Abstract:
We consider large-scale service systems with several customer classes and several server pools. Mean service time of a customer depends both on the customer class and the...Show MoreMetadata
Abstract:
We consider large-scale service systems with several customer classes and several server pools. Mean service time of a customer depends both on the customer class and the server type. The routing is restricted to a fixed set of "activities," i.e. (customer-class, server-type) pairs. We assume that the bipartite graph with vertices being customer-classes and server- types, and edges being the activities, is a tree. The system behavior under a natural load balancing routing/scheduling rule, Longest-queue freest-server (LQFS-LB), is studied in both fluid-limit and Halfin-Whitt asymptotic regimes. We show that, quite surprizingly, LQFS-LB may render the system unstable in the vicinity of the equilibrium point. Such instability cannot occur in systems with "small" number of customer classes. We prove stability in one important special case.
Published in: 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Date of Conference: 28-30 September 2011
Date Added to IEEE Xplore: 02 January 2012
ISBN Information:
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- IEEE Keywords
- Index Terms
- Load Balancing ,
- Equilibrium Point ,
- Asymptotic Regime ,
- Types Of Systems ,
- Scale Parameter ,
- Stationary Distribution ,
- Postural Stability ,
- Finite Time ,
- Restricted Diffusion ,
- Service Rate ,
- Distribution Of Sequences ,
- Nominal Rate ,
- Linear Differential Equations ,
- Arrival Rate ,
- Fluid Model ,
- Input Rate ,
- Critical Load ,
- Stable Cases ,
- Submanifold ,
- Types Of Customers ,
- Local Instability ,
- Stochastic Stability ,
- Instantaneous Load ,
- Global Stability ,
- Minimum Load
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Load Balancing ,
- Equilibrium Point ,
- Asymptotic Regime ,
- Types Of Systems ,
- Scale Parameter ,
- Stationary Distribution ,
- Postural Stability ,
- Finite Time ,
- Restricted Diffusion ,
- Service Rate ,
- Distribution Of Sequences ,
- Nominal Rate ,
- Linear Differential Equations ,
- Arrival Rate ,
- Fluid Model ,
- Input Rate ,
- Critical Load ,
- Stable Cases ,
- Submanifold ,
- Types Of Customers ,
- Local Instability ,
- Stochastic Stability ,
- Instantaneous Load ,
- Global Stability ,
- Minimum Load