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This paper discusses the use of computers in calculating the unserviceable probability of a class of telecommunication networks. The unserviceable probability for a pair of terminals in the network is derived and is so complicated that it is not feasible to calculate without the use of a computer. Under the condition that every junctor in the network has a small ratio of mean service time to mean time between failures, it is shown that the computer-aided methods available for calculating network unreliability and network blocking probability are also applicable to network unserviceable probability. For the general expression of the network unserviceable probability, no simple computer-aided method is yet known. However, no urgent need for a computer-aided method for the general expression of the network unserviceable probability is envisaged since practical networks usually have small ratios of mean service time to mean time between failures for each of its junctors.