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Note that the procedure will not calculate if .
L = input('Enter lambda '); % Type desired value, no extra space
M = input('Enter mu '); % Type desired value, no extra spacea = [' lambda mu'];b = [L M];disp(a)
disp(b)r = L/(2*M);EQ = (2*r^3)/(1 - r^2);
EN = EQ + 2*r;EW = EQ/L;
ED = EN/L;A = [' rho EN EQ EW ED']; % Identifies entries in B
B = [r EN EQ EW ED];
disp(A)disp(B)v = input('Enter row matrix of values v ');t = 2*M*EW*(1 - r)/(1 - 2*r);
PD2 = exp(-M*v).*(1 + t.*(1 - exp(-M*v + L*v))); % Calculates P(D>v) for L not equal MS = [' v P(D>v)'];s = [v; PD2]';disp(S)
disp(s)
queue2Enter lambda 0.1
Enter mu 0.2lambda mu
0.1000 0.2000rho EN EQ EW ED0.2500 0.5333 0.0333 0.3333 5.3333Enter row matrix of values v [4 8 16]
v P(D>v)
4.0000 0.47908.0000 0.2241
16.0000 0.0473 A queueing system has Poisson arrivals, rate λ and exponential service times.
queue1
Enter lambda 0.6Enter mu 1
lambda mu0.6000 1.0000rho EN EQ EW ED
0.6000 1.5000 0.9000 1.5000 2.5000Enter row matrix of values v [1 3 5 10]v P(D>v)
1.0000 0.67033.0000 0.3012
5.0000 0.135310.0000 0.0183
Ov = ones(1,length(v));R = r*Ov; % Row vector with all terms = r
r1 = R;E11 = B;
v11 = PD;queue1Enter lambda 0.9
Enter mu 1lambda mu
0.9000 1.0000rho EN EQ EW ED0.9000 9.0000 8.1000 9.0000 10.0000Enter row matrix of values v v % Calls for previously entered vv P(D>v)
1.0000 0.90483.0000 0.7408
5.0000 0.606510.0000 0.3679
R = r*Ov;r2 = R;
E12 = B;v12 = PD;queue1Enter lambda 0.99
Enter mu 1lambda mu
0.9900 1.0000rho EN EQ EW ED0.9900 99.0000 98.0100 99.0000 100.0000Enter row matrix of values v v
v P(D>v)
1.0000 0.99003.0000 0.9704
5.0000 0.951210.0000 0.9048
R = r*Ov;r3 = R;
E13 = B;v13 = PD;queue2 % Begin calculations for second system
Enter lambda 0.6Enter mu 0.5
lambda mu0.6000 0.5000rho EN EQ EW ED
0.6000 1.8750 0.6750 1.1250 3.1250Enter row matrix of values v vv P(D>v)
1.0000 0.75013.0000 0.3988
5.0000 0.201910.0000 0.0328
E21 = B; % Not necessary to determne r1, r2, r3, sincev21 = PD2; % they are the same as for system one.queue2
Enter lambda 0.9Enter mu 0.5
lambda mu0.9000 0.5000rho EN EQ EW ED
0.9000 9.4737 7.6737 8.5263 10.5263Enter row matrix of values v vv P(D>v)
1.0000 0.92453.0000 0.7749
5.0000 0.641010.0000 0.3916E22 = B;
v22 = PD2;queue2Enter lambda 0.99
Enter mu 0.5lambda mu
0.9900 0.5000rho EN EQ EW ED0.9900 99.4975 97.5175 98.5025 100.5025Enter row matrix of values v v
v P(D>v)
1.0000 0.99203.0000 0.9743
5.0000 0.955710.0000 0.9094
E23 = B;v23 = PD2;
C = [E11; E21; zeros(E11); E12; E22; zeros(E11); E13; E23]; % Zeros are spacersdisp(A)
rho EN EQ EW EDdisp(C)
0.6000 1.5000 0.9000 1.5000 2.50000.6000 1.8750 0.6750 1.1250 3.1250
0 0 0 0 00.9000 9.0000 8.1000 9.0000 10.0000
0.9000 9.4737 7.6737 8.5263 10.52630 0 0 0 0
0.9900 99.0000 98.0100 99.0000 100.00000.9900 99.4975 97.5175 98.5025 100.5025H = [' rho v P(D1>v) P(D2>v)'];PDV = [r1 r2 r3; v v v; v11 v12 v13; v21 v22 v23]';disp(H)rho v P(D1>v) P(D2>v)
disp(PDV)1.0000 1.0000 0.6703 0.7501
1.0000 3.0000 0.3012 0.39881.0000 5.0000 0.1353 0.2019
1.0000 10.0000 0.0183 0.03280.9000 1.0000 0.9048 0.9245
0.9000 3.0000 0.7408 0.77490.9000 5.0000 0.6065 0.6410
0.9000 10.0000 0.3679 0.39160.9900 1.0000 0.9900 0.9920
0.9900 3.0000 0.9704 0.97430.9900 5.0000 0.9512 0.9557
0.9900 10.0000 0.9048 0.9094
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