Concepedia

Insensitivity of blocking probabilities in a circuit-switching network

David Y. Burman, John P. Lehoczky, Y. M. Lim

Journal of Applied Probability · 1984 · 171 citations · 10 references

TL;DR

A circuit‑switching network consists of nodes connected by links that contain multiple channels; calls seize a route of channels for a random duration and are blocked if no channel is available, and for exponential call holding times Erlang showed that steady‑state blocking probabilities have a product form. This paper extends Erlang’s result to general networks with a unique route between each node pair, showing that blocking probabilities remain in product form. The authors analyze general networks with unique routes and derive that blocking probabilities are product‑form and depend only on the mean call duration. Blocking probabilities are product‑form and insensitive to the call holding‑time distribution, depending only on its mean.

Abstract

Consider a network of nodes (switches) and connecting links. Each link consists of a group of channels (trunks). A call instantaneously seizes channels along a route between the originating and terminating node, holds them for a randomly distributed length of time and frees them instantaneously at the end of the call. If no channels are available, the call is blocked. For special networks with exponential call holding times, Erlang has shown that the steady-state probabilities are in product form. In this paper, we extend this work to general networks and show that if for each pair of nodes there is a unique route, then the blocking probabilities are in product form and are insensitive to the call holding-time distribution, which means that they depend on the call duration only through its mean.