How to Staff When Customers Arrive in Batches

Published Online:https://doi.org/10.1287/mnsc.2021.03979

References

  • Aksin Z, Armony M, Mehrotra V (2007) The modern call center: A multi-disciplinary perspective on operations management research. Production Oper. Management 16(6):665–688.CrossrefGoogle Scholar
  • Atar R (2012) A diffusion regime with nondegenerate slowdown. Oper. Res. 60(2):490–500.LinkGoogle Scholar
  • Atar R, Gurvich I (2014) Scheduling parallel servers in the nondegenerate slowdown diffusion regime: Asymptotic optimality results. Ann. Appl. Probab. 24(2):760–810.CrossrefGoogle Scholar
  • Atar R, Solomon N (2011) Asymptotically optimal interruptible service policies for scheduling jobs in a diffusion regime with nondegenerate slowdown. Queueing Systems 69(3):217–235.CrossrefGoogle Scholar
  • Atar R, Mandelbaum A, Zviran A (2012) Control of fork-join networks in heavy traffic. 2012 50th Annual Allerton Conf. Comm. Control Comput. (Allerton) (IEEE, Piscataway, NJ), 823–830.Google Scholar
  • Baccelli F, Makowski AM, Shwartz A (1989) The fork-join queue and related systems with synchronization constraints: Stochastic ordering and computable bounds. Adv. Appl. Probab. 21(3):629–660.CrossrefGoogle Scholar
  • Baily DE, Neuts MF (1981) Algorithmic methods for multi-server queues with group arrivals and exponential services. Eur. J. Oper. Res. 8(2):184–196.CrossrefGoogle Scholar
  • Bassamboo A, Randhawa RS, Zeevi A (2010) Capacity sizing under parameter uncertainty: Safety staffing principles revisited. Management Sci. 56(10):1668–1686.LinkGoogle Scholar
  • Blaney K, Foerster S, Baumgartner J, Benckert M, Blake J, Bray J, Chamany S, et al. (2022) Covid-19 case investigation and contact tracing in New York City, June 1, 2020, to October 31, 2021. JAMA Network Open 5(11):e2239661.CrossrefGoogle Scholar
  • Borst S, Mandelbaum A, Reiman MI (2004) Dimensioning large call centers. Oper. Res. 52(1):17–34.LinkGoogle Scholar
  • Brockwell PJ (1977) Stationary distributions for dams with additive input and content-dependent release rate. Adv. Appl. Probab. 9(3):645–663.CrossrefGoogle Scholar
  • Brockwell PJ, Resnick SI, Tweedie RL (1982) Storage processes with general release rule and additive inputs. Adv. Appl. Probab. 14(2):392–433.CrossrefGoogle Scholar
  • Chaudhry ML, Kim JJ (2016) Analytically elegant and computationally efficient results in terms of roots for the GIX/M/c queueing system. Queueing Systems 82(1–2):237–257.CrossrefGoogle Scholar
  • Chen YD, Brown SA, Hu PJH, King CC, Chen H (2011) Managing emerging infectious diseases with information systems: Reconceptualizing outbreak management through the lens of loose coupling. Inform. Systems Res. 22(3):447–468.LinkGoogle Scholar
  • Cinlar E, Pinsky M (1972) On dams with additive inputs and a general release rule. J. Appl. Probab. 9(2):422–429.CrossrefGoogle Scholar
  • Cohen I, Mandelbaum A, Zychlinski N (2014) Minimizing mortality in a mass casualty event: Fluid networks in support of modeling and staffing. IIE Trans. 46(7):728–741.CrossrefGoogle Scholar
  • Cramer EY, Ray EL, Lopez VK, Bracher J, Brennen A, Castro Rivadeneira AJ, Gerding A, et al. (2022) Evaluation of individual and ensemble probabilistic forecasts of Covid-19 mortality in the United States. Proc. Natl. Acad. Sci. USA 119(15):e2113561119.CrossrefGoogle Scholar
  • Cromie M, Chaudhry M, Grassmann W (1979) Further results for the queueing system MX/M/c. J. Oper. Res. Soc. 30(8):755–763.Google Scholar
  • Daw A, Pender J (2019) On the distributions of infinite server queues with batch arrivals. Queueing Systems 91(3–4):367–401.CrossrefGoogle Scholar
  • de Graaf W, Scheinhardt WR, Boucherie RJ (2017) Shot-noise fluid queues and infinite-server systems with batch arrivals. Performance Evaluation 116:143–155.CrossrefGoogle Scholar
  • Dong L, Jiang P, Xu F (2023) Impact of traceability technology adoption in food supply chain networks. Management Sci. 69(3):1518–1535.LinkGoogle Scholar
  • Eckberg A (1983) Generalized peakedness of teletraffic processes. Proc. 10th Internat. Teletraffic Congress (Montreal, Canada).Google Scholar
  • Emery SL, Erdman DD, Bowen MD, Newton BR, Winchell JM, Meyer RF, Tong S, et al. (2004) Real-time reverse transcription–polymerase chain reaction assay for SARS-associated coronavirus. Emerging Infectious Diseases 10(2):311–316.CrossrefGoogle Scholar
  • Feldman Z, Mandelbaum A, Massey WA, Whitt W (2008) Staffing of time-varying queues to achieve time-stable performance. Management Sci. 54(2):324–338.LinkGoogle Scholar
  • Fetzer T, Graeber T (2021) Measuring the scientific effectiveness of contact tracing: Evidence from a natural experiment. Proc. Natl. Acad. Sci. USA 118(33):e2100814118.CrossrefGoogle Scholar
  • Fox MD, Bailey DC, Seamon MD, Miranda ML (2021) Response to a COVID-19 outbreak on a university campus—Indiana, August 2020. Morbidity Mortality Weekly Rep. 70(4):118–122.CrossrefGoogle Scholar
  • Gans N, Koole G, Mandelbaum A (2003) Telephone call centers: Tutorial, review, and research prospects. Manufacturing Service Oper. Management 5(2):79–141.LinkGoogle Scholar
  • Gardner K, Harchol-Balter M, Scheller-Wolf A, Van Houdt B (2017a) A better model for job redundancy: Decoupling server slowdown and job size. IEEE/ACM Trans. Networking 25(6):3353–3367.CrossrefGoogle Scholar
  • Gardner K, Harchol-Balter M, Scheller-Wolf A, Velednitsky M, Zbarsky S (2017b) Redundancy-d: The power of d choices for redundancy. Oper. Res. 65(4):1078–1094.LinkGoogle Scholar
  • Garnett O, Mandelbaum A, Reiman M (2002) Designing a call center with impatient customers. Manufacturing Service Oper. Management 4(3):208–227.LinkGoogle Scholar
  • Gilbert E, Pollak H (1960) Amplitude distribution of shot noise. Bell Systems Tech. J. 39(2):333–350.CrossrefGoogle Scholar
  • Giufurta A, O’Connell S (2021) With full Statler, isolated students trickle into off-campus hotels. Cornell Daily Sun (February 9), https://cornellsun.com/2021/02/09/with-full-statler-isolated-students-trickle-into-off-campus-hotels/.Google Scholar
  • Gluckman N (2021) Some universities have less space to isolate students this fall. Is that a problem? Chronicle Higher Ed. (August 10), https://www.chronicle.com/article/some-universities-have-less-space-to-isolate-students-this-fall-is-that-a-problem.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.CrossrefGoogle Scholar
  • Gupta S, Starr MK, Farahani RZ, Asgari N (2022) OM forum—Pandemics/epidemics: Challenges and opportunities for operations management research. Manufacturing Service Oper. Management 24(1):1–23.LinkGoogle Scholar
  • Gurvich I, Luedtke J, Tezcan T (2010) Staffing call centers with uncertain demand forecasts: A chance-constrained optimization approach. Management Sci. 56(7):1093–1115.LinkGoogle Scholar
  • Halfin S, Whitt W (1981) Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29(3):567–588.LinkGoogle Scholar
  • Harrison JM, Resnick SI (1976) The stationary distribution and first exit probabilities of a storage process with general release rule. Math. Oper. Res. 1(4):347–358.LinkGoogle Scholar
  • Harrison JM, Resnick SI (1978) The recurrence classification of risk and storage processes. Math. Oper. Res. 3(1):57–66.LinkGoogle Scholar
  • Hong Y, Wang W (2022) Sharp waiting-time bounds for multiserver jobs. Proc. Twenty-Third Internat. Sympos. Theory, Algorithmic Foundations, Protocol Design for Mobile Networks Mobile Comput. (Association for Computing Machinery, New York), 161–170.Google Scholar
  • Ibrahim R, Ye H, L’Ecuyer P, Shen H (2016) Modeling and forecasting call center arrivals: A literature survey and a case study. Internat. J. Forecasting 32(3):865–874.CrossrefGoogle Scholar
  • Jennings OB, Mandelbaum A, Massey WA, Whitt W (1996) Server staffing to meet time-varying demand. Management Sci. 42(10):1383–1394.LinkGoogle Scholar
  • Jongbloed G, Koole G (2001) Managing uncertainty in call centres using Poisson mixtures. Appl. Stochastic Models Bus. Indust. 17(4):307–318.CrossrefGoogle Scholar
  • Kaspi H (1984) Storage processes with Markov additive input and output. Math. Oper. Res. 9(3):424–440.LinkGoogle Scholar
  • Kella O, Whitt W (1999) Linear stochastic fluid networks. J. Appl. Probab. 36(1):244–260.CrossrefGoogle Scholar
  • Kim SH, Whitt W (2014) Are call center and hospital arrivals well modeled by nonhomogeneous Poisson processes? Manufacturing Service Oper. Management 16(3):464–480.LinkGoogle Scholar
  • Kingman J (2009) The first Erlang century—and the next. Queueing Systems 63(1):3–12.CrossrefGoogle Scholar
  • Lash RR, Moonan PK, Byers BL, Bonacci RA, Bonner KE, Donahue M, Donovan CV, et al. (2021) Covid-19 case investigation and contact tracing in the US, 2020. JAMA Network Open 4(6):e2115850.CrossrefGoogle Scholar
  • Levi R, Singhvi S, Zheng Y (2020) Economically motivated adulteration in farming supply chains. Management Sci. 66(1):209–226.LinkGoogle Scholar
  • Lu H, Pang G (2017) Heavy-traffic limits for a fork-join network in the Halfin–Whitt regime. Stochastic Systems 6(2):519–600.LinkGoogle Scholar
  • Massey WA, Whitt W (1996) Stationary-process approximations for the nonstationary Erlang loss model. Oper. Res. 44(6):976–983.LinkGoogle Scholar
  • Mathijsen BW, Janssen A, van Leeuwaarden JS, Zwart B (2018) Robust heavy-traffic approximations for service systems facing overdispersed demand. Queueing Systems 90(3):257–289.CrossrefGoogle Scholar
  • Mills AF, Argon NT, Ziya S (2013) Resource-based patient prioritization in mass-casualty incidents. Manufacturing Service Oper. Management 15(3):361–377.LinkGoogle Scholar
  • National Association of County and City Health Officials (2020) Building Covid-19 contact tracing in health departments to support reopening American society safely. NACCHO position statement. Accessed May 4, 2023, https://www.naccho.org/uploads/full-width-images/Contact-Tracing-Statement-4-16-2020.pdf.Google Scholar
  • Neuts MF (1978) An algorithmic solution to the GI/M/C queue with group arrivals. Technical report, Delaware University Newark Department of Statistics and Computer Science, Newark.Google Scholar
  • NYC Department of Health and Mental Hygiene (2023) NYC coronavirus disease 2019 (Covid-19) data. Accessed May 4, 2023, https://www.nyc.gov/site/doh/covid/covid-19-data.page.Google Scholar
  • NYC Health + Hospitals (2022) COVID-19 contact tracing public report—Reporting period: April 24, 2022–April 29, 2022. Accessed May 4, 2023, https://hhinternet.blob.core.windows.net/uploads/2022/05/public_weekly_report_04302022_updated.pdf.Google Scholar
  • Özkan E, Ward AR (2019) On the control of fork-join networks. Math. Oper. Res. 44(2):532–564.LinkGoogle Scholar
  • Pang G, Whitt W (2012) The impact of dependent service times on large-scale service systems. Manufacturing Service Oper. Management 14(2):262–278.LinkGoogle Scholar
  • Prabhu NU (2012) Stochastic Storage Processes: Queues, Insurance Risk, Dams, and Data Communication, vol. 15 (Springer Science & Business Media, New York).Google Scholar
  • Rainisch G, Jeon S, Pappas D, Spencer KD, Fischer LS, Adhikari BB, Taylor MM, et al. (2022) Estimated Covid-19 cases and hospitalizations averted by case investigation and contact tracing in the US. JAMA Network Open 5(3):e224042.CrossrefGoogle Scholar
  • Reed J (2009) The G/GI/N queue in the Halfin–Whitt regime. Ann. Appl. Probab. 19(6):2211–2269.CrossrefGoogle Scholar
  • Rubinovitch M, Cohen J (1980) Level crossings and stationary distributions for general dams. J. Appl. Probab. 17(1):218–226.CrossrefGoogle Scholar
  • Ruebush E, Fraser MR, Poulin A, Allen M, Lane J, Blumenstock JS (2021) Covid-19 case investigation and contact tracing: Early lessons learned and future opportunities. J. Public Health Management Practice 27(1):S87–S97.CrossrefGoogle Scholar
  • Thomasian A (2014) Analysis of fork/join and related queueing systems. ACM Comput. Surveys 47(2):1–71.CrossrefGoogle 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
  • van Leeuwaarden JS, Mathijsen BW, Zwart B (2019) Economies-of-scale in many-server queueing systems: Tutorial and partial review of the QED Halfin–Whitt heavy-traffic regime. SIAM Rev. 61(3):403–440.CrossrefGoogle Scholar
  • Vasan A, Foote M, Long T (2022) Ensuring widespread and equitable access to treatments for Covid-19. J. Amer. Medical Assoc. 328(8):705–706.CrossrefGoogle Scholar
  • Wang W, Harchol-Balter M, Jiang H, Scheller-Wolf A, Srikant R (2019) Delay asymptotics and bounds for multitask parallel jobs. Queueing Systems 91(3):207–239.CrossrefGoogle Scholar
  • Wang X, Du Z, James E, Fox SJ, Lachmann M, Meyers LA, Bhavnani D (2022) The effectiveness of Covid-19 testing and contact tracing in a US city. Proc. Natl. Acad. Sci. USA 119(34):e2200652119.CrossrefGoogle Scholar
  • Watson C, Cicero A, Blumenstock JS, Fraser MR (2020) A national plan to enable comprehensive COVID-19 case finding and contact tracing in the US (Johns Hopkins Bloomberg School of Public Health, Center for Health Security). Accessed May 4, 2023, https://centerforhealthsecurity.org/sites/default/files/2023-02/200410-national-plan-to-contact-tracing.pdf.Google Scholar
  • Whitt W (1992) Understanding the efficiency of multi-server service systems. Management Sci. 38(5):708–723.LinkGoogle Scholar
  • Whitt W (2007) What you should know about queueing models to set staffing requirements in service systems. Naval Res. Logist. 54(5):476–484.CrossrefGoogle Scholar
  • Wolff RW (1982) Poisson arrivals see time averages. Oper. Res. 30(2):223–231.LinkGoogle Scholar
  • Yao DD (1985) Some results for the queues MX/M/c and GIX/G/c. Oper. Res. Lett. 4(2):79–83.CrossrefGoogle Scholar
  • Yao DD, Chaudhry M, Templeton J (1984) On bounds for bulk arrival queues. Eur. J. Oper. Res. 15(2):237–243.CrossrefGoogle Scholar
  • Yeo G (1974) A finite dam with exponential release. J. Appl. Probab. 11(1):122–133.CrossrefGoogle Scholar
  • Yeo G (1976) A dam with general release rule. ANZIAM J. 19(4):469–477.Google Scholar
  • Yom-Tov GB, Mandelbaum A (2014) Erlang-R: A time-varying queue with reentrant customers, in support of healthcare staffing. Manufacturing Service Oper. Management 16(2):283–299.LinkGoogle Scholar
  • Zeltyn S, Mandelbaum A (2005) Call centers with impatient customers: Many-server asymptotics of the M/M/n+ G queue. Queueing Systems 51(3):361–402.CrossrefGoogle Scholar
  • Zhao Y (1994) Analysis of the GIX/M/c model. Queueing Systems 15(1–4):347–364.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.