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**Loss networks.**
*(English)*
Zbl 0743.60099

From the summary: “This paper describes work on the stochastic modelling of loss networks. Such systems have long been of interest to telephone engineers and are becoming increasingly important as models of computer and information systems. Throughout the century problems from this field have provided an impetus to the development of probability theory, pure and applied. This paper provides an introduction to the area and a review of recent work.”

After describing shortly the known exact results on loss systems as generalizations of Erlang’s loss formula and the results on insensitivity the author’s interest then is centered around the problems of large networks. “Large” is interpreted in different meanings, all leading to asymptotic results. E.g., if the network graph structure is fixed, but capacity and offered load increase, then central limit theorems are proved; or, if the network graph increases, the local structure being fixed, then similarities with problems of statistical mechanics emerge and are discussed in some detail. Another important point discussed is that of optimal routing of calls and trunc reservation.

After describing shortly the known exact results on loss systems as generalizations of Erlang’s loss formula and the results on insensitivity the author’s interest then is centered around the problems of large networks. “Large” is interpreted in different meanings, all leading to asymptotic results. E.g., if the network graph structure is fixed, but capacity and offered load increase, then central limit theorems are proved; or, if the network graph increases, the local structure being fixed, then similarities with problems of statistical mechanics emerge and are discussed in some detail. Another important point discussed is that of optimal routing of calls and trunc reservation.

Reviewer: H.Daduna (Hamburg)

### MSC:

60K25 | Queueing theory (aspects of probability theory) |

60K30 | Applications of queueing theory (congestion, allocation, storage, traffic, etc.) |

90B15 | Stochastic network models in operations research |

68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |

90B22 | Queues and service in operations research |