4,931 research outputs found
Randomized Assignment of Jobs to Servers in Heterogeneous Clusters of Shared Servers for Low Delay
We consider the job assignment problem in a multi-server system consisting of
parallel processor sharing servers, categorized into ()
different types according to their processing capacity or speed. Jobs of random
sizes arrive at the system according to a Poisson process with rate . Upon each arrival, a small number of servers from each type is
sampled uniformly at random. The job is then assigned to one of the sampled
servers based on a selection rule. We propose two schemes, each corresponding
to a specific selection rule that aims at reducing the mean sojourn time of
jobs in the system.
We first show that both methods achieve the maximal stability region. We then
analyze the system operating under the proposed schemes as which
corresponds to the mean field. Our results show that asymptotic independence
among servers holds even when is finite and exchangeability holds only
within servers of the same type. We further establish the existence and
uniqueness of stationary solution of the mean field and show that the tail
distribution of server occupancy decays doubly exponentially for each server
type. When the estimates of arrival rates are not available, the proposed
schemes offer simpler alternatives to achieving lower mean sojourn time of
jobs, as shown by our numerical studies
Redundancy Scheduling with Locally Stable Compatibility Graphs
Redundancy scheduling is a popular concept to improve performance in
parallel-server systems. In the baseline scenario any job can be handled
equally well by any server, and is replicated to a fixed number of servers
selected uniformly at random. Quite often however, there may be heterogeneity
in job characteristics or server capabilities, and jobs can only be replicated
to specific servers because of affinity relations or compatibility constraints.
In order to capture such situations, we consider a scenario where jobs of
various types are replicated to different subsets of servers as prescribed by a
general compatibility graph. We exploit a product-form stationary distribution
and weak local stability conditions to establish a state space collapse in
heavy traffic. In this limiting regime, the parallel-server system with
graph-based redundancy scheduling operates as a multi-class single-server
system, achieving full resource pooling and exhibiting strong insensitivity to
the underlying compatibility constraints.Comment: 28 pages, 4 figure
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