Some analytical results for congestion in subscriber line modules.

*(English)*Zbl 0786.60116From the authors’ abstract: In modern telephone exchanges, subscriber lines are usually connected to the so-called subscriber line modules. These modules serve both incoming and outgoing traffic. A difference between these two types of calls lies in the fact that in the case of blocking due to all channels busy in the module, outgoing calls can be queued whereas incoming calls get busy signal and must be re-initiated in order to establish the required connection. The corresponding queueing model was discussed recently by Lederman, but only the model with losses was studied analytically. In the present contribution the authors study the model which takes into account subscriber retrials and investigate some of its properties such as existence of stationary regime, derive explicit formulas for the system characteristics, limit theorems for systems under high repetition intensity of blocked calls and limit theorems for systems under heavy traffic.

Reviewer: D.N.Shanbhag (Sheffield)

##### MSC:

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

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

90B18 | Communication networks in operations research |

##### Keywords:

retrial queues; subscriber line modules; blocking; queueing model; limit theorems for systems under heavy traffic
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\textit{Z. Khalil} et al., Queueing Syst. 10, No. 4, 381--402 (1992; Zbl 0786.60116)

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