Relationships between characteristics in periodic Poisson queues
For the single server queue with periodic Poisson input and iid service times \(S_ i\), the workload, \(V^ p(t)\), the number of customers present, \(L^ p(t)\), and the departure rate, \(u^ p(t)\), are studied. Day equilibrium is assumed, i.e. it is assumed, that \(V^ p(t)\sim V^ p(t+p)\), where p is the period of the input. Results are: (i) E [V\({}^ p(t)]<\infty\) provided E [S\({}^ 2_ i]<\infty;\) (ii) E [S\({}_ i] E [L^ p(t)]=(\leq)(\geq)E [V^ p(t)]\), provided that \(S_ i\) is exponentially (NBUE), (NWUE) distributed; (iii) \(u^ p(t)=a(t)-(d/dt)E [L^ p(t)]\), where a(t) denotes the arrival intensity function.
scientific article; zbMATH DE number 4107893
scientific article