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The work establishes the exact performance limits of stochastic coded cachingwhen users share a bounded number of cache states, and when the associationbetween users and caches, is random. Under the premise that more balanceduser-to-cache associations perform better than unbalanced ones, our workprovides a statistical analysis of the average performance of such networks,identifying in closed form, the exact optimal average delivery time. Toinsightfully capture this delay, we derive easy to compute closed-formanalytical bounds that prove tight in the limit of a large number $\Lambda$ ofcache states. In the scenario where delivery involves $K$ users, we concludethat the multiplicative performance deterioration due to randomness -- ascompared to the well-known deterministic uniform case -- can be unbounded andcan scale as $\Theta\left( \frac{\log \Lambda}{\log \log \Lambda} \right)$ at$K=\Theta\left(\Lambda\right)$, and that this scaling vanishes when$K=\Omega\left(\Lambda\log \Lambda\right)$. To alleviate this adverse effect ofcache-load imbalance, we consider various load balancing methods, and show thatemploying proximity-bounded load balancing with an ability to choose from $h$neighboring caches, the aforementioned scaling reduces to $\Theta\left(\frac{\log(\Lambda / h)}{ \log \log(\Lambda / h)} \right)$, while whenthe proximity constraint is removed, the scaling is of a much slower order$\Theta \left( \log \log \Lambda \right)$. The above analysis is extensivelyvalidated numerically.

Fundamental Limits of Stochastic Shared Caches Networks