Loss networks under diverse routing: The symmetric star network. (English) Zbl 0823.60090

We have a symmetric star network consisting of \(K\) links, each link joining an external node to the central node. For processes related with the process \(x^ K (t) = (x^ K_ j (t))\), where \(x^ K_ j(t)\) is the proportion of links that have exactly \(j\) circuits in use at time \(t\), a new proof of W. Whitt’s convergence theorem (with a mild generalization) is proved [AT&T Bell. Lab. Tech. J. 64, 1807-1856 (1985; Zbl 0591.90035)], and in limit he obtains Ornstein-Uhlenbeck diffusion process.


60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research


Zbl 0591.90035
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