On a new numerical computation of the steady state solution for two infinite server parallel queues (Q2908366)

Two identical M/M/\(\infty\) queues in parallel with a joining the shortest queue (JSQ) policy are considered. We recall that in this system, customers arrive in accordance with a Poisson process of rate \(\lambda\). If two queues have the same length, the customer has the same probability of joining either one of them. The service time is an exponential random variable with the rate \(\mu\).NEWLINENEWLINEThe goal of the paper is to present the new numerical computation of the steady state probability \(p(i,j)\), where \(i\) is the number of customers in queue 1 and \(j\) the number of customers in queue 2. This method is different to the usual numerical methods involving a truncation of the state space and therefore does not need a normalisation equation. In the presented method, the steady state probabilities are expressed in terms of diagonal probabilities. These probabilities are then computed with high accuracy using a linear programming technique. The authors then adapt the ``methode des convexes'' and perform an algorithm for the numerical computation of the joint steady state distribution.NEWLINENEWLINEThe presented solution is original and worth to be noted.