Timely Updating on Ber/Geo/1/2 Queue Modeled Status Updating System with Eavesdropper

We consider that the source sends packets to the receiver through a Ber/Geo/1/2 queue modeled status updating system, where the transmitted packets are subject to potential eavesdropping. Time is discretized into identical time slots. This paper studies the tradeoffs between the information freshness and transmission security of a system, where freshness is characterized by the age of information (AoI) metric and transmission security is represented by the proportion of obtained insecure packets over a long period of time. We assume that in a time slot, the source generates a new packet with probability p, and a packet arrives at the receiver with probability γd. With probability γE, a transmitted packet is eavesdropped. At the receiver, AoI is defined as the elapsed time since the generation instant of the latest obtained packet. A packet is defined to be insecure if it is obtained by the eavesdropper earlier than the receiver. To control the proportion of insecure packets obtained in the receiver, we propose using the probabilistic deletion/retaining scheme. More specifically, when a packet is eavesdropped before arriving at the receiver, this packet is deleted with probability δ or retained with probability 1-δ. Under this transmission policy, we derive the system's average AoI which we call the average δ-secure AoI, and investigate its relations with the insecure packet proportion, which is denoted as η(δ). The obtained formulas are then calculated in three special cases, including γE=0, γE=1, and δ=1. We explain that these cases correspond to the average AoI of a basic status updating system with Ber/Geo/1/2 queue, packet with random geometric deadline in service process, and average age of secure information (AoSI), respectively. Numerical simulations of obtained results are provided. In particular, the tradeoffs between average δ-secure AoI and η(δ) are analyzed in detail. We demonstrate that depending on the value of the eavesdropping probability γE, average δ-secure AoI varies in different trends with η(δ), and in most cases the average δ-secure AoI and η(δ) can be minimized simultaneously.