A Markov Analysis of Selective Repeat ARQ with Variable Round Trip Time

Abstract

Many papers analyze selective repeat automatic repeat request schemes by means of a Markov chain representation for the channel and, by extension, the whole transmission system. This Markov approach precisely characterizes the queueing behavior and the statistics of several delay terms. In the vast majority of the investigations, the round-trip time of the channel, which determines the instant of reception of the feedback from the receiver, is taken as a fixed value. This letter explores the relaxation of this assumption, still framing the system within a Markov chain. The main conclusion is that the impact of a variable round trip time on the delay statistics is rather limited. The used approach can be promptly applied to any similar analysis of retransmission-based error control systems.Index Terms-Queueing analysis, automatic repeat request, Markov processes, error analysis.

Impact of Transmission Delays Over Age of Information Under Finite Horizon Scheduling

“…In particular, the most interesting future extension can be the investigation of scenarios where the transmission delay is not a pure externality, but may be, for example, connected to congestion [24], retransmissions [21] or multiple access from different sensors [4], thus leading to a joint optimization of the transmission schedule also accounting for a closed-loop interaction with the activity of the nodes.…”

“…It is however possible to combine all of these approaches, together with other non-idealities, for a more comprehensive treatment of real systems in the IoT. Similar to ARQ taxonomies [8], we can think of focusing on multiple statistics for different delay terms (e.g., including propagation, processing, retransmission), and also involve other aspects related to the accuracy of the update [33], error correlation and packet resequencing [21], as well as the costs implied for tracking them through stateful policies [22].…”

“…queueing at the buffer or delays due to congestion, which in turn depend on the presence of multiple users converging on the same node and their access discipline [18]- [20]. Finally, if status updates consist of packets that may be retransmitted over multiple attempts, following an automatic repeat request (ARQ) approach, further delay terms can be introduced, impacting AoI as argued in [21].…”

Status Update Scheduling in Remote Sensing Under Variable Activation Delay

“…This approach also addresses situations in which such delay is non-negligible but constant, as the resulting AoI at the receiver's side is simply biased by a constant offset. Conversely, if this delay is variable, it may make sense to include it and evaluate its overall impact [7], [8].…”