Establishing Convergence of Infinite-Server Queues with Batch Arrivals to Shot-Noise Processes

References

• Boxma O, Mandjes M (2021) Shot-noise queueing models. Queueing Systems 99(1–2):121–159.Crossref, Google Scholar
• Daw A, Fralix B, Pender J (2020) Non-stationary queues with batch arrivals. Preprint, submitted August 3, https://arxiv.org/abs/2008.00625.Google Scholar
• Daw A, Hampshire RC, Pender J (2024) How to staff when customers arrive in batches. Management Sci. Forthcoming.Link, Google Scholar
• de Graaf WF, Scheinhardt WR, Boucherie RJ (2017) Shot-noise fluid queues and infinite-server systems with batch arrivals. Performance Evaluation 116:143–155.Crossref, Google Scholar
• Ethier SN, Kurtz TG (2009) Markov Processes: Characterization and Convergence (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Feizi A, Carson A, Jaeker JB, Baker WE (2023) To batch or not to batch? Impact of admission batching on emergency department boarding time and physician productivity. Oper. Res. 71(3):939–957.Link, Google Scholar
• Fralix B (2020) On classes of Bitcoin-inspired infinite-server queueing systems. Queueing Systems 95(1–2):29–52.Crossref, Google Scholar
• Frolkova M, Mandjes M (2019) A Bitcoin-inspired infinite-server model with a random fluid limit. Stochastic Models 35(1):1–32.Crossref, Google Scholar
• Garnett O, Mandelbaum A, Reiman M (2002) Designing a call center with impatient customers. Manufacturing Service Oper. Management 4(3):208–227.Link, Google Scholar
• Green LV, Kolesar PJ, Whitt W (2007) Coping with time-varying demand when setting staffing requirements for a service system. Production Oper. Management 16(1):13–39.Crossref, Google Scholar
• Grosof I, Harchol-Balter M, Scheller-Wolf A (2022a) WCFS: A new framework for analyzing multiserver systems. Queueing Systems 102(1–2):143–174.Crossref, Google Scholar
• Grosof I, Scully Z, Harchol-Balter M, Scheller-Wolf A (2022b) Optimal scheduling in the multiserver-job model under heavy traffic. ACM SIGMETRICS Performance Evaluation Rev. 51(1):99–100.Google Scholar
• Gurvich I, Whitt W (2009) Queue-and-idleness-ratio controls in many-server service systems. Math. Oper. Res. 34(2):363–396.Link, Google Scholar
• Harchol-Balter M (2021) Open problems in queueing theory inspired by datacenter computing. Queueing Systems 97(1–2):3–37.Crossref, Google Scholar
• Hong Y, Wang W (2022) Sharp waiting-time bounds for multiserver jobs. Proc. Twenty-Third Internat. Sympos. Theory, Algorithmic Foundations, Protocol Design Mobile Networks Mobile Comput. (Association for Computing Machinery, New York), 161–170.Google Scholar
• Kella O, Whitt W (1999) Linear stochastic fluid networks. J. Appl. Probab. 36(1):244–260.Crossref, Google Scholar
• Liu Y, Whitt W (2011) A network of time-varying many-server fluid queues with customer abandonment. Oper. Res. 59(4):835–846.Link, Google Scholar
• Mandelbaum A, Massey WA, Reiman MI (1998) Strong approximations for Markovian service networks. Queueing Systems 30:149–201.Crossref, Google Scholar
• Mehra S, Taylor PG, McCaw JM, Flegg JA (2024) A hybrid transmission model for Plasmodium vivax accounting for superinfection, immunity and the hypnozoite reservoir. J. Math. Biol. 89:7.Google Scholar
• Mehra S, Stadler E, Khoury D, McCaw JM, Flegg JA (2022) Hypnozoite dynamics for Plasmodium vivax malaria: The epidemiological effects of radical cure. J. Theoret. Biology 537:111014.Crossref, Google Scholar
• Stadje W, Perry D (2022) Growth-collapse effects applied to cash management and queues. Queueing Systems 100(3–4):257–259.Crossref, Google Scholar
• Tirmazi M, Barker A, Deng N, Haque ME, Qin ZG, Hand S, Harchol-Balter M, Wilkes J (2020) Borg: The next generation. Proc. Fifteenth Eur. Conf. Comput. Systems (Association for Computing Machinery, New York), 1–14.Google Scholar
• Wang W, Xie Q, Harchol-Balter M (2021) Zero queueing for multi-server jobs. ACM SIGMETRICS Performance Evaluation Rev. 49(1):13–14.Google Scholar
• Whitt W (1985) The renewal-process stationary-excess operator. J. Appl. Probab. 22(1):156–167.Crossref, Google Scholar