12 research outputs found
A Dynamic Jamming Game for Real-Time Status Updates
We study timely status updates of a real-time system in an adversarial
setting. The system samples a physical process, and sends the samples from the
source (e.g., a sensor) to the destination (e.g, a control center) through a
channel. For real-time monitoring/control tasks, it is crucial for the system
to update the status of the physical process "timely". We measure the
timeliness of status updates by the time elapsed since the latest update at the
destination was generated at the source, and define the time elapsed as age of
information, or age in short. To sabotage the system, an attacker aims to
maximize the age by jamming the channel and hence causing delay in status
updates. The system aims to minimize the age by judiciously choosing when to
sample and send the updates. We model the ongoing repeated interaction between
the attacker and the system as a dynamic game. In each stage game, the attacker
chooses the jamming time according to the jamming time distribution, and the
system responds by delaying the sampling according to the sampling policy. We
prove that there exists a unique stationary equilibrium in the game, and
provide a complete analytical characterization of the equilibrium. Our results
shed lights on how the attacker sabotages the system and how the system should
defend against the attacker.Comment: 7 pages, 3 figures, INFOCOM 2018 Workshop on Age of Informatio
How to Price Fresh Data
We introduce the concept of a fresh data market, in which a destination user
requests, and pays for, fresh data updates from a source provider. Data
freshness is captured by the {\it age of information} (AoI) metric, defined as
the time elapsed since the latest update has reached the destination. The
source incurs an operational cost, modeled as an increasing convex function of
the number of updates. The destination incurs an age-related cost, modeled as
an increasing convex function of the AoI. The source charges the destination
for each update and designs a pricing mechanism to maximize its profit; the
destination on the other hand chooses a data update schedule to minimize the
summation of its payments to the source and its age-related cost. The
interaction among the source and destination is hence game-theoretic. Motivated
by the existing pricing literature, we first study a time-dependent pricing
scheme, in which the price for each update depends on when it is requested. We
show in this case that the game equilibrium leads to only one data update,
which does not yield the maximum profit to the source. This motivates us to
consider a quantity-based pricing scheme, in which the price of each update
depends on how many updates have been previously requested. We show that among
all pricing schemes in which the price of an update may vary according to both
time and quantity, the quantity-based pricing scheme performs best: it
maximizes the source's profit and minimizes the social cost of the system,
defined as the aggregate source's operational cost and the destination's
age-related cost. Numerical results show that the optimal quantity-based
pricing can be 27% more profitable for the source and incurs 54% less social
cost, compared with the optimal time-dependent pricing.Comment: to appear in WiOpt 201
Secure Status Updates under Eavesdropping: Age of Information-based Physical Layer Security Metrics
This letter studies the problem of maintaining information freshness under
passive eavesdropping attacks. The classical three-node wiretap channel model
is considered, in which a source aims to send its latest status wirelessly to
its intended destination, while protecting the message from being overheard by
an eavesdropper. Considering that conventional channel capacity-based secrecy
metrics are no longer adequate to measure the information timeliness in status
update systems, we define two new age of information-based metrics to
characterize the secrecy performance of the considered system. We further
propose, analyze, and optimize a randomized stationary transmission policy
implemented at the source for further enhancing the secrecy performance.
Simulation results are provided to validate our analysis and optimization.Comment: Submitted for possible publication. The first two authors contributed
equally to this wor
A Non-Cooperative Multiple Access Game for Timely Updates
We consider a network of selfish nodes that would like to minimize the age of
their updates at the other nodes. The nodes send their updates over a shared
spectrum using a CSMA/CA based access mechanism. We model the resulting
competition as a non-cooperative one-shot multiple access game and investigate
equilibrium strategies for two distinct medium access settings (a) collisions
are shorter than successful transmissions and (b) collisions are longer. We
investigate competition in a CSMA/CA slot, where a node may choose to transmit
or stay idle. We find that medium access settings exert strong incentive
effects on the nodes. We show that when collisions are shorter, transmit is a
weakly dominant strategy. This leads to all nodes transmitting in the CSMA/CA
slot, therefore guaranteeing a collision. In contrast, when collisions are
longer, no weakly dominant strategy exists and under certain conditions on the
ages at the beginning of the slot, we derive the mixed strategy Nash
equilibrium
Coexistence of Age and Throughput Optimizing Networks: A Game Theoretic Approach
Real-time monitoring applications have Internet-of-Things (IoT) devices sense
and communicate information (status updates) to a monitoring facility. Such
applications desire the status updates available at the monitor to be fresh and
would like to minimize the age of delivered updates. Networks of such devices
may share wireless spectrum with WiFi networks. Often, they use a CSMA/CA based
medium access similar to WiFi. However, unlike them, a WiFi network would like
to provide high throughputs for its users. We model the coexistence of such
networks as a repeated game with two players, an age optimizing network (AON)
and a throughput optimizing network (TON), where an AON aims to minimize the
age of updates and a TON seeks to maximize throughput. We define the stage
game, parameterized by the average age of the AON at the beginning of the
stage, and derive its mixed strategy Nash equilibrium (MSNE). We study the
evolution of the equilibrium strategies over time, when players play the MSNE
in each stage, and the resulting average discounted payoffs of the networks. It
turns out that it is more favorable for a TON to share spectrum with an AON in
comparison to sharing with another TON. The key to this lies in the MSNE
strategy of the AON that occasionally refrains all its nodes from transmitting
during a stage. Such stages allow the TON competition free access to the
medium
Sampling for Remote Estimation through Queues: Age of Information and Beyond
The age of information, as a metric for evaluating information freshness, has
received a lot of attention. Recently, an interesting connection between the
age of information and remote estimation error was found in a sampling problem
of Wiener processes: If the sampler has no knowledge of the signal being
sampled, the optimal sampling strategy is to minimize the age of information;
however, by exploiting causal knowledge of the signal values, it is possible to
achieve a smaller estimation error. In this paper, we extend a previous study
by investigating a problem of sampling a stationary Gauss-Markov process,
namely the Ornstein-Uhlenbeck (OU) process. The optimal sampling problem is
formulated as a constrained continuous-time Markov decision process (MDP) with
an uncountable state space. We provide an exact solution to this MDP: The
optimal sampling policy is a threshold policy on instantaneous estimation error
and the threshold is found. Further, if the sampler has no knowledge of the OU
process, the optimal sampling problem reduces to an MDP for minimizing a
nonlinear age of information metric. The age-optimal sampling policy is a
threshold policy on expected estimation error and the threshold is found. These
results hold for (i) general service time distributions of the queueing server
and (ii) sampling problems both with and without a sampling rate constraint.
Numerical results are provided to compare different sampling policies.Comment: 21 pages, 10 figures. This document has been submitted in IEEE/ACM
Transactions on Networkin
Sampling for Data Freshness Optimization: Non-linear Age Functions
In this paper, we study how to take samples at a data source for improving
the freshness of received data samples at a remote receiver. We use non-linear
functions of the age of information to measure data freshness, and provide a
survey of non-linear age functions and their applications. The sampler design
problem is studied to optimize these data freshness metrics, even when there is
a sampling rate constraint. This sampling problem is formulated as a
constrained Markov decision process (MDP) with a possibly uncountable state
space. We present a complete characterization of the optimal solution to this
MDP: The optimal sampling policy is a deterministic or randomized threshold
policy, where the threshold and the randomization probabilities are
characterized based on the optimal objective value of the MDP and the sampling
rate constraint. The optimal sampling policy can be computed by bisection
search, and the curse of dimensionality is circumvented. These age optimality
results hold for (i) general data freshness metrics represented by monotonic
functions of the age of information, (ii) general service time distributions of
the queueing server, (iii) both continuoustime and discrete-time sampling
problems, and (iv) sampling problems both with and without the sampling rate
constraint. Numerical results suggest that the optimal sampling policies can be
much better than zero-wait sampling and the classic uniform sampling
The Age of Information in Networks: Moments, Distributions, and Sampling
A source provides status updates to monitors through a network with state
defined by a continuous-time finite Markov chain. An age of information (AoI)
metric is used to characterize timeliness by the vector of ages tracked by the
monitors. Based on a stochastic hybrid systems (SHS) approach, first order
linear differential equations are derived for the temporal evolution of both
the moments and the moment generating function (MGF) of the age vector
components. It is shown that the existence of a non-negative fixed point for
the first moment is sufficient to guarantee convergence of all higher order
moments as well as a region of convergence for the stationary MGF vector of the
age. The stationary MGF vector is then found for the age on a line network of
preemptive memoryless servers. From this MGF, it is found that the age at a
node is identical in distribution to the sum of independent exponential service
times. This observation is then generalized to linear status sampling networks
in which each node receives samples of the update process at each preceding
node according to a renewal point process. For each node in the line, the age
is shown to be identical in distribution to a sum of independent renewal
process age random variables.Comment: This work was presented in part at the 2018 IEEE Infocom Age of
Information Workshop. This version will be (more or less) the same as what
will appear in the IEEE Transactions on Information Theory. This work was
supported by NSF award 171704
Minimizing Age of Information in Cognitive Radio-based IoT Systems: Underlay or Overlay?
We consider a cognitive radio-based Internet-of-Things (CR-IoT) network
consisting of one primary IoT (PIoT) system and one secondary IoT (SIoT)
system. The IoT devices of both the PIoT and the SIoT respectively monitor one
physical process and send randomly generated status updates to their associated
access points (APs). The timeliness of the status updates is important as the
systems are interested in the latest condition (e.g., temperature, speed and
position) of the IoT device. In this context, two natural questions arise: (1)
How to characterize the timeliness of the status updates in CR-IoT systems? (2)
Which scheme, overlay or underlay, is better in terms of the timeliness of the
status updates. To answer these two questions, we adopt a new performance
metric, named the age of information (AoI). We analyze the average peak AoI of
the PIoT and the SIoT for overlay and underlay schemes, respectively. Simple
asymptotic expressions of the average peak AoI are also derived when the PIoT
operates at high signal-to-noise ratio (SNR). Based on the asymptotic
expressions, we characterize a critical generation rate of the PIoT system,
which can determine the superiority of overlay and underlay schemes in terms of
the average peak AoI of the SIoT. Numerical results validate the theoretical
analysis and uncover that the overlay and underlay schemes can outperform each
other in terms of the average peak AoI of the SIoT for different system setups
Coexistence of Age and Throughput Optimizing Networks: A Spectrum Sharing Game
We investigate the coexistence of an age optimizing network (AON) and a
throughput optimizing network (TON) that share a common spectrum band. We
consider two modes of long run coexistence: (a) networks compete with each
other for spectrum access, causing them to interfere and (b) networks cooperate
to achieve non-interfering access.
To model competition, we define a non-cooperative stage game parameterized by
the average age of the AON at the beginning of the stage, derive its mixed
strategy Nash equilibrium (MSNE), and analyze the evolution of age and
throughput over an infinitely repeated game in which each network plays the
MSNE at every stage. Cooperation uses a coordination device that performs a
coin toss during each stage to select the network that must access the medium.
Networks use the grim trigger punishment strategy, reverting to playing the
MSNE every stage forever if the other disobeys the device. We determine if
there exists a subgame perfect equilibrium, i.e., the networks obey the device
forever as they find cooperation beneficial. We show that networks choose to
cooperate only when they consist of a sufficiently small number of nodes,
otherwise they prefer to disobey the device and compete