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Transient distribution of the length of \(GI/G/N\) queueing systems. (English) Zbl 1054.60095

The continuous time Markov skeleton process \(X\) is introduced as a process where an embedded Markov chain may be constructed at a sequence of stopping times with respect to a natural filtration of the process \(X\). Some properties of the Markov skeleton process, first of all measurability, are studied. Connections between transition kernels of the underlying Markov skeleton process and the embedded Markov chain are established by means of the backward equation which is reduced to Chapman-Kolmogorov backward equation in a special case. The concept of Markov skeleton process is illustrated by an \(M/M/N\) queue.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
60K15 Markov renewal processes, semi-Markov processes
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