On the number in the non-homogeneous service system \(M^ X(t)/M(t)/\infty\) (Q790549)

Authors consider a non-homogeneous service system with time dependent parameters, where the arrivals are in groups of variable size. Denoting by \(N_ 1(t)\) the number of units in the system at time t and by \(N_ 2(t)\) the number of departures up to time t, they obtain expressions for \(E[N_ 1(t)]\), \(E[N_ 2(t)]\), \(Var[N_ 1(t)]\), \(Var[N_ 2(t)]\) and \(cov[N_ 1(t),N_ 2(t)]\).