Conjecture: Constant RoE algorithms for related stochastic delay network design problems

Prove that online algorithms achieving constant ratio of expectations exist for the following problems in the Poisson arrival model: online service with delays (and k-services with delays), facility location with delays, and Steiner tree/forest with delays.

Background

In the concluding section, the authors extend their stochastic MLA perspective to a broader family of network design problems with delays. They note the conceptual proximity of online service with delays, its generalization to k-services, facility location with delays, and Steiner tree/forest with delays.

They go beyond stating an open direction by formulating a conjecture that constant ratio-of-expectations algorithms should exist for these problems under Poisson arrivals, positioning this as a natural generalization of the paper’s main contribution.