Abstract
We consider networks where at each node there is a single exponential server with a service rate which is a non-decreasing function of the queue length. The asymptotic profile of a sequence of networks consists of the set of persistent service rates, the limiting customer-to-node ratio, and the limiting service-rate measure. For a sequence of cyclic networks whose asymptotic profile exists, we compute upper and lower bounds for the limit points of the sequence of throughputs as functions of the limiting customer-to-node ratio. We then find conditions under which the limiting throughput exists and is expressible in terms of the asymptotic profile. Under these conditions, we determine the limiting queue-length distributions for persistent service rates. In the absence of these conditions, the limiting throughput need not exist, even for increasing sequences of cyclic networks.
Original language | English (US) |
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Pages (from-to) | 191-219 |
Number of pages | 29 |
Journal | Queueing Systems |
Volume | 58 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2008 |
Keywords
- Asymptotic queue length
- Convergence of throughput
- Cyclic networks
- Product form
- State-dependent service
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics