Stationary state probabilities at arrival instants for closed queueing networks with multiple types of customers
- 1 March 1980
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 17 (04) , 1048-1061
- https://doi.org/10.1017/s0021900200097333
Abstract
We consider closed networks of interconnected service centers with multiple types of customers and multiple classes, whose stationary state probabilities at arbitrary times have a product form. A customer can change its class but not its type as it traverses the network. We show that the stationary state probabilities at instants at which customers of a particular type arrive at a particular service center and enter a particular class are equal to the stationary state probabilities at arbitrary times for the network with one less customer of that type. Applications of this result are given.Keywords
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