To simulate a system where arrivals follow a Poisson process and service durations are exponentially distributed, you'll use MATLAB's exprnd function for both inter-arrival times and service durations, not poissrnd. Here's a brief guide:
Generating Inter-Arrival Times
For an average arrival rate λ:
lambda = 5; % Example average arrival rate
numServices = 4; % Number of services
interArrivalTimes = exprnd(1/lambda, 1, numServices);
Generating Service Durations
For an average service rate μ:
mu = 10; % Example service rate
serviceDurations = exprnd(1/mu, 1, numServices);
Connecting Both
Calculate arrival times by summing the inter-arrival times:
arrivalTimes = cumsum(interArrivalTimes);
This way, you have interArrivalTimes for when services enter the system and serviceDurations for how long each service lasts, modeling a system with traffic load characterized by λ/μ.
Follwing documentation might help you in your implementation
- exprnd: https://www.mathworks.com/help/stats/exprnd.html
- cumsum: https://www.mathworks.com/help/matlab/ref/cumsum.html
Hope this helps!
