On the convergence to stationarity of the many-server poisson queue
Autor(en): | Stadje, W. Parthasarathy, P.R. |
Stichwörter: | Many-server Poisson queue; Speed of convergence; Stationarity; Transient probabilities | Erscheinungsdatum: | 1999 | Enthalten in: | Journal of Applied Probability | Band: | 36 | Ausgabe: | 2 | Startseite: | 546 | Seitenende: | 557 | Zusammenfassung: | We consider the many-server Poisson queue M/M/c with arrival intensity λ, mean service time 1 and λ/c < 1. Let X(t) be the number of customers in the system at time t and assume that the system is initially empty. Then pn(t) = P(X(t) = n) converges to the stationary probability πn = P(X = n). The integrals ∫0∞[E(X) − E(X(t))] dt and ∫0∞[P(X ≤ n) − P(X(t) ≤ n)] dt are a measure of the speed of convergence towards stationarity. We express these integrals in terms of λ and c. © 1999 Applied Probability Trust. |
ISSN: | 00219002 | DOI: | 10.1239/jap/1032374470 | Externe URL: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85037906899&doi=10.1239%2fjap%2f1032374470&partnerID=40&md5=fd704c8c494e9b89073a5be779f8047e |
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