Matching Queues with Abandonments in Quantum Switches: Stability and Throughput Analysis

References

• Anton E, Ayesta U, Jonckheere M, Verloop IM (2021) On the stability of redundancy models. Oper. Res. 69(5):1540–1565.Link, Google Scholar
• Armstrong S, Morizur JF, Janousek J, Hage B, Treps N, Lam PK, Bachor HA (2012) Programmable multimode quantum networks. Nature Comm. 3(1):1–8.Crossref, Google Scholar
• Aveklouris A, DeValve L, Ward AR (2024) Matching impatient and heterogeneous demand and supply. Oper. Res., ePub ahead of print May 15, https://doi.org/10.1287/opre.2022.0005.Google Scholar
• Baccelli F, Foss S (1995) On the saturation rule for the stability of queues. J. Appl. Probab. 32:494–507.Crossref, Google Scholar
• Bhaskar MK, Riedinger R, Machielse B, Levonian DS, Nguyen CT, Knall EN, Park H, et al. (2020) Experimental demonstration of memory-enhanced quantum communication. Nature 580(7801):60–64.Crossref, Google Scholar
• Blanchet JH, Reiman MI, Shah V, Wein LM, Wu L (2022) Asymptotically optimal control of a centralized dynamic matching market with general utilities. Oper. Res. 70(6):3355–3370.Link, Google Scholar
• Boxma O, Perry D, Stadje W (2023) Perishable inventories with random input: A unifying survey with extensions. Ann. Oper. Res. 332:1069–1105.Google Scholar
• Bušić A, Gupta V, Mairesse J (2013) Stability of the bipartite matching model. Adv. Appl. Probab. 45:351–378.Crossref, Google Scholar
• Cadas A, Bušić A, Doncel J (2019) Optimal control of dynamic bipartite matching models. Proc. 12th EAI Internat. Conf. Performance Evaluation Methodologies and Tools (Association for Computing Machinery, New York), 39–46.Google Scholar
• Cadas A, Doncel J, Fourneau JM, Busic A (2022) Flexibility Can Hurt Dynamic Matching System Performance, vol. 49 (ACM, New York), 37–42.Crossref, Google Scholar
• Castro F, Nazerzadeh H, Yan C (2020) Matching queues with reneging: A product form solution. Queueing Systems 96:359–385.Crossref, Google Scholar
• Dai JG, Harrison MJ (2020) Processing Networks: Fluid Models and Stability (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Dai W, Rinaldi A, Towsley D (2021) Entanglement swapping in quantum switches: Protocol design and stability analysis. Preprint, submitted October 8, https://arxiv.org/abs/2110.04116v1.Google Scholar
• Diamant A, Baron O (2019) Double-sided matching queues: Priority and impatient customers. Oper. Res. Lett. 47(3):219–224.Crossref, Google Scholar
• Fittipaldi P, Giovanidis A, Grosshans F (2023) A linear algebraic framework for dynamic scheduling over memory-equipped quantum networks. IEEE Trans. Quantum Engrg. 5:1–18.Google Scholar
• Fonda L, Ghirardi GC, Rimini A (1978) Decay theory of unstable quantum systems. Rep. Prog. Phys. 41(4):587.Crossref, Google Scholar
• Gamarnik D, Tsitsiklis JN, Zubeldia M (2018) Delay, memory, and messaging tradeoffs in distributed service systems. Stochastic Systems 8(1):45–74.Link, Google Scholar
• Graves SC (1982) The application of queueing theory to continuous perishable inventory systems. Management Sci. 28(4):400–406.Link, Google Scholar
• Guha S, Krovi H, Fuchs CA, Dutton Z, Slater JA, Simon C, Tittel W (2015) Rate-loss analysis of an efficient quantum repeater architecture. Phys. Rev. A 92:022357.Crossref, Google Scholar
• Gupta V (2024) Technical Note—Greedy algorithm for multiway matching with bounded regret. Oper. Res. 72(3):1139–1155.Google Scholar
• Gurvich I, Ward AR (2014) On the dynamic control of matching queues. Stochastic Systems 4(2):479–523.Link, Google Scholar
• Gyongyosi L, Imre S (2022) Advances in the quantum internet. Comm. ACM 65(8):52–63.Crossref, Google Scholar
• Hall MA, Altepeter JB, Kumar P (2011) Ultrafast switching of photonic entanglement. Phys. Rev. Lett. 106(5):053901.Crossref, Google Scholar
• Herbauts I, Blauensteiner B, Poppe A, Jennewein T, Hübel H (2013) Demonstration of active routing of entanglement in a multi-user network. Optics Express 21(23):29013–29024.Crossref, Google Scholar
• Jonckheere M, Moyal P, Ramírez C, Soprano-Loto N (2022) Generalized max-weight policies in stochastic matching. Stochastic Systems 13(1):40–58.Google Scholar
• Kerimov S, Ashlagi I, Gurvich I (2023) On the optimality of greedy policies in dynamic matching. Oper. Res. 73(1):560–582.Google Scholar
• Lee Y, Bersin E, Dahlberg A, Wehner S, Englund D (2022) A quantum router architecture for high-fidelity entanglement flows in quantum networks. NPJ Quantum Inform. 8(1):1–8.Crossref, Google Scholar
• Li R, Petit L, Franke DP, Dehollain JP, Helsen J, Steudtner M, Thomas NK, et al. (2018) A crossbar network for silicon quantum dot qubits. Sci. Adv. 4(7):eear3960.Crossref, Google Scholar
• Luczak MJ, Norris JR (2013) Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory. Ann. Appl. Probab. 23(3):957–986.Crossref, Google Scholar
• Maglaras C (2000) Discrete-review policies for scheduling stochastic networks: Trajectory tracking and fluid-scale asymptotic optimility. Ann. Appl. Probab. 10(3):897–929.Crossref, Google Scholar
• Menshikov M, Popov S, Wade A (2016) Non-Homogeneous Random Walks: Lyapunov Function Methods for Near-Critical Stochastic Systems, vol. 209 (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Meyn SP, Tweedie RL (1992) Stability of Markovian processes I: Criteria for discrete-time chains. Adv. Appl. Probab. 24(3):542–574.Crossref, Google Scholar
• Moyal P, Perry O (2017) On the instability of matching queues. Ann. Appl. Probab. 27(6):3385–3434.Crossref, Google Scholar
• Moyal P, Bušić A, Mairesse J (2021) A product form for the general stochastic matching model. J. Appl. Probab. 58:449–468.Crossref, Google Scholar
• Nain P, Vardoyan G, Guha S, Towsley D (2022) Analysis of a tripartite entanglement distribution switch. Queueing Systems 101:291–328.Crossref, Google Scholar
• Nazari M, Stolyar AL (2018) Reward maximization in general dynamic matching systems. Queueing Systems 91:143–170.Crossref, Google Scholar
• Plambeck EL, Ward AR (2006) Optimal control of a high-volume assemble-to-order system. Math. Oper. Res. 31(3):453–477.Link, Google Scholar
• Rahme Y, Moyal P (2021) A stochastic matching model on hypergraphs. Adv. Appl. Probab. 53(4):951–980.Crossref, Google Scholar
• Schoute E, Mancinska L, Islam T, Kerenidis I, Wehner S (2016) Shortcuts to quantum network routing. Technical report, Cornell University, Ithaca, NY.Google Scholar
• Stolyar AL (2004) Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. Ann. Appl. Probab. 14(1):1–53.Crossref, Google Scholar
• van Meter R (2014) Quantum Networking (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Vardoyan G, Guha S, Nain P, Towsley D (2020) On the exact analysis of an idealized quantum switch. Performance Evaluation 144:102–141.Crossref, Google Scholar
• Vardoyan G, Guha S, Nain P, Towsley D (2021) On the stochastic analysis of a quantum entanglement distribution switch. IEEE Trans. Quantum Engrg. 2:1–16.Crossref, Google Scholar
• Vardoyan G, Guha S, Nain P, Towsley D (2022) On the capacity region of bipartite and tripartite entanglement switching. Sigmetrics Performance Evaluation Rev. 49(3):79–80.Crossref, Google Scholar
• Vasantam T, Towsley D (2021) Stability analysis of a quantum network with max-weight scheduling. Preprint, submitted June 1, https://arxiv.org/abs/2106.00831v1.Google Scholar