Abstract
We consider a Jackson network in which some of the nodes have an infinite supply of work: when all the customers queued at such a node have departed, the node will process a customer from this supply. Such nodes will be processing jobs all the time, so they will be fully utilized and experience a traffic intensity of 1. We calculate flow rates for such networks, obtain conditions for stability, and investigate the stationary distributions. Standard nodes in this network continue to have product-form distributions, while nodes with an infinite supply of work have geometric marginal distributions and Poisson inflows and outflows, but their joint distribution is not of product form.
Original language | English |
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Pages (from-to) | 879-882 |
Number of pages | 4 |
Journal | Journal of Applied Probability |
Volume | 42 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2005 |
Keywords
- Infinite virtual buffer
- Jackson network
- Queue
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty