-10 0.20836 0.104567 1.78E-11 1.568509 1.72E-13

7.11181E-11 0.20836 0.098032 1.61E-12 1.568509 1.55E-14

6.52004E-12 0.20836 0.092265 1.38E-13 1.568509 1.33E-15

5.64962E-13 0.20836 0.087139 1.12E-14 1.568509 1.08E-16

4.64062E-14 0.20836 0.082553 8.7E-16 1.568509 8.4E-18

3.62313E-15 0.20836 0.078425 6.42E-17 1.568509 6.2E-19

2.69522E-16 0.20836 0.074691 4.53E-18 1.568509 4.38E-20

1.91456E-17 0.20836 0.071296 3.06E-19 1.568509 2.96E-21


22/55

W(S)

-0.02663

0.03933

0.01791

0.015672

0.015246

0.01516

0.015144


23/55

0.015141

0.01514

0.01514

0.01514

0.01514

0.01514

0.015140.01514

0.01514

0.01514

0.01514

0.01514

0.01514

0.01514

0.01514


24/55

ICICI (WEEK DAYS FREE)

Waiting Lines M/M/s

DataArrival rate (l) 75.8

Service rate (m) 74.22

Number of servers(s) 2

Server cost $/time) 12

Waiting cost ($/time) 10

Probabilities

Number Probability Cumulative

0 0.323939 0.323939

1 0.330835 0.654773

2 0.168939 0.823712

3 0.086268 0.909980

4 0.044052 0.954032

5 0.022495 0.976527

6 0.011487 0.988013

7 0.005866 0.993879

8 0.002995 0.9968749 0.001530 0.998404

10 0.000781 0.999185

11 0.000399 0.999584

12 0.000204 0.999787

13 0.000104 0.999891

14 0.000053 0.999945

15 0.000027 0.999972

16 0.000014 0.999986

17 0.000007 0.999993

18 0.000004 0.999996

19 0.000002 0.999998

20 0.000001 0.999999

0 1.000000

1 1.02128806 1

2 0.52151465 2.0212881

3 0.1775389 2.5428027

4 0.04532959 2.7203416

5 0.00925891 2.7656712


25/55


26/55


27/55

0.00189929 0.36012 0.170215 0.00014 1.021428 1.85E-06

0.000269214 0.36013 0.145898 1.66E-05 1.021305 2.18E-07

3.36496E-05 0.36013 0.127661 1.77E-06 1.02129 2.34E-08

3.75734E-06 0.36013 0.113476 1.73E-07 1.021288 2.29E-09

3.78883E-07 0.36013 0.102129 1.55E-08 1.021288 2.05E-10

3.48172E-08 0.36013 0.092844 1.28E-09 1.021288 1.69E-11

2.93814E-09 0.36013 0.085107 9.84E-11 1.021288 1.3E-122.29182E-10 0.36013 0.078561 7.04E-12 1.021288 9.28E-14

1.66174E-11 0.36013 0.072949 4.71E-13 1.021288 6.21E-15

1.12551E-12 0.36013 0.068086 2.96E-14 1.021288 3.91E-16

7.15151E-14 0.36013 0.063831 1.76E-15 1.021288 2.32E-17

4.27916E-15 0.36013 0.060076 9.85E-17 1.021288 1.3E-18

2.41933E-16 0.36013 0.056738 5.24E-18 1.021288 6.91E-20

1.29634E-17 0.36013 0.053752 2.65E-19 1.021288 3.5E-21

6.60091E-19 0.36013 0.051064 1.28E-20 1.021288 1.69E-22

3.202E-20 0.36013 0.048633 5.89E-22 1.021288 7.78E-24

1.48299E-21 0.36013 0.046422 2.6E-23 1.021288 3.43E-25


28/55

W(S)

-0.63291

0.018226

0.014125

0.013572

0.013488


29/55


30/55


31/55

6 0.03557721 5.5207635

7 0.00872619 5.5563407

8 0.00187277 5.5650669

9 0.00035727 5.5669396

10 6.134E-05 5.5672969

11 9.5742E-06 5.5673583

12 1.3698E-06 5.567367813 1.8092E-07 5.5673692

14 2.2187E-08 5.5673694

15 2.5396E-09 5.5673694

16 2.7252E-10 5.5673694

17 2.7523E-11 5.5673694

18 2.6253E-12 5.5673694

19 2.3723E-13 5.5673694

20 2.0365E-14 5.5673694

21 1.665E-15 5.5673694

22 1.2994E-16 5.5673694

23

24

25

26

27

28

29

30


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0.049838761 0.17951 0.286154 0.003586 1.720509 2.81E-05

0.011562072 0.1796 0.245275 0.000675 1.717598 5.3E-06

0.002384531 0.17962 0.214615 0.000117 1.71704 9.18E-07

0.00044149 0.17962 0.190769 1.87E-05 1.716941 1.47E-07

7.40547E-05 0.17962 0.171692 2.76E-06 1.716925 2.16E-08

1.1345E-05 0.17962 0.156084 3.77E-07 1.716923 2.96E-09

1.59856E-06 0.17962 0.143077 4.79E-08 1.716923 3.76E-102.08447E-07 0.17962 0.132071 5.7E-09 1.716923 4.47E-11

2.52885E-08 0.17962 0.122637 6.35E-10 1.716923 4.98E-12

2.86783E-09 0.17962 0.114462 6.66E-11 1.716923 5.22E-13

3.05274E-10 0.17962 0.107308 6.59E-12 1.716923 5.17E-14

3.06148E-11 0.17962 0.100995 6.18E-13 1.716923 4.85E-15

2.90207E-12 0.17962 0.095385 5.5E-14 1.716923 4.31E-16

2.60797E-13 0.17962 0.090364 4.65E-15 1.716923 3.65E-17

2.22777E-14 0.17962 0.085846 3.76E-16 1.716923 2.95E-18

1.81328E-15 0.17962 0.081758 2.9E-17 1.716923 2.28E-19

1.40941E-16 0.17962 0.078042 2.14E-18 1.716923 1.68E-20


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W(S)

-0.01879

0.051221

0.016834

0.014134

0.013613


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ICICI (Weekend Busy)

Waiting Lines M/M/s

Data ResultsArrival rate (l) 100.7 Average server utilization(r)Service rate (m) 84.7 Average number of customers in the queue(Lq)

Number of servers(s) 2 Average number of customers in the system(L)

Server cost $/time) 12 Average waiting time in the queue(Wq)

Waiting cost ($/time) 10 Average time in the system(W)

Probability (% of time) system is empty (P0)

Cost - based on waiting

Cost - based on system

ProbabilitiesNumber Probability Cumulative Probability

0 0.254350 0.254350

1 0.302398 0.556748

2 0.179761 0.736508

3 0.106859 0.843367

4 0.063522 0.906889

5 0.037761 0.944650

6 0.022447 0.967097

7 0.013344 0.980441

8 0.007932 0.988373

9 0.004715 0.993088

10 0.002803 0.995891

11 0.001666 0.997558

12 0.000991 0.998548

13 0.000589 0.999137

14 0.000350 0.999487

15 0.000208 0.999695

16 0.000124 0.999819

17 0.000074 0.999892

18 0.000044 0.999936

19 0.000026 0.99996220 0.000015 0.999977 term2

0 1.000000

1 1.18890201 1 -6.29375

2 0.70674399 2.188902 1.742684601

3 0.28008312 2.895646 0.463944719

4 0.08324784 3.1757291 0.118455984

5 0.01979471 3.258977 0.02596982

6 0.00392233 3.2787717 0.0048916


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7 0.00066618 3.282694 0.000802475

8 9.9003E-05 3.2833602 0.000116284

9 1.3078E-05 3.2834592 1.50689E-05

10 1.5549E-06 3.2834723 1.76469E-06

11 1.6805E-07 3.2834738 1.8842E-07

12 1.665E-08 3.283474 1.84811E-08

13 1.5227E-09 3.283474 1.67599E-0914 1.2931E-10 3.283474 1.41312E-10

15 1.0249E-11 3.283474 1.11315E-11

16 7.6158E-13 3.283474 8.22716E-13

17 5.3262E-14 3.283474 5.72666E-14

18 3.5179E-15 3.283474 3.76673E-15

19 2.2013E-16 3.283474 2.34825E-16

20 1.3086E-17 3.283474 1.39127E-17

21 7.4084E-19 3.283474 7.85297E-19

22 4.0036E-20 3.283474 4.23228E-20

23

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26

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0.30455 0.169843 5E-05 1.188952 4.97E-07 0.011807

0.30456 0.148613 6.18E-06 1.188908 6.14E-08 0.011806

0.30456 0.1321 6.99E-07 1.188903 6.94E-09 0.011806

0.30456 0.11889 7.25E-08 1.188902 7.2E-10 0.011806

0.30456 0.108082 6.95E-09 1.188902 6.91E-11 0.011806

0.30456 0.099075 6.19E-10 1.188902 6.15E-12 0.011806

0.30456 0.091454 5.14E-11 1.188902 5.1E-13 0.0118060.30456 0.084922 3.99E-12 1.188902 3.97E-14 0.011806

0.30456 0.07926 2.92E-13 1.188902 2.9E-15 0.011806

0.30456 0.074306 2.01E-14 1.188902 2E-16 0.011806

0.30456 0.069935 1.31E-15 1.188902 1.3E-17 0.011806

0.30456 0.06605 8.11E-17 1.188902 8.06E-19 0.011806

0.30456 0.062574 4.77E-18 1.188902 4.74E-20 0.011806

0.30456 0.059445 2.68E-19 1.188902 2.66E-21 0.011806

0.30456 0.056614 1.44E-20 1.188902 1.43E-22 0.011806

0.30456 0.054041 7.36E-22 1.188902 7.31E-24 0.011806


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ResultsAverage server utilization(r) 0.59016Average number of customers in the queue(Lq) 0.63079







robability


-6.545738858 -0.1803 1.180319 -7.72606 -6.54574 -0.09228

1.699626336 0.25774 0.590159 0.630786 1.811105 0.007534

0.451827264 0.30042 0.39344 0.088044 1.268362 0.001052

0.114721747 0.30622 0.29508 0.014705 1.195024 0.000176

0.02498952 0.30705 0.236064 0.002371 1.18269 2.83E-05


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0.004675155 0.30716 0.19672 0.000352 1.18067 4.2E-06

0.000761663 0.30718 0.168617 4.75E-05 1.180366 5.67E-07

0.000109597 0.30718 0.14754 5.83E-06 1.180324 6.96E-08

1.41021E-05 0.30718 0.131147 6.54E-07 1.180319 7.81E-09

1.63975E-06 0.30718 0.118032 6.74E-08 1.180319 8.05E-10

1.73833E-07 0.30718 0.107302 6.42E-09 1.180319 7.67E-11

1.69286E-08 0.30718 0.09836 5.67E-10 1.180319 6.78E-121.52422E-09 0.30718 0.090794 4.68E-11 1.180319 5.58E-13

1.27595E-10 0.30718 0.084308 3.61E-12 1.180319 4.31E-14

9.9789E-12 0.30718 0.078688 2.62E-13 1.180319 3.13E-15

7.32234E-13 0.30718 0.07377 1.79E-14 1.180319 2.14E-16

5.06023E-14 0.30718 0.069431 1.16E-15 1.180319 1.39E-17

3.30446E-15 0.30718 0.065573 7.12E-17 1.180319 8.51E-19

2.04524E-16 0.30718 0.062122 4.16E-18 1.180319 4.97E-20

1.20304E-17 0.30718 0.059016 2.32E-19 1.180319 2.77E-21

6.7416E-19 0.30718 0.056206 1.23E-20 1.180319 1.47E-22

3.60716E-20 0.30718 0.053651 6.28E-22 1.180319 7.5E-24


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W(S)

-0.07819

0.021633

0.01515

0.014274

0.014127


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0.014103

0.014099

0.014098

0.014098

0.014098

0.014098

0.0140980.014098

0.014098

0.014098

0.014098

0.014098

0.014098

0.014098

0.014098

0.014098

0.014098


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ICICI ( WEEK END FREE)

Waiting Lines M/M/s

Data

Arrival rate (l) 65.45

Service rate (m) 69.9

Number of servers(s) 2

Server cost $/time) 12

Waiting cost ($/time) 10

Probabilities

Number Probability Cumulative

0 0.362241 0.362241

1 0.339180 0.701421

2 0.158794 0.860215

3 0.074342 0.934557

4 0.034805 0.969362

5 0.016294 0.985656

6 0.007629 0.993285

7 0.003571 0.996856

8 0.001672 0.9985289 0.000783 0.999311

10 0.000366 0.999677

11 0.000172 0.999849

12 0.000080 0.999929

13 0.000038 0.999967

14 0.000018 0.999985

15 0.000008 0.999993

16 0.000004 0.999997

17 0.000002 0.999998

18 0.000001 0.999999

19 0.000000 1.000000

20 0.000000 1.000000

0 1.000000

1 0.93633763 1

2 0.43836407 1.9363376

3 0.13681893 2.3747017

4 0.03202718 2.5115206

5 0.00599765 2.5435478


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6 0.00093597 2.5495455

7 0.0001252 2.5504814

8 1.4653E-05 2.5506066

9 1.5245E-06 2.5506213

10 1.4275E-07 2.5506228

11 1.2151E-08 2.5506229

12 9.481E-10 2.55062313 6.8288E-11 2.550623

14 4.5672E-12 2.550623

15 2.8509E-13 2.550623

16 1.6684E-14 2.550623

17 9.1893E-16 2.550623

18 4.7802E-17 2.550623

19 2.3557E-18 2.550623

20 1.1029E-19 2.550623

21 4.9174E-21 2.550623

22 2.0929E-22 2.550623

23

24

25

26

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30


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ResultsAverage server utilization(r) 0.46817Average number of customers in the queue(Lq) 0.26284







robability


14.70786517 0.06366 0.936338 13.77153 14.70787 0.210413

0.82425417 0.36224 0.468169 0.262838 1.199175 0.004016

0.198897252 0.38856 0.312113 0.035066 0.971403 0.000536

0.041815544 0.39164 0.234084 0.005005 0.941343 7.65E-05

0.007379612 0.39201 0.187268 0.000667 0.937004 1.02E-05


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W(S)

0.224719

0.018322

0.014842

0.014383

0.014316


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4 0.583813359 6.0133476 1.130727814

5 0.225904739 6.597161 0.368491278

6 0.072844272 6.8230657 0.107512192

7 0.020133473 6.89591 0.027823675

8 0.004869115 6.9160435 0.006422294

9 0.001046716 6.9209126 0.001333346

10 0.000202512 6.9219593 0.00025109111 3.56188E-05 6.9221618 4.32206E-05

12 5.74274E-06 6.9221974 6.8466E-06

13 8.54667E-07 6.9222032 1.0041E-06

14 1.18111E-07 6.922204 1.37051E-07

15 1.52342E-08 6.9222041 1.74901E-08

16 1.84214E-09 6.9222042 2.09553E-09

17 2.0965E-10 6.9222042 2.36573E-10

18 2.25342E-11 6.9222042 2.5248E-11

19 2.29462E-12 6.9222042 2.55477E-12

20 2.21974E-13 6.9222042 2.45747E-13

21 2.04505E-14 6.9222042 2.25258E-14

22 1.79847E-15 6.9222042 1.97188E-15

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0.13998 0.483684 0.148271 2.083006 0.000947 0.013308

0.14356 0.386947 0.03339 1.968124 0.000213 0.012574

0.14429 0.322456 0.007383 1.942117 4.72E-05 0.012408

0.14443 0.276391 0.001535 1.936269 9.81E-06 0.012371

0.14446 0.241842 0.000296 1.93503 1.89E-06 0.012363

0.14446 0.21497 5.27E-05 1.934787 3.37E-07 0.012361

0.14446 0.193473 8.7E-06 1.934743 5.56E-08 0.0123610.14446 0.175885 1.33E-06 1.934736 8.51E-09 0.012361

0.14446 0.161228 1.9E-07 1.934734 1.21E-09 0.012361

0.14446 0.148826 2.54E-08 1.934734 1.62E-10 0.012361

0.14446 0.138195 3.17E-09 1.934734 2.03E-11 0.012361

0.14446 0.128982 3.74E-10 1.934734 2.39E-12 0.012361

0.14446 0.120921 4.16E-11 1.934734 2.66E-13 0.012361

0.14446 0.113808 4.39E-12 1.934734 2.8E-14 0.012361

0.14446 0.107485 4.39E-13 1.934734 2.81E-15 0.012361

0.14446 0.101828 4.18E-14 1.934734 2.67E-16 0.012361

0.14446 0.096737 3.8E-15 1.934734 2.43E-17 0.012361

0.14446 0.09213 3.3E-16 1.934734 2.11E-18 0.012361

0.14446 0.087942 2.75E-17 1.934734 1.75E-19 0.012361

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