Reliable Transmission of Short Packets through Queues and Noisy Channels under Latency and Peak-Age Violation Guarantees

This work investigates the probability that the delay and the peak-age of information exceed a desired threshold in a point-to-point communication system with short information packets. The packets are generated according to a stationary memoryless Bernoulli process, placed in a single-server queue and then transmitted over a wireless channel. A variable-length stop-feedback coding scheme---a general strategy that encompasses simple automatic repetition request (ARQ) and more sophisticated hybrid ARQ techniques as special cases---is used by the transmitter to convey the information packets to the receiver. By leveraging finite-blocklength results, the delay violation and the peak-age violation probabilities are characterized without resorting to approximations based on large-deviation theory as in previous literature. Numerical results illuminate the dependence of delay and peak-age violation probability on system parameters such as the frame size and the undetected error probability, and on the chosen packet-management policy. The guidelines provided by our analysis are particularly useful for the design of low-latency ultra-reliable communication systems.Comment: To appear in IEEE journal on selected areas of communication (IEEE JSAC

Human activity modeling and Barabasi's queueing systems

It has been shown by A.-L. Barabasi that the priority based scheduling rules in single stage queuing systems (QS) generates fat tail behavior for the tasks waiting time distributions (WTD). Such fat tails are due to the waiting times of very low priority tasks which stay unserved almost forever as the task priority indices (PI) are "frozen in time" (i.e. a task priority is assigned once for all to each incoming task). Relaxing the "frozen in time" assumption, this paper studies the new dynamic behavior expected when the priority of each incoming tasks is time-dependent (i.e. "aging mechanisms" are allowed). For two class of models, namely 1) a population type model with an age structure and 2) a QS with deadlines assigned to the incoming tasks which is operated under the "earliest-deadline-first" policy, we are able to analytically extract some relevant characteristics of the the tasks waiting time distribution. As the aging mechanism ultimately assign high priority to any long waiting tasks, fat tails in the WTD cannot find their origin in the scheduling rule alone thus showing a fundamental difference between the present and the A.-L. Barabasi's class of models.Comment: 16 pages, 2 figure

Content Based Status Updates

Consider a stream of status updates generated by a source, where each update is of one of two types: high priority or ordinary (low priority). These updates are to be transmitted through a network to a monitor. However, the transmission policy of each packet depends on the type of stream it belongs to. For the low priority stream, we analyze and compare the performances of two transmission schemes: (i) Ordinary updates are served in a First-Come-First-Served (FCFS) fashion, whereas, in (ii), the ordinary updates are transmitted according to an M/G/1/1 with preemption policy. In both schemes, high priority updates are transmitted according to an M/G/1/1 with preemption policy and receive preferential treatment. An arriving priority update discards and replaces any currently-in-service high priority update, and preempts (with eventual resume for scheme (i)) any ordinary update. We model the arrival processes of the two kinds of updates, in both schemes, as independent Poisson processes. For scheme (i), we find the arrival and service rates under which the system is stable and give closed-form expressions for average peak age and a lower bound on the average age of the ordinary stream. For scheme (ii), we derive closed-form expressions for the average age and average peak age of the high priority and low priority streams. We finally show that, if the service time is exponentially distributed, the M/M/1/1 with preemption policy leads to an average age of the low priority stream higher than the one achieved using the FCFS scheme. Therefore, the M/M//1/1 with preemption policy, when applied on the low priority stream of updates and in the presence of a higher priority scheme, is not anymore the optimal transmission policy from an age point of view

Perfect and Nearly Perfect Sampling of Work-conserving Queues

We present sampling-based methods to treat work-conserving queueing systems. A variety of models are studied. Besides the First Come First Served (FCFS) queues, many efforts are putted on the accumulating priority queue (APQ), where a customer accumulates priority linearly while waiting. APQs have Poisson arrivals, multi-class customers with corresponding service durations, and single or multiple servers. Perfect sampling is an approach to draw a sample directly from the steady-state distribution of a Markov chain without explicitly solving for it. Statistical inference can be conducted without initialization bias. If an error can be tolerated within some limit, i.e. the total variation distance between the simulated draw and the stationary distribution can be bounded by a specified number, then we get a so called nearly perfect sampling. Coupling from the past (CFTP) is one approach to perfect sampling, but it usually requires a bounded state space. One strategy for perfect sampling on unbounded state spaces relies on construction of a reversible dominating process. If only the dominating property is guaranteed, then regenerative method (RM) becomes an alternative choice. In the case where neither the reversibility nor dominance hold, a nearly perfect sampling method will be proposed. It is a variant of dominated CFTP that we call the CFTP Block Absorption (CFTP-BA) method. Time-varying queues with periodic Poisson arrivals are being considered in this thesis. It has been shown that a particular limiting distribution can be obtained for each point in time in the periodic cycle. Because there are no analytical solutions in closed forms, we explore perfect (or nearly perfect) sampling of these systems