Hierarchical Caching System with Hotplug Model Using HpPDA

Caching is a method to ease the strain on the network during peak hours. Many caching approaches consider a single-layer system in which the server is connected to the users via an error-free shared link. However, in these systems, all the users involved in the placement phase must be present during the delivery phase. To address this, a hotplug model was presented, in which only some users may actually reveal their demand and be present during the delivery phase. On the other hand, a single-layered caching system was extended to the two-layered coded caching system. In this work, we consider a two-layered hierarchical system in which a server with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> files is connected to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K_{1}$</tex> mirrors and each mirror is connected to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K_{2}$</tex> users. Out of all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K_{1}K_{2}$</tex> users, only <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K^{\prime}$</tex> users are online during the delivery phase. All the mirrors and users are equipped with caches. We refer to this system as a hotplug hierarchical caching system. Here, we consider this system with the case when the cache memory of each mirror is zero, and propose a scheme using the concept of hotplug placement delivery arrays (HpPDAs).