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**On extending the scope of bounding techniques for closed queueing networks.**
*(English)*
Zbl 0659.90046

The author studies product form closed queueing networks with load dependent service rates at each node. It is well known that exact solution algorithms require complex computations to obtain performance measures. But for engineering purposes simple bounds which can be obtained at low computational expense may be sufficient. With the help of a simple algebraic technique the author obtains bounds on the cycle time and throughput. At first the case when service rates have a special form (a so-called parameterized rate function) which includes the single as well as the infinite server case is studied. Next, these results are applied to the case when service rates are non-decreasing concave functions of queue lengths. To this end each node is replaced by one or more parameterized rates nodes in such a manner that the new network can be guaranteed to bound the initial network.

Reviewer: G.Falin

### MSC:

90B22 | Queues and service in operations research |

60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |

90B10 | Deterministic network models in operations research |