Joint Modeling and Performance Evaluation of Communication and Memory Systems in the Classical and the Quantum Internet: A Time-to-Live Approach

Memory systems are indispensable in communication networks, enabling data processing for various fundamental tasks in every aspect of communication networks, including scheduling, routing, etc. This thesis focuses on network memories that store the most relevant data for its future use by application requests, which are essential, e.g., to meet strict latency requirements. The performance of such network memories depends on the strategies that manage their finite capacity. In addition, memories across communication networks are interconnected to collaboratively fulfill application requests. Accordingly, jointly evaluating their performance under the impact of communication latency between the interconnected network memories is necessary. In this thesis, we study network memories that store either replicable time-independent objects or consumable time-dependent objects in the context of the classical and the quantum Internet, respectively. In the classical Internet, network memories are cache memories that store copies of objects from network servers closer to the users. In the quantum Internet, memories emerge to hold the unique quantum links, also called entanglements, which are consumed to enable data transmission. Due to the adverse effects of noise, the entanglement quality, also called fidelity, decays in quantum memories, which limits the object storage lifetime. We take a Time-to-Live (TTL) analytical approach to model the occupancy of objects in network memories under consumption and copying, as well as time-independent storage versus time-dependent degeneracy. We provide a universal TTL occupancy model, which models the object TTL in memory as a delayed jump and drift process that models the jumps in the TTL as well as intercommunication delays under arbitrary management strategies. On the one hand, TTLs model the assigned timers to objects in cache memories under time-driven management strategies. On the other hand, TTLs model the inherent lifetime of entanglements in quantum memories. Accordingly, we use the universal TTL model to analytically evaluate the performance in both memory systems. First, we provide an exact analytical evaluation framework using Markov arrival processes for hierarchical interconnected cache memories under the impact of non-zero network delays. Markov arrival processes are instrumental to model non-renewal request and miss processes at each cache memory in the hierarchy. Our results show the detrimental impact of delays on the probability of finding an object upon request, i.e., the hit probability. Surprisingly, results show that the delay impact on the hit probability may be non-monotonic when the request process becomes periodic. Accordingly, we derive the range of delays giving rise to such non-monotonic hit probability. Further, we build on the exact hit probability performance evaluation to optimize the utility of interconnected cache memories. Our results show that by optimally choosing the TTL parameters of each object, the same utility can be maintained under longer fetch delays. Second, for quantum memories, management strategies of the entanglement lifetime depend on quantum purification, a process that consumes two entanglements in memory to produce a higher fidelity one with a longer lifetime. Using purification as a basis for memory management protocols is still primitive. To this end, we design static purification-based management protocols for quantum link-level systems with more than one long-term quantum memory. Our rationale for considering the quantum link-level system is that the fidelity of link-level entanglement represents the bottleneck of remote communication. We show that the exact modeling of purification-based protocols is challenging due to the dependence of the jumps in the TTL delayed jump and drift process on the TTL at purification times. To this end, we propose an approximate analytical discrete-time Markov chain model based on the discretization of the TTL. Our results show that different static purification protocols and system sizes result in diverse trade-offs between the availability and fidelity of link-level entanglements. Further, we propose a tunable utility-aware strategy, denoted as General Pumping Strategy, which tunes the purification intensity depending on the lifetime of stored link-level entanglements and the loss risk of entanglements on the utility. Our evaluations show that tuning the general pumping strategy to optimize the utility of quantum link-level systems outperforms the performance of static purification strategies. Overall, using the universal TTL occupancy model as a delayed jump and drift process, this thesis develops analytical performance evaluation and utility optimization frameworks for network memories with diverse storage properties. The developed frameworks provide a unified analytical basis for studying interconnected memory systems under copying, consumption, delays and time-dependent degradation in both classical and quantum communication networks.