Discrete-time Queueing Model of Age of Information with Multiple Information Sources

Information freshness in IoT-based status update systems has recently been studied through the Age of Information (AoI) and Peak AoI (PAoI) performance metrics. In this paper, we study a discrete-time server arising in multi-source IoT systems which accepts incoming information packets from multiple information sources so as to be forwarded to a remote monitor for status update purposes. Under the assumption of Bernoulli information packet arrivals and a common geometric service time distribution across all the sources, we numerically obtain the exact per-source distributions of AoI and PAoI in matrix-geometric form for three different queueing disciplines: i) Non-Preemptive Bufferless (NPB) ii) Preemptive Bufferless (PB) iii) Non-Preemptive Single Buffer with Replacement (NPSBR). The proposed numerical algorithm employs the theory of Discrete-Time Markov Chains (DTMC) of Quasi-Birth-Death (QBD) type and is matrix analytical, i.e, the algorithm is based on numerically stable and efficient vector-matrix operations.Numerical examples are provided to validate the accuracy and effectiveness of the proposed queueing model. We also present a numerical example on the optimum choice of the Bernoulli parameters in a practical IoT system with two sources with diverse AoI requirements.Comment: 15 pages, 3 figure

The Multi-Source Preemptive M/PH/1/1 Queue with Packet Errors: Exact Distribution of the Age of Information and Its Peak

Age of Information (AoI) and Peak AoI (PAoI) and their analytical models have recently drawn substantial amount of attention in information theory and wireless communications disciplines, in the context of qualitative assessment of information freshness in status update systems. We take a queueing-theoretic approach and study a probabilistically preemptive bufferless $M/PH/1/1$ queueing system with arrivals stemming from $N$ separate information sources, with the aim of modeling a generic status update system. In this model, a new information packet arrival from source $m$ is allowed to preempt a packet from source $n$ in service, with a probability depending on $n$ and $m$. To make the model even more general than the existing ones, for each of the information sources, we assume a distinct PH-type service time distribution and a distinct packet error probability. Subsequently, we obtain the exact distributions of the AoI and PAoI for each of the information sources using matrix-analytical algorithms and in particular the theory of Markov fluid queues and sample path arguments. This is in contrast with existing methods that rely on Stochastic Hybrid Systems (SHS) which obtain only the average values and in less general settings. Numerical examples are provided to validate the proposed approach as well as to give engineering insight on the impact of preemption probabilities on certain AoI and PAoI performance figures.Comment: 16 pages, 6 figures, 3 table

Exact and approximate decoupling and noninteracting control problems

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1989.Thesis (Master's) -- Bilkent University, 1989.Includes bibliographical refences.In this thesis, we consider “exact” and “approximate” versions of the disturbance decoupling problem and the noninteracting control problem for linear, time-invariant systems. In the exact versions of these problems, we obtain necessary and sufficient conditions for the existence of an internally stabilizing dynamic output feedback controller such that prespecified interactions between certain sets of inputs and certain sets of outputs are annihilated in the closed-loop system. In the approximate version of these problems we require these interactions to be quenched in the ‘Hoo sense, up to any degree of accuracy. The solvability of the noninteracting control problems are shown to be equivalent to the existence of a common solution to two linear matrix equations over a principal ideal domain. A common solution to these equations exists if and only if the equations each have a solution and a bilateral matrix equation is solvable. This yields a system theoretical interpretation for the solvability of the original noninteracting control problem.Akar, NailM.S

Performance analysis of an asynchronous transfer mode multiplexer with Markov modulated inputs

Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 1993.Thesis (Ph.D.) -- Bilkent Iniversity, 1993.Includes bibliographical references leaves 108-113.Asynchronous Transfer Mode (ATM) networks have inputs which consist of superpositions of correlated cell streams. Markov modulated processes are commonly used to characterize this correlation. The first step through gaining an analytical insight in the performance issues of an ATM network is the analysis of a single channel. One objective of this study is the performance analysis of an ATM multiplexer whose input is a Markov modulated periodic arrival process. Based on the transient behavior of the nD/D/1 queue, we present an approximate method to compute the queue length distribution accurately. The method reduces to the solution of a linear differential equation with variable coefficients. Another general traffic model is the Markov Modulated Poisson Process (MMPP). We employ Pade approximations in transform domain for the deterministic service time distribution in an M MPP/D/1 queue so as to compute the distribution of the buffer occupancy. For both models, we also provide algorithms for analysis in the case of finite queue capacities and for computation of effective bandwidth.Akar, NailPh.D

Minimizing the Age of Two Heterogeneous Sources With Packet Drops Via Cyclic Schedulers

In a communication setting where multiple sources share a single channel to provide status updates to a remote monitor, source transmissions need to be scheduled appropriately to maintain timely communication between each of the sources and the monitor. We consider age-agnostic scheduling policies which are advantageous due to their simplicity of implementation. Further, we focus on a special class of age-agnostic policies, called cyclic schedulers, where each source is scheduled based on a fixed cyclic pattern. We use weighted average age of information (AoI) to quantify the timeliness of communication. We develop a Markov chain formulation to compute the exact mean AoI for the case of two-source cyclic schedulers. Based on the obtained age expression, we develop an algorithm that generates near-optimal cyclic schedulers to minimize the weighted average AoI for two heterogeneous sources, in the presence of channel errors

Modeling AoII in Push- and Pull-Based Sampling of Continuous Time Markov Chains

Age of incorrect information (AoII) has recently been proposed as an alternative to existing information freshness metrics for real-time sampling and estimation problems involving information sources that are tracked by remote monitors. Different from existing metrics, AoII penalizes the incorrect information by increasing linearly with time as long as the source and the monitor are de-synchronized, and is reset when they are synchronized back. While AoII has generally been investigated for discrete time information sources, we develop a novel analytical model in this paper for push- and pull-based sampling and transmission of a continuous time Markov chain (CTMC) process. In the pull-based model, the sensor starts transmitting information on the observed CTMC only when a pull request from the monitor is received. On the other hand, in the push-based scenario, the sensor, being aware of the AoII process, samples and transmits when the AoII process exceeds a random threshold. The proposed analytical model for both scenarios is based on the construction of a discrete time MC (DTMC) making state transitions at the embedded epochs of synchronization points, using the theory of absorbing CTMCs, and in particular phase-type distributions. For a given sampling policy, analytical models to obtain the mean AoII and the average sampling rate are developed. Numerical results are presented to validate the analytical model as well as to provide insight on optimal sampling policies under sampling rate constraints

AoII-Optimum Sampling of CTMC Information Sources Under Sampling Rate Constraints

We consider a sensor that samples an $N$-state continuous-time Markov chain (CTMC)-based information source process, and transmits the observed state of the source, to a remote monitor tasked with timely tracking of the source process. The mismatch between the source and monitor processes is quantified by age of incorrect information (AoII), which penalizes the mismatch as it stays longer, and our objective is to minimize the average AoII under an average sampling rate constraint. We assume a perfect reverse channel and hence the sensor has information of the estimate while initiating a transmission or preempting an ongoing transmission. First, by modeling the problem as an average cost constrained semi-Markov decision process (CSMDP), we show that the structure of the problem gives rise to an optimum threshold policy for which the sensor initiates a transmission once the AoII exceeds a threshold depending on the instantaneous values of both the source and monitor processes. However, due to the high complexity of obtaining the optimum policy in this general setting, we consider a relaxed problem where the thresholds are allowed to be dependent only on the estimate. We show that this relaxed problem can be solved with a novel CSMDP formulation based on the theory of absorbing MCs, with a computational complexity of $\mathcal{O}(N^4)$, allowing one to obtain optimum policies for general CTMCs with over a hundred states

Minimizing Weighted Sum Age of Information with Open-Loop Cyclic Scheduling

We study the scheduling problem in a status update system composed of an arbitrary number of information sources with different service time distributions and weights for the purpose of minimizing the weighted sum age of information (AoI). In particular, we study open-loop schedulers which rely only on the statistics (specifically, only on the first two moments) of the source service times, in contrast to closed-loop schedulers that also make use of the actual realizations of the service times and the AoI processes in making scheduling decisions. Open-loop scheduling policies can be constructed off-line and are simpler to implement compared to their closed-loop counterparts. We consider the generate-at-will (GAW) model, and develop an analytical method to calculate the exact AoI for the probabilistic and cyclic open-loop schedulers. In both cases, the server initiates the sampling of a source and the ensuing transmission of the update packet from the source to the server in an open-loop manner; either based on a certain probability (probabilistic scheme) or according to a deterministic cyclic pattern (cyclic scheme). We derive the optimum open-loop cyclic scheduling policy in closed form for the specific case of N=2 sources and propose well-performing heuristic cyclic schedulers for general number of sources, i.e., N>2. We study the proposed cyclic schedulers against probabilistic schedulers and several existing methods in the literature to validate their effectiveness.Comment: 10 pages, 5 figure