We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered by their speed, and arriving customers join the fastest idle server. A capacity allocation is an infinite sequence of service rates. We study the probabilistic properties of this system by considering overflows from sub-systems with a finite number of servers. Several stability measures are suggested and ana-lyzed. The tail of the series of service rates that minimizes the average expected delay (service time) is shown to be approximately geometrically decreasing. We use this property to ap-proximate the optimal allocation of service rates by constructing an appropriate dynamic program.
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History: Former designation of this paper was SSY-2017-528. Open Access Statement: This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to copy, distribute, transmit and adapt this work, but you must attribute this work as “Stochastic Systems. Copyright © 2019 The Author(s). https://doi.org/10.1287/stsy.2018.0020, used under a Creative Commons Attribution License: https://creativecommons.org/licenses/by/4.0/.” Funding: This research was supported by the Israel Science Foundation [Grant 355/15].
© 2019 The Author(s).
- capacity allocation
- heterogeneous servers
- infinite state dynamic programming
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty
- Management Science and Operations Research