Online Service with Delay

Yossi Azar, Arun Ganesh, Rong Ge, Debmalya Panigrahi

Research output: Contribution to journalArticlepeer-review


In this article, we introduce the online service with delay problem. In this problem, there are n points in a metric space that issue service requests over time, and there is a server that serves these requests. The goal is to minimize the sum of distance traveled by the server and the total delay (or a penalty function thereof) in serving the requests. This problem models the fundamental tradeoff between batching requests to improve locality and reducing delay to improve response time, which has many applications in operations management, operating systems, logistics, supply chain management, and scheduling. Our main result is to show a poly-logarithmic competitive ratio for the online service with delay problem. This result is obtained by an algorithm that we call the preemptive service algorithm. The salient feature of this algorithm is a process called preemptive service, which uses a novel combination of (recursive) time forwarding and spatial exploration on a metric space. We also generalize our results to k > 1 servers and obtain stronger results for special metrics such as uniform and star metrics that correspond to (weighted) paging problems.

Original languageEnglish
Article number23
JournalACM Transactions on Algorithms
Issue number3
StatePublished - Aug 2021


FundersFunder number
National Science FoundationCCF 1527084, CCF 1535972
Israel Science Foundation1506/16
Israeli Centers for Research Excellence4/11


    • Paging
    • competitive ratio
    • k-server
    • online algorithms
    • weighted paging


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