We optimize hierarchies of Time-to-Live (TTL) caches under network delays. A TTL cache assigns individual eviction timers to cached objects that are usually refreshed upon a hit where upon a miss the object requires a random time to be fetched from a parent cache. Due to their object decoupling property, TTL caches are of particular interest since the optimization of a per-object utility enables service differentiation. However, state-of-the-art exact TTL cache utility-based optimization does not extend beyond single TTL caches, especially under network delays. In this paper, we leverage the object decoupling effect to formulate the nonlinear utility maximization problem for TTL cache hierarchies in terms of the exact object hit probability under random network delays. We iteratively solve the utility maximization problem to find the optimal per-object TTLs. In addition, we propose a variant TTL policy, which we denote as exTTL to counteract the effect on the optimal utility of the storage mismatch between the actual realization of a TTL cache and its ideal infinite storage assumption. Further, we show that the exact model suffers from tractability issues for large hierarchies and propose a machine learning approach to estimate the optimal TTL values for large systems. Finally, we provide numerical and data center trace-based evaluations for both methods, showing the significant offloading improvement due to TTL optimization considering the network delays.

Given a quantum communication system that offers a service to a distributed quantum application, we consider the problem of optimizing purification strategies for link-level entanglements with respect to the offered teleportation fidelity. We study the trade-off between the entanglement generation and purification process, which may probabilistically fail, and the fidelity decay of application qubits due to waiting in memory for ready entanglements. Given application requests for entanglements that arrive at random time points, we devise a purification strategy that takes into account the current system state and a probabilistic notion of time-dependent risk to gauge the impact on the average teleportation fidelity. Numerical results show that the optimized purification strategy performs better when compared to always pumping across a number of different regimes and that always pumping is only optimal for certain intermediate decoherence time values.

The first step for entanglement distribution among quantum communication nodes is to generate link-level Ein-stein-Podolsky-Rosen (EPR) pairs between adjacent communication nodes. EPR pairs may be continuously generated and stored in a few quantum memories to be ready for utilization by quantum applications. A major challenge is that qubits suffer from unavoidable noise due to their interaction with the environment, which is called decoherence. This decoherence results in the known exponential decay model of the fidelity of the qubits with time, thus, limiting the lifetime of a qubit in a quantum memory and the performance of quantum applications. In this paper, we evaluate the fidelity of the stored EPR pairs under two opposite dynamical and probabilistic phenomena, first, the aforementioned decoherence and second purification, i.e. an operation to improve the fidelity of an EPR pair at the expense of sacrificing another EPR pair. Instead of applying the purification as soon as two EPR pairs are generated, we introduce a Purification scheme Beyond the Generation time (PBG) of two EPR pairs. We use discrete time Markov chain (DTMC) approach to analytically show the probability distribution of the fidelity of stored link-level EPR pairs in a system with two quantum memories at each node allowing a maximum of two stored EPR pairs. In addition, we apply a PBG scheme that purifies the two stored EPR pairs upon the generation of an additional one. We finally provide numerical evaluations of the analytical approach and show the fidelity-rate trade-off of the considered purification scheme.

We consider Time-to-Live (TTL) caches that tag every object in cache with a specific (and possibly renewable) expiration time. State-of-the-art models for TTL caches assume zero object fetch delay, i.e., the time required to fetch a requested object that is not in cache from a different cache or the origin server. Particularly, in cache hierarchies this delay has a significant impact on performance metrics such as the object hit probability. Recent work suggests that the impact of the object fetch delay on the cache performance will continue to increase due to the scaling mismatch between shrinking inter-request times (due to higher data center link rates) in contrast to processing and memory access times. In this paper, we analyze tree-based cache hierarchies with random object fetch delays and provide an exact analysis of the corresponding object hit probability. Our analysis allows understanding the impact of random delays and TTLs on cache metrics for a wide class of request stream models characterized through Markov arrival processes. This is expressed through a metric that we denote delay impairment of the hit probability. In addition, we analyze and extend state-of-the-art approximations of the hit probability to take the delay into account. We provide numerical and trace-based simulation-based evaluation results showing that larger TTLs do not efficiently compensate the detrimental effect of object fetch delays. Our evaluations also show that unlike our exact model the state-of-the-art approximations do not capture the impact of the object fetch delay well especially for cache hierarchies. Surprisingly, we show for single caches that the impact of the delay on the hit probability can be non-monotonic and that the range of delays for which a positive effect exists arises as a root of a polynomial in the ratio of the expected TTL to the expected inter-request time.