17,822 research outputs found
Structure-Aware Stochastic Control for Transmission Scheduling
In this paper, we consider the problem of real-time transmission scheduling
over time-varying channels. We first formulate the transmission scheduling
problem as a Markov decision process (MDP) and systematically unravel the
structural properties (e.g. concavity in the state-value function and
monotonicity in the optimal scheduling policy) exhibited by the optimal
solutions. We then propose an online learning algorithm which preserves these
structural properties and achieves -optimal solutions for an arbitrarily small
. The advantages of the proposed online method are that: (i) it does not
require a priori knowledge of the traffic arrival and channel statistics and
(ii) it adaptively approximates the state-value functions using piece-wise
linear functions and has low storage and computation complexity. We also extend
the proposed low-complexity online learning solution to the prioritized data
transmission. The simulation results demonstrate that the proposed method
achieves significantly better utility (or delay)-energy trade-offs when
comparing to existing state-of-art online optimization methods.Comment: 41page
Optimal Routing for Delay-Sensitive Traffic in Overlay Networks
We design dynamic routing policies for an overlay network which meet delay
requirements of real-time traffic being served on top of an underlying legacy
network, where the overlay nodes do not know the underlay characteristics. We
pose the problem as a constrained MDP, and show that when the underlay
implements static policies such as FIFO with randomized routing, then a
decentralized policy, that can be computed efficiently in a distributed
fashion, is optimal. Our algorithm utilizes multi-timescale stochastic
approximation techniques, and its convergence relies on the fact that the
recursions asymptotically track a nonlinear differential equation, namely the
replicator equation. Extensive simulations show that the proposed policy indeed
outperforms the existing policies
Structured Optimal Transmission Control in Network-coded Two-way Relay Channels
This paper considers a transmission control problem in network-coded two-way
relay channels (NC-TWRC), where the relay buffers random symbol arrivals from
two users, and the channels are assumed to be fading. The problem is modeled by
a discounted infinite horizon Markov decision process (MDP). The objective is
to find a transmission control policy that minimizes the symbol delay, buffer
overflow and transmission power consumption and error rate simultaneously and
in the long run. By using the concepts of submodularity, multimodularity and
L-natural convexity, we study the structure of the optimal policy searched by
dynamic programming (DP) algorithm. We show that the optimal transmission
policy is nondecreasing in queue occupancies or/and channel states under
certain conditions such as the chosen values of parameters in the MDP model,
channel modeling method, modulation scheme and the preservation of stochastic
dominance in the transitions of system states. The results derived in this
paper can be used to relieve the high complexity of DP and facilitate real-time
control.Comment: 32 page
Opportunities for Network Coding: To Wait or Not to Wait
It has been well established that wireless network coding can significantly
improve the efficiency of multi-hop wireless networks. However, in a stochastic
environment some of the packets might not have coding pairs, which limits the
number of available coding opportunities. In this context, an important
decision is whether to delay packet transmission in hope that a coding pair
will be available in the future or transmit a packet without coding. The paper
addresses this problem by formulating a stochastic dynamic program whose
objective is to minimize the long-run average cost per unit time incurred due
to transmissions and delays. In particular, we identify optimal control actions
that would balance between costs of transmission against the costs incurred due
to the delays. Moreover, we seek to address a crucial question: what should be
observed as the state of the system? We analytically show that observing queue
lengths suffices if the system can be modeled as a Markov decision process. We
also show that a stationary threshold type policy based on queue lengths is
optimal. We further substantiate our results with simulation experiments for
more generalized settings.Comment: 14 pages, journal version of arXiv:1105.4143v1, submitted to IEEE/ACM
Transaction on Networkin
A -Rule for Service Resource Allocation in Group-Server Queues
In this paper, we study a dynamic on/off server scheduling problem in a
queueing system with multi-class servers, where servers are heterogeneous and
can be classified into groups. Servers in the same group are homogeneous. A
scheduling policy determines the number of working servers (servers that are
turned on) in each group at every state (number of customers in the
system). Our goal is to find the optimal scheduling policy to minimize the
long-run average cost, which consists of an increasing convex holding cost and
a linear operating cost. We use the sensitivity-based optimization theory to
characterize the optimal policy. A necessary and sufficient condition of the
optimal policy is derived. We also prove that the optimal policy has monotone
structures and a quasi bang-bang control is optimal. We find that the optimal
policy is indexed by the value of , where is the operating
cost rate, is the service rate for a server, and is a computable
quantity called perturbation realization factor. Specifically, the group with
smaller negative is more preferred to be turned on, while the
group with positive should be turned off. However, the
preference ranking of each group is affected by and the preference order
may change with the state , the arrival rate, and the cost function. Under a
reasonable condition of scale economies, we further prove that the optimal
policy obeys a so-called /-rule. That is, the servers with smaller
/ should be turned on with higher priority and the preference order of
groups remains unchanged. This rule can be viewed as a sister version of the
famous -rule for polling queues. With the monotone property of , we
further prove that the optimal policy has a multi-threshold structure when the
/-rule is applied.Comment: 55 pages, 11 figures, present an optimal rule called -rule
which can be viewed as a sister version of the famous -rule in queueing
theor
Optimal Policies for Status Update Generation in a Wireless System with Heterogeneous Traffic
A large body of applications that involve monitoring, decision making, and
forecasting require timely status updates for their efficient operation. Age of
Information (AoI) is a newly proposed metric that effectively captures this
requirement. Recent research on the subject has derived AoI optimal policies
for the generation of status updates and AoI optimal packet queueing
disciplines. Unlike previous research we focus on low-end devices that
typically support monitoring applications in the context of the Internet of
Things. We acknowledge that these devices host a diverse set of applications
some of which are AoI sensitive while others are not. Furthermore, due to their
limited computational resources they typically utilize a simple First-In
First-Out (FIFO) queueing discipline. We consider the problem of optimally
controlling the status update generation process for a system with a
source-destination pair that communicates via a wireless link, whereby the
source node is comprised of a FIFO queue and two applications, one that is AoI
sensitive and one that is not. We formulate this problem as a dynamic
programming problem and utilize the framework of Markov Decision Processes to
derive optimal policies for the generation of status update packets. Due to the
lack of comparable methods in the literature, we compare the derived optimal
policies against baseline policies, such as the zero-wait policy, and
investigate the performance of all policies for a variety of network
configurations. Results indicate that existing status update policies fail to
capture the trade-off between frequent generation of status updates and
queueing delay and thus perform poorly
The Value of Service Rate Flexibility in an M/M/1 Queue with Admission Control
We consider a single server queueing system with admission control and the
possibility to switch dynamically between a low and a high service rate, and
examine the benefit of this service rate flexibility. We formulate a discounted
Markov Decision Process model for the problem of joint admission and service
control, and show that the optimal policy has a threshold structure for both
controls. Regarding the benefit due to flexibility, we show that it is
increasing in system congestion, and that its effect on the admission policy is
to increase the admission threshold. We also derive a simple approximate
condition between the admission reward and the relative cost of service rate
increase, so that the service rate flexibility is beneficial. We finally show
that the results extend to the expected average reward case
Load balancing with heterogeneous schedulers
Load balancing is a common approach in web server farms or inventory routing
problems. An important issue in such systems is to determine the server to
which an incoming request should be routed to optimize a given performance
criteria. In this paper, we assume the server's scheduling disciplines to be
heterogeneous. More precisely, a server implements a scheduling discipline
which belongs to the class of limited processor sharing (LPS-) scheduling
disciplines. Under LPS-, up to jobs can be served simultaneously, and
hence, includes as special cases First Come First Served () and Processor
Sharing ().
In order to obtain efficient heuristics, we model the above load-balancing
framework as a multi-armed restless bandit problem. Using the relaxation
technique, as first developed in the seminal work of Whittle, we derive
Whittle's index policy for general cost functions and obtain a closed-form
expression for Whittle's index in terms of the steady-state distribution.
Through numerical computations, we investigate the performance of Whittle's
index with two different performance criteria: linear cost criterion and a cost
criterion that depends on the first and second moment of the throughput. Our
results show that \emph{(i)} the structure of Whittle's index policy can
strongly depend on the scheduling discipline implemented in the server, i.e.,
on , and that \emph{(ii)} Whittle's index policy significantly outperforms
standard dispatching rules such as Join the Shortest Queue (JSQ), Join the
Shortest Expected Workload (JSEW), and Random Server allocation (RSA)
Channels, Remote Estimation and Queueing Systems With A Utilization-Dependent Component: A Unifying Survey Of Recent Results
In this article, we survey the main models, techniques, concepts, and results
centered on the design and performance evaluation of engineered systems that
rely on a utilization-dependent component (UDC) whose operation may depend on
its usage history or assigned workload. Specifically, we report on research
themes concentrating on the characterization of the capacity of channels and
the design with performance guarantees of remote estimation and queueing
systems. Causes for the dependency of a UDC on past utilization include the use
of replenishable energy sources to power the transmission of information among
the sub-components of a networked system, and the assistance of a human
operator for servicing a queue. Our analysis unveils the similarity of the UDC
models typically adopted in each of the research themes, and it reveals the
differences in the objectives and technical approaches employed. We also
identify new challenges and future research directions inspired by the
cross-pollination among the central concepts, techniques, and problem
formulations of the research themes discussed
Delay Optimal Scheduling of Arbitrarily Bursty Traffic over Multi-State Time-Varying Channels
In this paper, we study joint queue-aware and channel-aware scheduling of
arbitrarily bursty traffic over multi-state time-varying channels, where the
bursty packet arrival in the network layer, the backlogged queue in the data
link layer, and the power adaptive transmission with fixed modulation in the
physical layer are jointly considered from a cross-layer perspective. To
achieve minimum queueing delay given a power constraint, a probabilistic
cross-layer scheduling policy is proposed, and characterized by a Markov chain
model. To describe the delay-power tradeoff, we formulate a non-linear
optimization problem, which however is very challenging to solve. To handle
with this issue, we convert the optimization problem into an equivalent Linear
Programming (LP) problem, which allows us to obtain the optimal threshold-based
scheduling policy with an optimal threshold imposed on the queue length in
accordance with each channel state.Comment: 6 pages, conferenc
- …