Motivated by queueing systems with heterogeneous parallel servers, we consider a class of structured multi-dimensional Markov processes whose state space can be partitioned into two parts: a finite set $V$ containing boundary states and a set $W$, which has one infinite dimension and a fixed number of finite dimensions. Using a separation of variables technique we show that the equilibrium distribution can be represented as a linear combination of product forms. For an important subclass of queueing systems, we characterize explicitly the waiting time distribution in terms of a mixture of exponentials.

Original language | English |
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Publisher | s.n. |
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Number of pages | 23 |
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Publication status | Published - 2013 |
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Name | arXiv.org |
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Volume | 1310.8114 [math.PR] |
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