4 research outputs found
Global attraction of ODE-based mean field models with hyperexponential job sizes
Mean field modeling is a popular approach to assess the performance of large
scale computer systems. The evolution of many mean field models is
characterized by a set of ordinary differential equations that have a unique
fixed point. In order to prove that this unique fixed point corresponds to the
limit of the stationary measures of the finite systems, the unique fixed point
must be a global attractor. While global attraction was established for various
systems in case of exponential job sizes, it is often unclear whether these
proof techniques can be generalized to non-exponential job sizes. In this paper
we show how simple monotonicity arguments can be used to prove global
attraction for a broad class of ordinary differential equations that capture
the evolution of mean field models with hyperexponential job sizes. This class
includes both existing as well as previously unstudied load balancing schemes
and can be used for systems with either finite or infinite buffers. The main
novelty of the approach exists in using a Coxian representation for the
hyperexponential job sizes and a partial order that is stronger than the
componentwise partial order used in the exponential case.Comment: This paper was accepted at ACM Sigmetrics 201
Steady-State Analysis of Load Balancing with Coxian- Distributed Service Times
This paper studies load balancing for many-server ( servers) systems. Each
server has a buffer of size and can have at most one job in service and
jobs in the buffer. The service time of a job follows the Coxian-2
distribution. We focus on steady-state performance of load balancing policies
in the heavy traffic regime such that the normalized load of system is for We identify a set of policies that
achieve asymptotic zero waiting. The set of policies include several classical
policies such as join-the-shortest-queue (JSQ), join-the-idle-queue (JIQ),
idle-one-first (I1F) and power-of--choices (Po) with . The proof of the main result is based on Stein's method and state space
collapse. A key technical contribution of this paper is the iterative state
space collapse approach that leads to a simple generator approximation when
applying Stein's method
On the throughput optimization in large-scale batch-processing systems
We analyse a data-processing system with clients producing jobs which are processed in batches by parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function. In practice, throughput optimization relies on numerical searches for the optimal batch size, a process that can take up to multiple days in existing commercial systems. In this paper, we model the system in terms of a closed queueing network; a standard Markovian analysis yields the optimal throughput in time. Our main contribution is a mean-field model of the system for the regime where the system size is large. We show that the mean-field model has a unique, globally attractive stationary point which can be found in closed form and which characterizes the asymptotic throughput of the system as a function of the batch size. Using this expression we find the asymptotically optimal throughput in time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes