Allocation Problem in Remote Teleoperation: Online Matching with Offline Reusable Resources and Delayed Assignments

Many applications where tasks should be assigned to agents can be modeled as matching in bipartite graphs. In this paper, we consider applications where tasks arrive dynamically and rejection of a task may have significant adverse effects on the requester, therefore performing the task with some delay is preferred over complete rejection. The performance time of a task depends on the task, the agent, and the assignment, and only its distribution is known in advance. The actual time is known only after the task performance when the agent is available for a new assignment. We consider such applications to be one of two arrival types. With the first type, the arrival distribution is known in advance, while there is no assumption about the arrival times and order with the second type. For the first type, we present an LP-based online algorithm with a competitive ratio of 0.5. For the second type, we show no online algorithm with a constant competitive ratio. We run extensive experiments to evaluate our algorithm in a real-world dataset, demonstrating the advantages of the LP approach.