I know that the inter arrival times in a Possion process is exponentially distributed. So I assume when I use the matlab command as below, the outputs follow the definition.
services= poissrnd(20,1,4) %like for 4 time units. t=1,2,3,4
%output is like 18 19 14 19
But I want a traffic generation where each traffic service also has a service duration which is exponentially distributed. I believe this is different from the exp inter-arrival time aspect. So, how can I generate a duration for each service that is exp distributed so that I can depart it from the system once that duration is over. Do I need separate exp distribution? How can i connect the two then?
For e.g."Poisson process with an avg. arrival rate of λ requests per time-unit, and the lifetime of each request following negative exponential distribution with an average of 1/μ time units. So that the traffic load is λ/μ"