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Mean waiting time and probability of delay in a communication system with decentralized switching and purely internal traffic between a finite number of subscribers

: Mrozynski, G.

Archiv für Elektronik und Übertragungstechnik : AEÜ 32 (1978), No.3, pp.89-93
ISSN: 0001-1096
Journal Article
Fraunhofer HHI ()
queueing theory; telecommunication systems; probability of delay; communication system; decentralized switching; purely internal traffic; finite number of subscribers; state probabilities; mean waiting time

For a communication system of loop or branching structure with multiple access of all subscribers to a common channel average delay and probability of delay are derived considering the fact that incoming call attempts are with probability directed to a free subscriber (exclusion of busy subscribers). If there are no calls waiting the state probabilities can be derived by elementary means. The following considerations, however, specifically deal with waiting call attempts: in a fraction of time transitions between system states occur which differ by more than one call held, since one part of the waiting calls (depending on traffic volume and total number of subscribers) is directed to busy subscriber lines and therefore directly disappears from the system without producing any after-effects. After deriving the state probabilities the average delay and the probability of delay are derived and evaluated. This model is specially applicable to a system where the total internal traffic volume is produced by a small number of subscribers.