On the Relationships Among Traffic Load, Capacity, and Throughput for the M/M/1/m, M/G/1/m-PS, and M/G/c/c Queues

System throughput is one of the widely used performance measures in manufacturing, communication, and service networks. Although there are exceptions, throughput of such systems typically increases with additional capacity. We investigate how this improvement in throughput depends on the traffic load. More specifically, we consider M/M/1/m , M/G/1/m-PS , and M/G/c/c queues, all of which arise in a variety of contexts. For the M/G/c/c queue, we show that throughput improvement (both nominal and relative) that would be obtained by adding an extra server is increasing in the traffic load. For the M/M/1/m and M/G/1/m-PS queues, we show that throughput improvement (both nominal and relative) that would be obtained by adding an extra buffer space is unimodal in traffic load. In particular, the relative improvement is maximized when the traffic load is one regardless of the buffer size. We also prove a new structural property for the blocking probability of the M/M/1/m and M/G/1/m-PS queues.