Simulate a queue using Lindley's equation in Matlab - matlab

Question

I have to simulate a simple queue in Matlab using Lindley's equation:
W_{n+1}^Q = max(0, W_n^Q + S_n - X_{n+1}
I think I have done so, with the following code, but I am trying to run it several times and cannot save the information correct. The variables I want to save at the end of running the simulation are only saving the information from the last attempt (here for m=3).. while I clearly would like to see this for all runs (m=1,2,3).
for m=1:3
l = 1.1; % try this value for lambda
N = 10000; % let 1000 people arrive
X = exprnd(l,[1,N]); % make 1000 exponential interarrivals
S = 2*rand(1,N); % uniform on [0,2]
w = zeros(1,N);
sum1 = zeros(1,m);
avg1 = zeros(1,m);
max1 = zeros(1,m);
for i=1:N
if i==1 % first customer doesn't have to wait
w(i) = 0;
else % following customers follow lindley's equation
w(i) = max(w(i-1) + S(i-1) - X(i), 0); % n-th customer's waiting time
count(i) = w(i) > 15; % count number of times greater than 15
end
end
max1(m) = max(w);
sum1(m) = sum(count); % sum number of times greater than 15
avg1(m) = sum1(m)/N; % divide by 1000 to get probability delay is greater than 15
end

Answer 1

You are initializing sum1, avg1 and max1 inside the for loop so in every iteration, these variables are set to zero (i.e. by initialization). This is the reason you loose your previous iteration value. To avoid this, initialize sum1, avg1 and max1 before you for loop. Refer below code for reference. HTH
sum1 = zeros(1,m);
avg1 = zeros(1,m);
max1 = zeros(1,m);
for m=1:3
l = 1.1; % try this value for lambda
N = 10000; % let 1000 people arrive
X = exprnd(l,[1,N]); % make 1000 exponential interarrivals
S = 2*rand(1,N); % uniform on [0,2]
w = zeros(1,N);
for i=1:N
if i==1 % first customer doesn't have to wait
w(i) = 0;
else % following customers follow lindley's equation
w(i) = max(w(i-1) + S(i-1) - X(i), 0); % n-th customer's waiting time
count(i) = w(i) > 15; % count number of times greater than 15
end
end
max1(m) = max(w);
sum1(m) = sum(count); % sum number of times greater than 15
avg1(m) = sum1(m)/N; % divide by 1000 to get probability delay is greater than 15
end