This paper discusses the batch arrival GX/G/1/N queue with a single server and room for only N customers. For this model two different rejection strategies are conceivable: a batch finding upon arrival not enough space in the buffer is rejected completely or the buffer is filled up and only a part of the batch is rejected. For either strategy we are interested in the rejection probabilities both for a batch and for an individual customer. Also we want to investigate the waiting-time distribution for an accepted customer. In general we cannot find analytical solutions for this model. However, by specifying the service-time distribution to be an Erlang-r distribution, a Markov-chain approach is possible and exact results can be obtained. The next step is to get approximate results for the general case via interpolation with respect to the squared coefficient of variation of the service time. The paper gives approximations for the waiting-time percentiles and for the minimal buffer space such that the rejection probability is below a prespecified level. Also numerical results are given to illustrate the quality of the approximations.
