3,619 research outputs found
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
FCFS Parallel Service Systems and Matching Models
We consider three parallel service models in which customers of several types
are served by several types of servers subject to a bipartite compatibility
graph, and the service policy is first come first served. Two of the models
have a fixed set of servers. The first is a queueing model in which arriving
customers are assigned to the longest idling compatible server if available, or
else queue up in a single queue, and servers that become available pick the
longest waiting compatible customer, as studied by Adan and Weiss, 2014. The
second is a redundancy service model where arriving customers split into copies
that queue up at all the compatible servers, and are served in each queue on
FCFS basis, and leave the system when the first copy completes service, as
studied by Gardner et al., 2016. The third model is a matching queueing model
with a random stream of arriving servers. Arriving customers queue in a single
queue and arriving servers match with the first compatible customer and leave
immediately with the customer, or they leave without a customer. The last model
is relevant to organ transplants, to housing assignments, to adoptions and many
other situations.
We study the relations between these models, and show that they are closely
related to the FCFS infinite bipartite matching model, in which two infinite
sequences of customers and servers of several types are matched FCFS according
to a bipartite compatibility graph, as studied by Adan et al., 2017. We also
introduce a directed bipartite matching model in which we embed the queueing
systems. This leads to a generalization of Burke's theorem to parallel service
systems
Power-of-two sampling in redundancy systems:The impact of assignment constraints
A classical sampling strategy for load balancing policies is power-of-two, where any server pair is sampled with equal probability. This does not cover practical settings with assignment constraints which force non-uniform sampling. While intuition suggests that non-uniform sampling adversely impacts performance, this was only supported through simulations, and rigorous statements have remained elusive. Building on product-form distributions for redundancy systems, we prove the stochastic dominance of uniform sampling for a four-server system as well as arbitrary-size systems in light traffic.</p
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