
doi: 10.1007/bf01150853
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.
queue length, periodic Poisson input, output processes, arrival intensity function, Queueing theory (aspects of probability theory), workload
queue length, periodic Poisson input, output processes, arrival intensity function, Queueing theory (aspects of probability theory), workload
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