An ND/D/1 queueing model means that N independent periodic sources are served by a single server and the packets have the same size. These models have received close attention as general queueing models in telecommunications. Both discrete models, where it is only permitted to transmit packets at fixed time instances, and also continuous models, where the time of transmission is not restricted, can be applied in the modeling. This paper provides the exact distribution of the cumulative idle time duration in such queuing systems and also proposes accurate approximation formulae for large systems. The results of this paper are of practical significance because existing approximations of the distribution of the cumulative idle time can be replaced by the proposed formulae.
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