Paging and Registration in Cellular Networks: Jointly Optimal Policies and an Iterative Algorithm

Hajek, Bruce; Mitzel, K.; Yang, Sichao

doi:10.1109/tit.2007.913566

Cited by 56 publications

(67 citation statements)

References 21 publications

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“…The authors in [10] make use of majorization theory and the Riesz rearrangement inequality [11] in order to arrive at this result. The proof follows a similar guideline used for a related problem that studies the joint optimization of paging and registration policies in mobile networks [12]. The analysis of the asymptotic behavior of our iterative algorithm constitutes an alternative way to prove that symmetric event-triggering laws are optimal for first-order systems.…”

Section: A Related Workmentioning

confidence: 96%

Event-Triggered State Estimation: An Iterative Algorithm and Optimality Properties

Molin

Hirche

2017

IEEE Trans. Automat. Contr.

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This paper investigates the optimal design of event-triggered estimation for linear systems. The synthesis approach is posed as a team decision problem where the decision makers are given by the event-trigger and the estimator. The event-trigger decides upon its available measurements whether the estimator shall obtain the current state information by transmitting it through a resource constrained channel. The objective is to find the optimal trade-off between the mean square estimation error and the expected number of transmissions over a finite horizon. After deriving basic characteristics of the optimal solution, we propose an iterative algorithm that alternates between optimizing one decision maker while fixing the other and vice versa. By analyzing the dynamical behavior of the iterative method, it is shown that the algorithm converges to a symmetric threshold policy for first-order systems if the statistics of the uncertainties are even and unimodal. In the case of bimodal distributions, we show numerically that the iterative method may find asymmetric threshold policies that outperform symmetric rules. Index TermsEvent-triggered state estimation, Networked control systems, Distributed decision making, Team optimality A. Molin is with the

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Section: A Related Workmentioning

confidence: 96%

Event-Triggered State Estimation: An Iterative Algorithm and Optimality Properties

Molin

Hirche

2017

IEEE Trans. Automat. Contr.

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“…The algorithm iteratively alternates between optimizing one player while fixing the other player. Similar iterative procedures are shown to be very promising methods for calculating optimal policies for team problems with non-classical information patterns, as studied by Karlsson et al [2011] for the Witsenhausen counterexample or by Hajek et al [2008] for the joint optimization of paging and registration policies. It turns out that the proposed iterative method can yield a remarkable decrease of the overall cost compared to a design where the estimator is designed separately of the event-trigger.…”

Section: Introductionmentioning

confidence: 99%

An Iterative Algorithm for Optimal Event-Triggered Estimation*

Molin

Hirche

2012

IFAC Proceedings Volumes

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This paper investigates the optimal design of event-triggered estimation for firstorder linear stochastic systems. The problem is posed as a two-player team problem with a partially nested information pattern. The two players are given by an estimator and an eventtrigger. The event-trigger has full state information and decides whether the estimator shall obtain the current state information by transmitting it through a resource constrained channel. The objective is to find an optimal trade-off between the mean squared estimation error and the expected transmission rate. The proposed iterative algorithm alternates between optimizing one player while fixing the other player. It is shown that the solution of the algorithm converges to a linear predictor and a symmetric threshold policy, if the densities of the initial state and the noise variables are even and radially decreasing functions. The effectiveness of the approach is illustrated via numerical simulations. In case of a multimodal distribution of the noise variables a significant performance improvement can be achieved compared to a separate design that assumes a linear prediction and a symmetric threshold policy.

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“…where, the above relationships follow from the properties of the majorization operator for neat distributions [14]. Hence, φ (I,d+1) φ (I,d+1) , and, this is true for all d ≥ 0.…”

Section: Approximation Of Pdfs Using Majorization Theorymentioning

confidence: 83%

Stability analysis of multiple state-based schedulers with CSMA

Ramesh

Johansson

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Abstract-In this paper, we identify sufficient conditions for Lyapunov Mean Square Stability (LMSS) of a contention-based network of first-order systems, with state-based schedulers. The stability analysis helps us to choose policies for adapting the scheduler threshold to the delay from the network and scheduler. We show that three scheduling laws can result in LMSS: constant-probability laws and additively increasing or decreasing probability laws. Our results counter the notions that increasing probability scheduling laws alone can guarantee stability of the closed-loop system, or that decreasing probability scheduling laws are required to mitigate congestion in the network.

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Paging and Registration in Cellular Networks: Jointly Optimal Policies and an Iterative Algorithm

Cited by 56 publications

References 21 publications

Event-Triggered State Estimation: An Iterative Algorithm and Optimality Properties

Event-Triggered State Estimation: An Iterative Algorithm and Optimality Properties

An Iterative Algorithm for Optimal Event-Triggered Estimation*

Stability analysis of multiple state-based schedulers with CSMA

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