Stability, Memory, and Messaging Trade-Offs in Heterogeneous Service Systems
Name
2007.07219.pdf
Description
Submitted version
Size
233.49 KB
Format
Adobe PDF
Checksum (MD5)
65a99d16aac30737b684563e10c55c7d
Author(s)
Gamarnik, David
Tsitsiklis, John N
Zubeldia, Martin
Date Issued
2021
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Gamarnik, David, Tsitsiklis, John N and Zubeldia, Martin. 2021. "Stability, Memory, and Messaging Trade-Offs in Heterogeneous Service Systems." Mathematics of Operations Research.
Version
Original manuscript
Abstract
We consider a heterogeneous distributed service system consisting of n servers with unknown and possibly different processing rates. Jobs with unit mean arrive as a renewal process of rate proportional to n and are immediately dispatched to one of several queues associated with the servers. We assume that the dispatching decisions are made by a central dispatcher with the ability to exchange messages with the servers and endowed with a finite memory used to store information from one decision epoch to the next, about the current state of the queues and about the service rates of the servers. We study the fundamental resource requirements (memory bits and message exchange rate) in order for a dispatching policy to be always stable. First, we present a policy that is always stable while using a positive (but arbitrarily small) message rate and [Formula: see text] bits of memory. Second, we show that within a certain broad class of policies, a dispatching policy that exchanges [Formula: see text] messages per unit of time, and with [Formula: see text] bits of memory, cannot be always stable.
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/MOOR.2021.1191
