The variance constant for the actual waiting time of the PH/PH/1 queue. (English) Zbl 0881.60079

Let \(w_n\) denote the actual waiting time in the PH/PH/1 queue. Using Poisson’s equation the functional \({1\over n} \sum^{n-1}_{k=0} f(w_k)\) converges to the normal random variable in distribution. The variance of the limiting random variable has been refered to as (time average) variance constant. The author derives explicit solutions to Poisson’s equation using phase-type methodology. Some numerical examples are also presented for some particular cases.


60K25 Queueing theory (aspects of probability theory)
60K05 Renewal theory
60G42 Martingales with discrete parameter
Full Text: DOI


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