Comparison of the loss probability of the GIX/GI/1/k queues with a common traffic intensity

The loss probabilities of the GI^X/GI/1/k queues, which means the batch arrival GI/GI/1/k queues, are compared when the queues have a common waiting capacity k, a common batch size distribution and a common traffic intensity. The paper proves that, if the interarrival time and service time distributions are NBUE (NWUE), then the loss probabilities are not greater (less) than those of the corresponding M^X/M/1/k queues. The stronger results are obtained for the M/G/1/k queues with single arrivals.