Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Cached Files Updating Revisited: The Distribution of Popularity-Weighted Average File Age

Version 1 : Received: 4 September 2020 / Approved: 5 September 2020 / Online: 5 September 2020 (04:22:43 CEST)

How to cite: Zhang, J. Cached Files Updating Revisited: The Distribution of Popularity-Weighted Average File Age. Preprints 2020, 2020090113 (doi: 10.20944/preprints202009.0113.v1). Zhang, J. Cached Files Updating Revisited: The Distribution of Popularity-Weighted Average File Age. Preprints 2020, 2020090113 (doi: 10.20944/preprints202009.0113.v1).

## Abstract

In this paper, using the discrete time model, we consider the average age of all files for a cached-files-updating system where a server generates N files and transmits them to a local cache. In order that the cached files are fresh, in each time slot the server updates files with certain probabilities. The age of one file or its age of information (AoI) is defined as the time the file stays in cache since it was last time sent to cache. Assume that each file in cache has corresponding request popularity. In this paper, we obtain the distribution function of the popularity-weighted average age over all files, which gives a complete description of this average age. For the random age of single file, both the mean and its distribution have been derived before by establishing a simple Markov chain. Using the same idea, we show that an N dimensional stochastic process can be constituted to characterize the changes of N file ages simultaneously. By solving the steady-state of the resulting process, we obtain the explicit expression of stationary probability for an arbitrary state-vector. Then, the distribution function of the popularity-weighted average age can be derived by mergering a proper set of stationary probabilities. For the possible applications, the distribution function can be utilized to calculate the probability that the average age violates certain statistical guarantee.

## Keywords

age of information; cached files updating; stationary distribution; discrete time model

## Subject

ENGINEERING, Control & Systems Engineering

Views 0
Metrics 0