Computer science_ Queuing System

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9-10-1

Edge Convenience Store
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Arrival rate (l) 10 Average server utilization (r) 0.0333
Service rate (m) 300 Average number of customers in the queue (Lq) 0.0011
Number of servers (s) 1 Average number of customers in the system (L) 0.0345
Average waiting time in the queue (Wq) 0.0001
Average time in the system (W) 0.0034
Probability (% of time) system is empty (P0) 0.9667
0
Probabilities
Number of Units Probability Cumulative Probability
0 0.9667 0.9667
1 0.0322 0.9989
2 0.0011 1.0000
3 0.0000 1.0000
4 0.0000 1.0000
5 0.0000 1.0000
6 0.0000 1.0000
7 0.0000 1.0000
8 0.0000 1.0000
9 0.0000 1.0000
10 0.0000 1.0000
11 0.0000 1.0000
12 0.0000 1.0000
13 0.0000 1.0000
14 0.0000 1.0000
15 0.0000 1.0000
16 0.0000 1.0000
17 0.0000 1.0000
18 0.0000 1.0000
19 0.0000 1.0000
20 0.0000 1.0000
Computations
n or s (lam/mu)^n/n! Cumsum(n-1) term2 P0(s) Rho(s) Lq(s) L(s) Wq(s) W(S)
0 1
1 0.0333333333 1 0.0344827586 0.9666666667 0.0333333333 0.0011494253 0.0344827586 0.0001149425 0.0034482759
2 0.0005555556 1.033333333 0.0005649718 0.9672131148 0.0166666667 0.0000092618 0.0333425952 0.0000009262 0.0033342595
3 0.0000061728 1.033888889 0.0000062422 0.967216084 0.0111111111 0.0000000678 0.0333334012 0.0000000068 0.0033333401
4 0.0000000514 1.033895062 0.0000000519 0.9672161004 0.0083333333 0.0000000004 0.0333333337 4.21614E-11 0.0033333334
5 0.0000000003 1.033895113 0.0000000003 0.9672161005 0.0066666667 2.24107E-12 0.0333333333 2.24107E-13 0.0033333333
6 1.9052E-12 1.033895114 1.91584E-12 0.9672161005 0.0055555556 1.03521E-14 0.0333333333 1.03521E-15 0.0033333333
7 9.07237E-15 1.033895114 9.11578E-15 0.9672161005 0.0047619048 4.21862E-17 0.0333333333 4.21862E-18 0.0033333333
8 3.78015E-17 1.033895114 3.79597E-17 0.9672161005 0.0041666667 1.5362E-19 0.0333333333 1.5362E-20 0.0033333333
9 1.40006E-19 1.033895114 1.40526E-19 0.9672161005 0.0037037037 5.05276E-22 0.0333333333 5.05276E-23 0.0033333333
10 4.66686E-22 1.033895114 4.68246E-22 0.9672161005 0.0033333333 1.5147E-24 0.0333333333 1.5147E-25 0.0033333333
11 1.4142E-24 1.033895114 1.4185E-24 0.9672161005 0.003030303 4.17019E-27 0.0333333333 4.17019E-28 0.0033333333
12 3.92833E-27 1.033895114 3.93927E-27 0.9672161005 0.0027777778 1.06132E-29 0.0333333333 1.06132E-30 0.0033333333
13 1.00726E-29 1.033895114 1.00985E-29 0.9672161005 0.0025641026 2.51092E-32 0.0333333333 2.51092E-33 0.0033333333
14 2.39825E-32 1.033895114 2.40397E-32 0.9672161005 0.0023809524 5.54931E-35 0.0333333333 5.54931E-36 0.0033333333
15 5.32944E-35 1.033895114 5.34131E-35 0.9672161005 0.0022222222 1.1506E-37 0.0333333333 1.1506E-38 0.0033333333
16 1.1103E-37 1.033895114 1.11262E-37 0.9672161005 0.0020833333 2.24664E-40 0.0333333333 2.24664E-41 0.0033333333
17 2.17706E-40 1.033895114 2.18134E-40 0.9672161005 0.0019607843 4.14504E-43 0.0333333333 4.14504E-44 0.0033333333
18 4.03159E-43 1.033895114 4.03907E-43 0.9672161005 0.0018518519 7.24797E-46 0.0333333333 7.24797E-47 0.0033333333
19 7.07297E-46 1.033895114 7.0854E-46 0.9672161005 0.001754386 1.20441E-48 0.0333333333 1.20441E-49 0.0033333333
20 1.17883E-48 1.033895114 1.1808E-48 0.9672161005 0.0016666667 1.90665E-51 0.0333333333 1.90665E-52 0.0033333333
21 1.87115E-51 1.033895114 1.87413E-51 0.9672161005 0.0015873016 2.88186E-54 0.0333333333 2.88186E-55 0.0033333333
22 2.83508E-54 1.033895114 2.83939E-54 0.9672161005 0.0015151515 4.16737E-57 0.0333333333 4.16737E-58 0.0033333333
23 4.10882E-57 1.033895114 4.11478E-57 0.9672161005 0.0014492754 5.77632E-60 0.0333333333 5.77632E-61 0.0033333333
24 5.70669E-60 1.033895114 5.71463E-60 0.9672161005 0.0013888889 7.68745E-63 0.0333333333 7.68745E-64 0.0033333333
25 7.60892E-63 1.033895114 7.61908E-63 0.9672161005 0.0013333333 9.83884E-66 0.0333333333 9.83884E-67 0.0033333333
26 9.75502E-66 1.033895114 9.76755E-66 0.9672161005 0.0012820513 1.21275E-68 0.0333333333 1.21275E-69 0.0033333333
27 1.20432E-68 1.033895114 1.20581E-68 0.9672161005 0.0012345679 1.44163E-71 0.0333333333 1.44163E-72 0.0033333333
28 1.43372E-71 1.033895114 1.43543E-71 0.9672161005 0.0011904762 1.65479E-74 0.0333333333 1.65479E-75 0.0033333333
29 1.64795E-74 1.033895114 1.64985E-74 0.9672161005 0.0011494253 1.83632E-77 0.0333333333 1.83632E-78 0.0033333333
30 1.83106E-77 1.033895114 1.8331E-77 0.9672161005 0.0011111111 1.97219E-80 0.0333333333 1.97219E-81 0.0033333333
Default title
Queueing model being used
Important messages to be followed
Input values
Output values
This message is displayed only when the total service rate is not greater than the arrival rate.
Table shows probabilities of 0 through 20 units in the system.
1. Both l and m must be RATES, and use the same time unit. For example, given a service time such as 10 minutes per customer, convert it to a service rate such as 6 per hour. 2. The total service rate (rate x servers) must be greater than the arrival rate.

9-10-2

Edge Convenience Store
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Arrival rate (l) 6 Average server utilization (r) 0.0100
Service rate (m) 300 Average number of customers in the queue (Lq) 0.0000
Number of servers (s) 2 Average number of customers in the system (L) 0.0200
Average waiting time in the queue (Wq) 0.0000
Average time in the system (W) 0.0033
Probability (% of time) system is empty (P0) 0.9802
0
Probabilities
Number of Units Probability Cumulative Probability
0 0.9802 0.9802
1 0.0196 0.9998
2 0.0002 1.0000
3 0.0000 1.0000
4 0.0000 1.0000
5 0.0000 1.0000
6 0.0000 1.0000
7 0.0000 1.0000
8 0.0000 1.0000
9 0.0000 1.0000
10 0.0000 1.0000
11 0.0000 1.0000
12 0.0000 1.0000
13 0.0000 1.0000
14 0.0000 1.0000
15 0.0000 1.0000
16 0.0000 1.0000
17 0.0000 1.0000
18 0.0000 1.0000
19 0.0000 1.0000
20 0.0000 1.0000
Computations
n or s (lam/mu)^n/n! Cumsum(n-1) term2 P0(s) Rho(s) Lq(s) L(s) Wq(s) W(S)
0 1
1 0.02 1 0.0204081633 0.98 0.02 0.0004081633 0.0204081633 0.0000680272 0.0034013605
2 0.0002 1.02 0.0002020202 0.9801980198 0.01 0.0000020002 0.0200020002 0.0000003334 0.0033336667
3 0.0000013333 1.0202 0.0000013423 0.9801986711 0.0066666667 0.0000000088 0.0200000088 0.0000000015 0.0033333348
4 0.0000000067 1.020201333 0.0000000067 0.9801986733 0.005 3.30025E-11 0.02 5.50041E-12 0.0033333333
5 2.66667E-11 1.02020134 2.67738E-11 0.9801986733 0.004 1.05396E-13 0.02 1.7566E-14 0.0033333333
6 8.88889E-14 1.02020134 8.91862E-14 0.9801986733 0.0033333333 2.92375E-16 0.02 4.87292E-17 0.0033333333
7 2.53968E-16 1.02020134 2.54696E-16 0.9801986733 0.0028571429 7.15337E-19 0.02 1.19223E-19 0.0033333333
8 6.34921E-19 1.02020134 6.36512E-19 0.9801986733 0.0025 1.56368E-21 0.02 2.60613E-22 0.0033333333
9 1.41093E-21 1.02020134 1.41408E-21 0.9801986733 0.0022222222 3.08703E-24 0.02 5.14505E-25 0.0033333333
10 2.82187E-24 1.02020134 2.82752E-24 0.9801986733 0.002 5.55418E-27 0.02 9.25697E-28 0.0033333333
11 5.13067E-27 1.02020134 5.14002E-27 0.9801986733 0.0018181818 9.17712E-30 0.02 1.52952E-30 0.0033333333
12 8.55112E-30 1.02020134 8.5654E-30 0.9801986733 0.0016666667 1.40163E-32 0.02 2.33606E-33 0.0033333333
13 1.31556E-32 1.02020134 1.31758E-32 0.9801986733 0.0015384615 1.98998E-35 0.02 3.31663E-36 0.0033333333
14 1.87937E-35 1.02020134 1.88206E-35 0.9801986733 0.0014285714 2.63918E-38 0.02 4.39864E-39 0.0033333333
15 2.50582E-38 1.02020134 2.50917E-38 0.9801986733 0.0013333333 3.28369E-41 0.02 5.47282E-42 0.0033333333
16 3.13228E-41 1.02020134 3.1362E-41 0.9801986733 0.00125 3.84743E-44 0.02 6.41239E-45 0.0033333333
17 3.68503E-44 1.02020134 3.68937E-44 0.9801986733 0.0011764706 4.2595E-47 0.02 7.09917E-48 0.0033333333
18 4.09448E-47 1.02020134 4.09904E-47 0.9801986733 0.0011111111 4.46927E-50 0.02 7.44878E-51 0.0033333333
19 4.30998E-50 1.02020134 4.31452E-50 0.9801986733 0.0010526316 4.45636E-53 0.02 7.42727E-54 0.0033333333
20 4.30998E-53 1.02020134 4.31429E-53 0.9801986733 0.001 4.2331E-56 0.02 7.05517E-57 0.0033333333
21 4.10474E-56 1.02020134 4.10866E-56 0.9801986733 0.000952381 3.83918E-59 0.02 6.39863E-60 0.0033333333
22 3.73158E-59 1.02020134 3.73498E-59 0.9801986733 0.0009090909 3.33123E-62 0.02 5.55205E-63 0.0033333333
23 3.24486E-62 1.02020134 3.24768E-62 0.9801986733 0.0008695652 2.77056E-65 0.02 4.6176E-66 0.0033333333
24 2.70405E-65 1.02020134 2.7063E-65 0.9801986733 0.0008333333 2.21244E-68 0.02 3.6874E-69 0.0033333333
25 2.16324E-68 1.02020134 2.16497E-68 0.9801986733 0.0008 1.69904E-71 0.02 2.83173E-72 0.0033333333
26 1.66403E-71 1.02020134 1.66531E-71 0.9801986733 0.0007692308 1.25661E-74 0.02 2.09435E-75 0.0033333333
27 1.23261E-74 1.02020134 1.23353E-74 0.9801986733 0.0007407407 8.96295E-78 0.02 1.49383E-78 0.0033333333
28 8.80439E-78 1.02020134 8.81068E-78 0.9801986733 0.0007142857 6.17313E-81 0.02 1.02886E-81 0.0033333333
29 6.07199E-81 1.02020134 6.07618E-81 0.9801986733 0.0006896552 4.11033E-84 0.02 6.85055E-85 0.0033333333
30 4.04799E-84 1.02020134 4.05069E-84 0.9801986733 0.0006666667 2.64876E-87 0.02 4.41459E-88 0.0033333333
Problem title
M/M/s with s = 1 is the M/M/1 model
1.6 customer per hour
Mechanic is busy 67% of the time
300 cust per hour
One mechanic
0.67 hours = 40 minutes
= 60 minutes
Probability that there are <= 4 cars in the system.
1. Both l and m must be RATES, and use the same time unit. For example, given a service time such as 10 minutes per customer, convert it to a service rate such as 6 per hour. 2. The total service rate (rate x servers) must be greater than the arrival rate.

9-10-3

Edge Convenience Store
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Arrival rate (l) 4 Average server utilization (r) 0.0044
Service rate (m) 300 Average number of customers in the queue (Lq) 0.0000
Number of servers (s) 3 Average number of customers in the system (L) 0.0133
Average waiting time in the queue (Wq) 0.0000
Average time in the system (W) 0.0033
Probability (% of time) system is empty (P0) 0.9868
0
Probabilities
Number of Units Probability Cumulative Probability
0 0.9868 0.9868
1 0.0132 0.9999
2 0.0001 1.0000
3 0.0000 1.0000
4 0.0000 1.0000
5 0.0000 1.0000
6 0.0000 1.0000
7 0.0000 1.0000
8 0.0000 1.0000
9 0.0000 1.0000
10 0.0000 1.0000
11 0.0000 1.0000
12 0.0000 1.0000
13 0.0000 1.0000
14 0.0000 1.0000
15 0.0000 1.0000
16 0.0000 1.0000
17 0.0000 1.0000
18 0.0000 1.0000
19 0.0000 1.0000
20 0.0000 1.0000
Computations
n or s (lam/mu)^n/n! Cumsum(n-1) term2 P0(s) Rho(s) Lq(s) L(s) Wq(s) W(S)
0 1
1 0.0133333333 1 0.0135135135 0.9866666667 0.0133333333 0.0001801802 0.0135135135 0.000045045 0.0033783784
2 0.0000888889 1.013333333 0.0000894855 0.9867549669 0.0066666667 0.0000005926 0.013333926 0.0000001482 0.0033334815
3 0.0000003951 1.013422222 0.0000003968 0.9867551614 0.0044444444 0.0000000017 0.0133333351 0.0000000004 0.0033333338
4 0.0000000013 1.013422617 0.0000000013 0.9867551618 0.0033333333 4.36046E-12 0.0133333333 1.09011E-12 0.0033333333
5 3.51166E-12 1.013422619 3.52105E-12 0.9867551618 0.0026666667 9.28988E-15 0.0133333333 2.32247E-15 0.0033333333
6 7.80369E-15 1.013422619 7.82107E-15 0.9867551618 0.0022222222 1.71882E-17 0.0133333333 4.29704E-18 0.0033333333
7 1.48642E-17 1.013422619 1.48925E-17 0.9867551618 0.0019047619 2.80444E-20 0.0133333333 7.01111E-21 0.0033333333
8 2.47736E-20 1.013422619 2.4815E-20 0.9867551618 0.0016666667 4.08786E-23 0.0133333333 1.02197E-23 0.0033333333
9 3.67017E-23 1.013422619 3.67561E-23 0.9867551618 0.0014814815 5.3812E-26 0.0133333333 1.3453E-26 0.0033333333
10 4.89355E-26 1.013422619 4.90009E-26 0.9867551618 0.0013333333 6.45552E-29 0.0133333333 1.61388E-29 0.0033333333
11 5.93158E-29 1.013422619 5.93878E-29 0.9867551618 0.0012121212 7.1118E-32 0.0133333333 1.77795E-32 0.0033333333
12 6.59064E-32 1.013422619 6.59798E-32 0.9867551618 0.0011111111 7.24203E-35 0.0133333333 1.81051E-35 0.0033333333
13 6.75964E-35 1.013422619 6.76658E-35 0.9867551618 0.001025641 6.85519E-38 0.0133333333 1.7138E-38 0.0033333333
14 6.43775E-38 1.013422619 6.44388E-38 0.9867551618 0.000952381 6.06152E-41 0.0133333333 1.51538E-41 0.0033333333
15 5.72244E-41 1.013422619 5.72753E-41 0.9867551618 0.0008888889 5.02818E-44 0.0133333333 1.25704E-44 0.0033333333
16 4.7687E-44 1.013422619 4.77268E-44 0.9867551618 0.0008333333 3.92783E-47 0.0133333333 9.81957E-48 0.0033333333
17 3.74016E-47 1.013422619 3.74309E-47 0.9867551618 0.0007843137 2.89915E-50 0.0133333333 7.24788E-51 0.0033333333
18 2.77049E-50 1.013422619 2.77254E-50 0.9867551618 0.0007407407 2.02804E-53 0.0133333333 5.07009E-54 0.0033333333
19 1.9442E-53 1.013422619 1.94557E-53 0.9867551618 0.0007017544 1.34817E-56 0.0133333333 3.37043E-57 0.0033333333
20 1.29613E-56 1.013422619 1.297E-56 0.9867551618 0.0006666667 8.53783E-60 0.0133333333 2.13446E-60 0.0033333333
21 8.22943E-60 1.013422619 8.23465E-60 0.9867551618 0.0006349206 5.16238E-63 0.0133333333 1.2906E-63 0.0033333333
22 4.98753E-63 1.013422619 4.99056E-63 0.9867551618 0.0006060606 2.98633E-66 0.0133333333 7.46582E-67 0.0033333333
23 2.89132E-66 1.013422619 2.893E-66 0.9867551618 0.0005797101 1.65585E-69 0.0133333333 4.13962E-70 0.0033333333
24 1.60629E-69 1.013422619 1.60718E-69 0.9867551618 0.0005555556 8.81543E-73 0.0133333333 2.20386E-73 0.0033333333
25 8.56688E-73 1.013422619 8.57145E-73 0.9867551618 0.0005333333 4.5133E-76 0.0133333333 1.12833E-76 0.0033333333
26 4.39327E-76 1.013422619 4.39553E-76 0.9867551618 0.0005128205 2.2254E-79 0.0133333333 5.5635E-80 0.0033333333
27 2.16952E-79 1.013422619 2.17059E-79 0.9867551618 0.0004938272 1.05822E-82 0.0133333333 2.64555E-83 0.0033333333
28 1.0331E-82 1.013422619 1.0336E-82 0.9867551618 0.0004761905 4.85901E-86 0.0133333333 1.21475E-86 0.0033333333
29 4.7499E-86 1.013422619 4.75209E-86 0.9867551618 0.0004597701 2.15692E-89 0.0133333333 5.3923E-90 0.0033333333
30 2.11107E-89 1.013422619 2.11201E-89 0.9867551618 0.0004444444 9.26649E-93 0.0133333333 2.31662E-93 0.0033333333
0.25 hours = 15 minutes
= 30 minutes
1. Both l and m must be RATES, and use the same time unit. For example, given a service time such as 10 minutes per customer, convert it to a service rate such as 6 per hour. 2. The total service rate (rate x servers) must be greater than the arrival rate.

9-10-4

Edge Convenience Store
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Arrival rate (l) 4 Average server utilization (r) 0.0033
Service rate (m) 300 Average number of customers in the queue (Lq) 0.0000
Number of servers (s) 4 Average number of customers in the system (L) 0.0133
Average waiting time in the queue (Wq) 0.0000
Average time in the system (W) 0.0033
Probability (% of time) system is empty (P0) 0.9868
0
Probabilities
Number of Units Probability Cumulative Probability
0 0.9868 0.9868
1 0.0132 0.9999
2 0.0001 1.0000
3 0.0000 1.0000
4 0.0000 1.0000
5 0.0000 1.0000
6 0.0000 1.0000
7 0.0000 1.0000
8 0.0000 1.0000
9 0.0000 1.0000
10 0.0000 1.0000
11 0.0000 1.0000
12 0.0000 1.0000
13 0.0000 1.0000
14 0.0000 1.0000
15 0.0000 1.0000
16 0.0000 1.0000
17 0.0000 1.0000
18 0.0000 1.0000
19 0.0000 1.0000
20 0.0000 1.0000
Computations
n or s (lam/mu)^n/n! Cumsum(n-1) term2 P0(s) Rho(s) Lq(s) L(s) Wq(s) W(S)
0 1
1 0.0133333333 1 0.0135135135 0.9866666667 0.0133333333 0.0001801802 0.0135135135 0.000045045 0.0033783784
2 0.0000888889 1.013333333 0.0000894855 0.9867549669 0.0066666667 0.0000005926 0.013333926 0.0000001482 0.0033334815
3 0.0000003951 1.013422222 0.0000003968 0.9867551614 0.0044444444 0.0000000017 0.0133333351 0.0000000004 0.0033333338
4 0.0000000013 1.013422617 0.0000000013 0.9867551618 0.0033333333 4.36046E-12 0.0133333333 1.09011E-12 0.0033333333
5 3.51166E-12 1.013422619 3.52105E-12 0.9867551618 0.0026666667 9.28988E-15 0.0133333333 2.32247E-15 0.0033333333
6 7.80369E-15 1.013422619 7.82107E-15 0.9867551618 0.0022222222 1.71882E-17 0.0133333333 4.29704E-18 0.0033333333
7 1.48642E-17 1.013422619 1.48925E-17 0.9867551618 0.0019047619 2.80444E-20 0.0133333333 7.01111E-21 0.0033333333
8 2.47736E-20 1.013422619 2.4815E-20 0.9867551618 0.0016666667 4.08786E-23 0.0133333333 1.02197E-23 0.0033333333
9 3.67017E-23 1.013422619 3.67561E-23 0.9867551618 0.0014814815 5.3812E-26 0.0133333333 1.3453E-26 0.0033333333
10 4.89355E-26 1.013422619 4.90009E-26 0.9867551618 0.0013333333 6.45552E-29 0.0133333333 1.61388E-29 0.0033333333
11 5.93158E-29 1.013422619 5.93878E-29 0.9867551618 0.0012121212 7.1118E-32 0.0133333333 1.77795E-32 0.0033333333
12 6.59064E-32 1.013422619 6.59798E-32 0.9867551618 0.0011111111 7.24203E-35 0.0133333333 1.81051E-35 0.0033333333
13 6.75964E-35 1.013422619 6.76658E-35 0.9867551618 0.001025641 6.85519E-38 0.0133333333 1.7138E-38 0.0033333333
14 6.43775E-38 1.013422619 6.44388E-38 0.9867551618 0.000952381 6.06152E-41 0.0133333333 1.51538E-41 0.0033333333
15 5.72244E-41 1.013422619 5.72753E-41 0.9867551618 0.0008888889 5.02818E-44 0.0133333333 1.25704E-44 0.0033333333
16 4.7687E-44 1.013422619 4.77268E-44 0.9867551618 0.0008333333 3.92783E-47 0.0133333333 9.81957E-48 0.0033333333
17 3.74016E-47 1.013422619 3.74309E-47 0.9867551618 0.0007843137 2.89915E-50 0.0133333333 7.24788E-51 0.0033333333
18 2.77049E-50 1.013422619 2.77254E-50 0.9867551618 0.0007407407 2.02804E-53 0.0133333333 5.07009E-54 0.0033333333
19 1.9442E-53 1.013422619 1.94557E-53 0.9867551618 0.0007017544 1.34817E-56 0.0133333333 3.37043E-57 0.0033333333
20 1.29613E-56 1.013422619 1.297E-56 0.9867551618 0.0006666667 8.53783E-60 0.0133333333 2.13446E-60 0.0033333333
21 8.22943E-60 1.013422619 8.23465E-60 0.9867551618 0.0006349206 5.16238E-63 0.0133333333 1.2906E-63 0.0033333333
22 4.98753E-63 1.013422619 4.99056E-63 0.9867551618 0.0006060606 2.98633E-66 0.0133333333 7.46582E-67 0.0033333333
23 2.89132E-66 1.013422619 2.893E-66 0.9867551618 0.0005797101 1.65585E-69 0.0133333333 4.13962E-70 0.0033333333
24 1.60629E-69 1.013422619 1.60718E-69 0.9867551618 0.0005555556 8.81543E-73 0.0133333333 2.20386E-73 0.0033333333
25 8.56688E-73 1.013422619 8.57145E-73 0.9867551618 0.0005333333 4.5133E-76 0.0133333333 1.12833E-76 0.0033333333
26 4.39327E-76 1.013422619 4.39553E-76 0.9867551618 0.0005128205 2.2254E-79 0.0133333333 5.5635E-80 0.0033333333
27 2.16952E-79 1.013422619 2.17059E-79 0.9867551618 0.0004938272 1.05822E-82 0.0133333333 2.64555E-83 0.0033333333
28 1.0331E-82 1.013422619 1.0336E-82 0.9867551618 0.0004761905 4.85901E-86 0.0133333333 1.21475E-86 0.0033333333
29 4.7499E-86 1.013422619 4.75209E-86 0.9867551618 0.0004597701 2.15692E-89 0.0133333333 5.3923E-90 0.0033333333
30 2.11107E-89 1.013422619 2.11201E-89 0.9867551618 0.0004444444 9.26649E-93 0.0133333333 2.31662E-93 0.0033333333
&C&"Times New Roman,Regular"&12&A
&C&"Times New Roman,Regular"&12Page &P
0.25 hours = 15 minutes
= 30 minutes
1. Both l and m must be RATES, and use the same time unit. For example, given a service time such as 10 minutes per customer, convert it to a service rate such as 6 per hour. 2. The total service rate (rate x servers) must be greater than the arrival rate.