\(\text{M/M}/m/\text{K}\) queue with nopassing and additional servers (Q2743863)

A multiserver queue with Poisson input exponential service times and finite buffer is considered, where customers leave the system in the same order in which they arrive. It may be treated as the presence of two types of customers having 1) zero service time and 2) exponential service time. Moreover, if the number of customers is greater than \(jN\) and less than \((j+1)N\), there will be \(j\) additional servers in the system (added to initial \(m\) ones), \(j+m\leq s\) for some \(s\). Steady-state distribution and expected waiting time are derived in an explicit form.