Inequalities Between Time and Customer Averages for GI/G/c/K Queues

The relationship between time and customer averages for GI/G/c/K queues is studied based on the convex-order inequality between the distribution of interarrival times of customers (packets) and the exponential distribution with the same mean. It is shown that the interarrival time distribution being smaller (or larger) than an exponential distribution with respect to the convex order is a sufficient condition for the inequalities between time and customer averages. The results of this study are an extension of existing results on the inequalities between time and customer averages.