Transient staffing at the beginning of work

References

• Abate, J., and W. Whitt. 1987. “Transient Behavior of the M/M/1 Queue: Starting At the Origin.” Queueing Systems 2 (1): 41–65. https://doi.org/10.1007/BF01182933.
   Google Scholar
• Al-Seedy, R., A. El-Sherbiny, S. El-Shehawy, and S. Ammar. 2009. “Transient Solution of the M/M/c Queue with Balking and Reneging.” Computers & Mathematics with Applications 57 (8): 1280–1285. https://doi.org/10.1016/j.camwa.2009.01.017.
   Web of Science ®Google Scholar
• Ammar, S., M. Helan, and F. Al Amri. 2013. “The Busy Period of An M/M/1 Queue with Balking and Reneging.” Applied Mathematical Modelling 37 (22): 9223–9229. https://doi.org/10.1016/j.apm.2013.04.023.
   Web of Science ®Google Scholar
• Armony, M., S. Israelit, A. Mandelbaum, Y. Marmor, Y. Tseytlin, and G. Yom-Tov. 2015. “On Patient Flow in Hospitals: A Data-based Queueing-science Perspective.” Stochastic Systems 5 (1): 146–194. https://doi.org/10.1287/14-SSY153.
   Google Scholar
• Armony, M., E. Plambeck, and S. Seshadri. 2009. “Sensitivity of Optimal Capacity to Customer Impatience in An Unobservable M/M/s Queue (why You Shouldn't Shout At the DMV).” Manufacturing & Service Operations Management 11 (1): 19–32. https://doi.org/10.1287/msom.1070.0194.
   Web of Science ®Google Scholar
• Baccelli, F., and G. Hebuterne. 1981. “On Queues with Impatient Customers.” Doctoral dissertation, INRIA.
   Google Scholar
• Bailey, N. 1954. “A Continuous Time Treatment of a Simple Queue Using Generating Functions.” Journal of the Royal Statistical Society. Series B (Methodological) 16 (2): 288–291. https://doi.org/10.1111/rssb.1954.16.issue-2.
   Web of Science ®Google Scholar
• Bhattacharya, P., and A. Ephremides. 1991. “Stochastic Monotonicity Properties of Multiserver Queues with Impatient Customers.” Journal of Applied Probability 28 (3): 673–682. https://doi.org/10.2307/3214501.
   Web of Science ®Google Scholar
• Brown, L., N. Gans, A. Mandelbaum, A. Sakov, H. Shen, S. Zeltyn, and L. Zhao. 2005. “Statistical Analysis of a Telephone Call Center: A Queueing-science Perspective.” Journal of the American Statistical Association 100 (469): 36–50. https://doi.org/10.1198/016214504000001808.
   Web of Science ®Google Scholar
• Chen, W., H. Guo, and K. Tsui. 2020. “A New Medical Staff Allocation Via Simulation Optimisation for An Emergency Department in Hong Kong.” International Journal of Production Research 58 (19): 6004–6023. https://doi.org/10.1080/00207543.2019.1665201.
   Web of Science ®Google Scholar
• Daw, A., and J. Pender. 2019. “New Perspectives on the Erlang-A Queue.” Advances in Applied Probability 51 (1): 268–299. https://doi.org/10.1017/apr.2019.11.
   Web of Science ®Google Scholar
• Fralix, B. 2013. “On the Time-dependent Moments of Markovian Queues with Reneging.” Queueing Systems 75 (2): 149–168. https://doi.org/10.1007/s11134-012-9281-2.
   Web of Science ®Google Scholar
• Fu, M., S. Marcus, and I. Wang. 2000. “Monotone Optimal Policies for a Transient Queueing Staffing Problem.” Operations Research 48 (2): 327–331. https://doi.org/10.1287/opre.48.2.327.13375.
   Web of Science ®Google Scholar
• Grassmann, W. 1990. “Finding Transient Solutions in Markovian Event Systems through Randomization.” In The First International Conference on the Numerical Solution of Markov Chains, 375–395.
   Google Scholar
• Graves, S. 1982. “The Application of Queueing Theory to Continuous Perishable Inventory Systems.” Management Science 28 (4): 400–406. https://doi.org/10.1287/mnsc.28.4.400.
   Web of Science ®Google Scholar
• Green, L., P. Kolesar, and J. Soares. 2001. “Improving the SIPP Approach for Staffing Service Systems that Have Cyclic Demands.” Operations Research 49 (4): 549–564. https://doi.org/10.1287/opre.49.4.549.11228.
   Web of Science ®Google Scholar
• Gross, D., and C Harris 1998. Fundamentals of Queueing Theory. 3rd ed. Wiley Series in Probability and Mathematical Statistics.
   Google Scholar
• Gross, D., and D. Miller. 1984. “The Randomization Technique As a Modeling Tool and Solution Procedure for Transient Markov Processes.” Operations Research 32 (2): 343–361. https://doi.org/10.1287/opre.32.2.343.
   Web of Science ®Google Scholar
• Gupta, U., and O. Sharma. 1983. “On the Transient Behaviour of a Model for Queues in Series with Finite Capacity.” International Journal of Production Research 21 (6): 869–879. https://doi.org/10.1080/00207548308942419.
   Web of Science ®Google Scholar
• Jensen, A. 1953. “Markoff Chains As An Aid in the Study of Markoff Processes.” Scandinavian Actuarial Journal 1953 (1): 87–91. https://doi.org/10.1080/03461238.1953.10419459.
   Google Scholar
• Jia, Y., Z. Zhang, and L. Tang. 2021. “M/PH/C Queue Under a Congestion-based Staffing Policy with Applications in Steel Industry Operations.” International Journal of Production Research 59 (5): 1319–1330. https://doi.org/10.1080/00207543.2020.1735656.
   Web of Science ®Google Scholar
• Jouini, O., and Y. Dallery. 2007. “Monotonicity Properties for Multiserver Queues with Reneging and Finite Waiting Lines.” Probability in the Engineering and Informational Sciences 21 (3): 335–360. https://doi.org/10.1017/S0269964807000010.
   Web of Science ®Google Scholar
• Kelton, W., and A. Law. 1985. “The Transient Behavior of the M/M/s Queue, with Implications for Steady-state Simulation.” Operations Research 33 (2): 378–396. https://doi.org/10.1287/opre.33.2.378.
   Web of Science ®Google Scholar
• Knessl, C., and J. van Leeuwaarden. 2015. “Transient Analysis of the Erlang A Model.” Mathematical Methods of Operations Research 82 (2): 143–173. https://doi.org/10.1007/s00186-015-0498-9.
   PubMed Web of Science ®Google Scholar
• Koole, G. 2013. “Call Center Optimization.” Lulu. com.
   Google Scholar
• Krishnamoorthy, A., R. Manikandan, and D. Shajin. 2015. “Analysis of a Multiserver Queueing-inventory System.” Advances in Operations Research 2015:747328. https://doi.org/10.1155/2015/747328.
   Google Scholar
• Ledermann, W., and G. Reuter. 1954. “Spectral Theory for the Differential Equations of Simple Birth and Death Processes.” Philosophical Transactions of the Royal Society A 246 (914): 321–369.
   Google Scholar
• Legros, B. 2019. “Transient Analysis of a Markovian Queue with Deterministic Rejection.” Operations Research Letters 47 (5): 391–397. https://doi.org/10.1016/j.orl.2019.07.005.
   Web of Science ®Google Scholar
• Legros, B. 2021. “Transient Analysis of An Affine Queue-Hawkes Process.” Operations Research Letters 49 (3): 393–399. https://doi.org/10.1016/j.orl.2021.04.001.
   Web of Science ®Google Scholar
• Liu, L., X. Liu, and D. Yao. 2004. “Analysis and Optimization of a Multistage Inventory-queue System.” Management Science 50 (3): 365–380. https://doi.org/10.1287/mnsc.1030.0196.
   Web of Science ®Google Scholar
• Liu, R., and X. Xie. 2021. “Weekly Scheduling of Emergency Department Physicians to Cope with Time-varying Demand.” IISE Transactions 53 (10): 1109–1123.
   Web of Science ®Google Scholar
• Mandelbaum, A., and P. Momčilović. 2012. “Queues with Many Servers and Impatient Customers.” Mathematics of Operations Research 37 (1): 41–65. https://doi.org/10.1287/moor.1110.0530.
   Web of Science ®Google Scholar
• Massey, W., and J. Pender. 2018. “Dynamic Rate Erlang-A Queues.” Queueing Systems 89 (1): 127–164. https://doi.org/10.1007/s11134-018-9581-2.
   Web of Science ®Google Scholar
• Melamed, B., and M. Yadin. 1984. “Randomization Procedures in the Computation of Cumulative-time Distributions Over Discrete State Markov Processes.” Operations Research 32 (4): 926–944. https://doi.org/10.1287/opre.32.4.926.
   Web of Science ®Google Scholar
• Parthasarathy, P., and M. Sharafali. 1989. “Transient Solution to the Many-server Poisson Queue: a Simple Approach.” Journal of Applied Probability 26 (3): 584–594. https://doi.org/10.2307/3214415.
   Web of Science ®Google Scholar
• Pulungan, R., and H. Hermanns. 2018. “Transient Analysis of CTMCs: Uniformization Or Matrix Exponential.” IAENG International Journal of Computer Science 45 (2): 267–274.
   Google Scholar
• Reibman, A., and K. Trivedi. 1988. “Numerical Transient Analysis of Markov Models.” Computers & Operations Research 15 (1): 19–36. https://doi.org/10.1016/0305-0548(88)90026-3.
   Web of Science ®Google Scholar
• Rodriguez, C., T. Garaix, X. Xie, and V. Augusto. 2015. “Staff Dimensioning in Homecare Services with Uncertain Demands.” International Journal of Production Research 53 (24): 7396–7410. https://doi.org/10.1080/00207543.2015.1081427.
   Web of Science ®Google Scholar
• Sidje, R., K. Burrage, and S. MacNamara. 2007. “Inexact Uniformization Method for Computing Transient Distributions of Markov Chains.” SIAM Journal on Scientific Computing 29 (6): 2562–2580. https://doi.org/10.1137/060662629.
   Web of Science ®Google Scholar
• Van de Coevering, M. 1995. “Computing Transient Performance Measures for the M/M/1 Queue.” Operations-Research-Spektrum 17 (1): 19–22. https://doi.org/10.1007/BF01719726.
   Google Scholar
• Van Moorsel, A., and W. Sanders. 1994. “Adaptive Uniformization.” Stochastic Models 10 (3): 619–647. https://doi.org/10.1080/15326349408807313.
   Google Scholar
• Ward, A. 2012. “Asymptotic Analysis of Queueing Systems with Reneging: A Survey of Results for FIFO, Single Class Models.” Surveys in Operations Research and Management Science 17 (1): 1–14. https://doi.org/10.1016/j.sorms.2011.08.002.
   Google Scholar
• Wu, C., J. Lin, and W. Chien. 2010. “Dynamic Production Control in a Serial Line with Process Queue Time Constraint.” International Journal of Production Research 48 (13): 3823–3843. https://doi.org/10.1080/00207540902922836.
   Web of Science ®Google Scholar
• Xie, J., P. Cao, B. Huang, and M. E. Ong. 2016. “Determining the Conditions for Reverse Triage in Emergency Medical Services Using Queuing Theory.” International Journal of Production Research 54 (11): 3347–3364. https://doi.org/10.1080/00207543.2015.1109718.
   Web of Science ®Google Scholar
• Yoo, J. 1996. Queueing Models for Staffing Service Operations. College Park: University of Maryland.
   Google Scholar