Query-based sampling has become an increasingly popular technique for monitoring Markov sources in pull-based update systems. However, most of the contemporary literature on this assumes an exponential distribution for query delay and often relies on the assumption that the feedback or replies to the queries are instantaneous. In this work, we relax both of these assumptions and find optimal sampling policies for monitoring continuous-time Markov chains (CTMC) under generic delay distributions. In particular, we show that one can obtain significant gains in terms of mean binary freshness (MBF) by employing a waiting based strategy for query-based sampling.

In recent literature, when modeling for information freshness in remote estimation settings, estimators have been mainly restricted to the class of martingale estimators, meaning the remote estimate at any time is equal to the most recently received update. This is mainly due to its simplicity and ease of analysis. However, these martingale estimators are far from optimal in some cases, especially in pull-based update systems. For such systems, maximum aposteriori probability (MAP) estimators are optimum, but can be challenging to analyze. Here, we introduce a new class of estimators, called structured estimators, which retain useful characteristics from a MAP estimate while still being analytically tractable. Our proposed estimators move seamlessly from a martingale estimator to a MAP estimator.

We develop a novel source coding strategy for sampling and monitoring of a Wiener process. For the encoding process, we employ a four level “quantization” scheme, which employs monotone function thresholds as opposed to fixed constant thresholds. Leveraging the hitting times of the Wiener process with these thresholds, we devise a sampling and encoding strategy which does not incur any quantization errors. We give analytical expressions for the mean squared error (MSE) and find the optimal source code lengths to minimize the MSE under this monotone function threshold scheme, subject to a sampling rate constraint.

Use of multipath network topologies has become a prominent technique to assert timeliness in terms of Age of Information (AoI) and to improve resilience to link disruptions in communication systems. However, establishing multiple dedicated communication links among network nodes is a costly endeavor. Therefore, quite often, these secondary communication links are shared among multiple entities. Moreover, these multipath networks come with the added challenge of out-of-order transmissions. In this article, we study an amalgamation of the above two aspects, i.e., multipath transmissions and link sharing. In contrast to the existing literature where the main focus has been scheduling multiple sources on a single shared server, we delve into the realm where each source sharing the shared server is also supplemented with its dedicated server so as to improve its timeliness. In this multipath link sharing setting with generate-at-will transmissions, we first present the optimal probabilistic scheduler, and then propose several heuristic-based cyclic scheduling algorithms for the shared server, to minimize the weighted average AoI of the sources.

In many federated learning (FL) models, a common strategy employed to ensure the progress in the training process, is to wait for at least M clients out of the total N clients to send back their local gradients based on a reporting deadline T, once the parameter server (PS) has broadcasted the global model. If enough clients do not report back within the deadline, the particular round is considered to be a failed round and the training round is restarted from scratch. If enough clients have responded back, the round is deemed successful and the local gradients of all the clients that responded back are used to update the global model. In either case, the clients that failed to report back an update within the deadline would have wasted their computational resources. Having a tighter deadline (small T) and waiting for a larger number of participating clients (large M) leads to a large number of failed rounds and therefore greater communication cost and computation resource wastage. However, having a larger T leads to longer round durations whereas smaller M may lead to noisy gradients. Therefore, there is a need to optimize the parameters M and T such that communication cost and the resource wastage is minimized while having an acceptable convergence rate. In this regard, we show that the average age of a client at the PS appears explicitly in the theoretical convergence bound, and therefore, can be used as a metric to quantify the convergence of the global model. We provide an analytical scheme to select the parameters M and T in this setting.

In many existing communication models, the channel state (i.e., busy or idle) is conveyed to the sampler via ACKs which are often assumed to be instantaneous. Previous literature shows that in this ideal feedback setting, an optimal sampling policy that minimizes the age of information (AoI), should not sample when the channel is busy, and therefore, must always wait for the ACK of the previous sample before taking the next sample. However, this may not be optimal when the feedback channel (backward channel) has a random delay. In this work, we study the structure of the optimal sampling policy to minimize the AoI when the channel state (forward channel state) is not immediately perceived by the sampler due to random delays in the feedback channel. In this setting, we show that it is not always optimal to wait for ACKs before sampling, and thus,early samplingwith the available channel state information may be better. We show that, under certain conditions on the distribution of the ACK delays, the (asymptotically) optimal sampling policy reduces to a mixture of two threshold policies.