ERLANG C

Consider the classic M/M/c queueing model: Poisson arrival process, exponential service time and no abandonment by the customers (that is, customers have infinite patience time). The queue capacity can be finite or infinite. Because there are no abandonments, the number of servers must be greater than the offered load for the queue to be stable and reach steady state. Let \(\lambda\) be the arrival rate and \(1/\mu\) the average waiting time, then the offered load is \(\rho = \lambda/\mu\)... Service level (SL): This measure is defined as the expected ratio of customers that waited less or equal to the acceptable waiting time \(t\). That is, $$\textrm{SL}(y, t) = \mathbb{E}[X(y, t)] / \mathbb{E}[A],$$ where \(y\) is the number of servers, \(X(y, t)\) is the number of customers that waited at most \(t\) as a function of \(y\) and \(t\), \(A\) is the total number of customers, and \(\mathbb{E}\) is the expected value operator in statistics... This script evaluates the performance..