Equity-effectiveness tradeoff in the allocation of flows in closed queueing networks

Tradeoffs between multiple dimensions of performance are inherent in the allocation resources in many systems, particularly those with multiple stakeholders. This paper presents numerical results for the case of allocating flows in central-server closed queueing networks considering several inequity measures over many network configurations. These results show the conflict between server and customer perspectives of equity using multiple measures (server utilization, flow, wait time, and queue length). This paper first compares the effectiveness of the most equitable allocation for each measure relative to the most effective allocation for many network configurations. The complete efficient frontier is then generated using an optimization methodology. The results indicate that for low levels of server rate heterogeneity, all equity measures provide zero inequity allocations with high levels of effectiveness. However, as server rate heterogeneity increases, the total system effectiveness decreases and significant differences between the inequity measures are evident. In particular, the flow equity measure shows marked decreases in effectiveness relative to the other three measures. Further, inequity with respect to wait time, server utilization, and queue length can be eliminated with relatively small impact on total system throughput (i.e., system effectiveness). In contrast, reductions in inequity with respect to customer flow incur large decreases in total system throughput.