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Large-scale heterogeneous service systems with general packing constraints

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  17 March 2017

A. L. Stolyar
A. L. Stolyar*
Affiliation:
Lehigh University
*
* Current address: Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, 104 S. Mathews Avenue, Urbana, IL 61801, USA. Email address: stolyar@illinois.edu
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Abstract

A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers can also be of multiple types. Each customer has an independent, exponentially distributed service time, with the mean determined by its type. Multiple customers (possibly of different types) can be placed for service into one 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 large-scale asymptotic regime is considered such that the customer arrival rates grow to ∞. 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 steady state. (This version of GRAND generalizes that introduced by Stolyar and Zhong (2015) for homogeneous systems, with all servers of the same type.) We then introduce a natural extension of the 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.

Keywords

Queueing networkstochastic bin packingheterogeneous service systempacking constraintblockinglossgreedy random (GRAND) algorithmfluid limitcloud computing

MSC classification

Primary: 90B15: Network models, stochastic
Secondary: 60K25: Queueing theory
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 1 , March 2017 , pp. 61 - 83
Copyright
Copyright © Applied Probability Trust 2017 

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