3,153 research outputs found
Index Policies for Optimal Mean-Variance Trade-Off of Inter-delivery Times in Real-Time Sensor Networks
A problem of much current practical interest is the replacement of the wiring
infrastructure connecting approximately 200 sensor and actuator nodes in
automobiles by an access point. This is motivated by the considerable savings
in automobile weight, simplification of manufacturability, and future
upgradability.
A key issue is how to schedule the nodes on the shared access point so as to
provide regular packet delivery. In this and other similar applications, the
mean of the inter-delivery times of packets, i.e., throughput, is not
sufficient to guarantee service-regularity. The time-averaged variance of the
inter-delivery times of packets is also an important metric.
So motivated, we consider a wireless network where an Access Point schedules
real-time generated packets to nodes over a fading wireless channel. We are
interested in designing simple policies which achieve optimal mean-variance
tradeoff in interdelivery times of packets by minimizing the sum of
time-averaged means and variances over all clients. Our goal is to explore the
full range of the Pareto frontier of all weighted linear combinations of mean
and variance so that one can fully exploit the design possibilities. We
transform this problem into a Markov decision process and show that the problem
of choosing which node's packet to transmit in each slot can be formulated as a
bandit problem. We establish that this problem is indexable and explicitly
derive the Whittle indices. The resulting Index policy is optimal in certain
cases. We also provide upper and lower bounds on the cost for any policy.
Extensive simulations show that Index policies perform better than previously
proposed policies
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
Three Puzzles on Mathematics, Computation, and Games
In this lecture I will talk about three mathematical puzzles involving
mathematics and computation that have preoccupied me over the years. The first
puzzle is to understand the amazing success of the simplex algorithm for linear
programming. The second puzzle is about errors made when votes are counted
during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure
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