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Large-scale Service Systems with Packing Constraints and Heterogeneous Servers

Published: 29 September 2016 Publication History

Abstract

A service system with multiple types of arriving customers and multiple types of servers is considered. Several customers (possibly of different types) can be placed for concurrent service into same server, subject to "packing" constraints, which depend on the server type. Service times of different customers are independent, even if served simultaneously by the same server. The largescale asymptotic regime is considered such that the customer arrival rates grow to infinity. We consider two variants of the model. For the infinite-server model, we prove asymptotic optimality of the Greedy Random (GRAND) algorithm in the sense of minimizing the weighted (by type) number of occupied servers in steadystate. (This version of GRAND generalizes that introduced in [1] for the homogeneous systems, with all servers of same type.) We then introduce a natural extension of GRAND algorithm for finite-server systems with blocking. Assuming subcritical system load, we prove existence, uniqueness, and local stability of the large-scale system equilibrium point such that no blocking occurs. This result strongly suggests a conjecture that the steady-state blocking probability under the algorithm vanishes in the large-scale limit.

References

[1]
A. L. Stolyar, Y. Zhong. Asymptotic optimality of a greedy randomized algorithm in a large-scale service system with general packing constraints. Queueing Systems, 2015, Vol.79, No.2, pp. 117--143.
[2]
A. L. Stolyar. Large-scale heterogeneous service systems with general packing constraints. http://arxiv.org/abs/1508.07512
[3]
Q. Xie, X. Dong, Y. Lu and R. Srikant. Power of d Choices for Large-Scale Bin Packing: A Loss Model. SIGMETRICS-2015, pp.321--334.

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 44, Issue 2
September 2016
98 pages
ISSN:0163-5999
DOI:10.1145/3003977
  • Editor:
  • Nidhi Hegde
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 29 September 2016
Published in SIGMETRICS Volume 44, Issue 2

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