Bundle Length Tradeoffs in Decentralized Multi-Robot Task Allocation Under Degraded Communications

Bundle length B is commonly fixed when configuring multi-task multi-robot task allocation (MRTA) algorithms. MinSum and MinMax are known to favor different task distributions, but the role of B in this objective tradeoff has not been systematically characterized. Additionally, degraded-communication evaluations also often retain settings selected under ideal communication, leaving whether nominal bundle-length tuning transfers under message loss unresolved. We examine both questions for ACBBA, PI, and HIPC across six bundle lengths in 300 paired ten-target Collaborative Visit scenarios under ideal communication and 25% Bernoulli packet loss. Under ideal communication, increasing B from 1 to 12 reduces MinSum cost by 19.0%, 23.0%, and 31.8% for ACBBA, PI, and HIPC, respectively, while increasing MinMax cost by 45.6%, 94.3%, and 67.6%. Under packet loss, the lowest-mean MinSum setting shifts from B = 12 to B = 2 for ACBBA and PI. Repeated paired cross-fitting shows that retaining the ideal-network setting incurs held-out MinSum penalties of 14.4% and 7.2%, respectively, and increases MinMax cost by 30.0% and 41.8% relative to the loss-conditioned MinSum setting. HIPC retains a deep MinSum operating region, while the MinMax setting remains stable for all three allocators. Experiments at two additional target loads reproduce the ACBBA and PI MinSum shifts.