A Survey and Experimental Comparison of Service-Level-Approximation Methods for Nonstationary M(t)/M/s(t) Queueing Systems with Exhaustive Discipline

Published Online:https://doi.org/10.1287/ijoc.1050.0157

References

  • Arkin B. L., Leemis L. M. Nonparametric estimation of the cumulative intensity function for a nonhomogeneous Poisson process from overlapping realizations. Management Sci. (2000) 46:989–998LinkGoogle Scholar
  • Atlason J., Epelman M. A., Henderson S. G. Call center staffing with simulation and cutting plane methods. Ann. Oper. Res. (2004) 127:333–358CrossrefGoogle Scholar
  • Barnhart C., Belobaba P., Odoni A. R. Applications of operations research in the air transport industry. Transportation Sci. (2003) 37:368–391LinkGoogle Scholar
  • Bookbinder J. H. Multiple queues of aircraft under time-dependent conditions. INFOR (1986) 24:280–288Google Scholar
  • Bookbinder J. H., Martell D. L. Time-dependent queuing approach to helicopter allocation for forest fire initial-attack. INFOR (1979) 17:58–72Google Scholar
  • Clark G. M. Use of Polya distributions in approximate solutions to nonstationary M/M/s queues. Comm. ACM (1981) 24:206–217CrossrefGoogle Scholar
  • Cleveland B., Mayben J.Call Center Management on Fast Forward (1997) (Call Center Press, Annapolis, MD) Google Scholar
  • Eick S. G., Massey W. A., Whitt W. Mt/G/∞ queues with sinusoidal arrival rates. Management Sci. (1993a) 39:241–252LinkGoogle Scholar
  • Eick S. G., Massey W. A., Whitt W. The physics of the Mt/G/∞ queue. Oper. Res. (1993b) 41:731–742LinkGoogle Scholar
  • Grassmann W. K. Transient solutions in Markovian queueing systems. Comput. Oper. Res. (1977) 4:47–53CrossrefGoogle Scholar
  • Grassmann W. Numerical solutions for Markovian event systems. Quantitative Methoden in den Wirtschaftswissenschaften (1989) (Springer-Verlag, Berlin, Germany) 73–87CrossrefGoogle Scholar
  • Grassmann W. K.Computational Probability (2000) (Kluwer Academic Publishers, Boston, MA) CrossrefGoogle Scholar
  • Green L. V., Kolesar P. J. The pointwise stationary approximation with nonstationary arrivals. Management Sci. (1991) 37:84–97LinkGoogle Scholar
  • Green L. V., Soares J. Computing time-dependent waiting time probabilities in M(t)/M/s(t) queueing systems. Manufacturing Service Oper. Management (2007) 2:54–61LinkGoogle Scholar
  • Green L. V., Kolesar P. J., Soares J. Improving the SIPP approach for staffing service systems that have cyclic demands. Oper. Res. (2001) 49:549–564LinkGoogle Scholar
  • Green L. V., Kolesar P. J., Soares J. An improved heuristic for staffing telephone call centers with limited operating hours. Production Oper. Management (2003) 12:1–16CrossrefGoogle Scholar
  • Green L. V., Kolesar P. J., Svoronos A. Some effects of nonstationarity on multiserver Markovian queueing systems. Oper. Res. (1991) 39:502–511LinkGoogle Scholar
  • Gross D., Miller D. R. The randomization technique as a modeling tool and solution procedure for transient Markov processes. Oper. Res. (1983) 32:343–361LinkGoogle Scholar
  • Heyman D. P., Whitt W. The asymptotic behavior of queues with time-varying arrival rates. J. Appl. Probab. (1984) 21:143–156CrossrefGoogle Scholar
  • Ingolfsson A. Modeling the M(t)/M/s(t) queue with an exhaustive discipline. (2005) . Working paper, Department of Finance and Management Science, School of Business, University of Alberta, Edmonton, Alberta, Canada, http://www.bus.ualberta.ca/aingolfsson/working_papers.htmGoogle Scholar
  • Ingolfsson A., Cabral E., Wu X. Combining integer programming and the randomization method to schedule employees. (2002a) . Research Report 02-1, Department of Finance and Management Science, Faculty of Business, University of Alberta, Edmonton, Alberta, CanadaGoogle Scholar
  • Ingolfsson A., Haque M. A., Umnikov A. Accounting for time-varying queueing effects in tour scheduling. Eur. J. Oper. Res. (2002b) 139:585–597CrossrefGoogle Scholar
  • Jagerman D. L. Nonstationary blocking in telephone traffic. Bell Systems Tech. J. (1975) 54:625–661CrossrefGoogle Scholar
  • Jennings O. B., Massey W. A. A modified offered load approximation for nonstationary circuit switched networks. Telecomm. Systems (1997) 7:229–251CrossrefGoogle Scholar
  • Jennings O. B., Mandelbaum A., Massey W. A., Whitt W. Server staffing to meet time-varying demand. Management Sci. (1996) 42:1383–1394LinkGoogle Scholar
  • Jensen A. Markoff chains as an aid in the study of Markoff processes. Skandinavisk Aktuarietidskrift (1953) 36:87–91Google Scholar
  • Johnson N. L., Kotz S., Kemp A. W.Univariate Discrete Distributions (1993) (Wiley, New York) Google Scholar
  • Kleinrock L.Queueing Systems, Volume 1: Theory (1974) (Wiley, New York) Google Scholar
  • Koopman B. O. Air terminal queues under time-dependent conditions. Oper. Res. (1972) 20:1089–1114LinkGoogle Scholar
  • Leese E. L., Boyd D. W. Numerical methods of determining the transient behaviour of queues with variable arrival rates. INFOR (1966) 4:1–13Google Scholar
  • Massey W. A., Whitt W. Peak congestion in multi-server systems with slowly varying arrival rates. Queueing Systems (1997) 25:157–172CrossrefGoogle Scholar
  • Massey W. A., Parker G. A., Whitt W. Estimating the parameters of a nonhomogeneous Poisson process with linear rate. Telecomm. Systems (1996) 5:361–388CrossrefGoogle Scholar
  • Odoni A. R., Roth E. An empirical investigation of the transient behavior of stationary queueing systems. Oper. Res. (1983) 31:432–455LinkGoogle Scholar
  • Reibman A., Trivedi K. Numerical transient analysis of Markov models. Comput. Oper. Res. (1988) 15:19–36CrossrefGoogle Scholar
  • Rothkopf M. H., Oren S. S. A closure approximation for the nonstationary M/M/s queue. Management Sci. (1979) 25:522–534LinkGoogle Scholar
  • Shampine L. F., Reichelt M. W. The Matlab ODE suite. SIAM J. Sci. Comput. (1997) 18:1–22CrossrefGoogle Scholar
  • Stewart W. J.Introduction to the Numerical Solution of Markov Chains (1994) (Princeton University Press, Princeton, NJ) Google Scholar
  • Sze D. Y. A queueing model for telephone operator staffing. Oper. Res. (1984) 32:229–249LinkGoogle Scholar
  • Taaffe M. R., Ong K. L. Approximating nonstationary Ph(t)/M(t)/s/c queueing systems. Ann. Oper. Res. (1987) 8:103–116CrossrefGoogle Scholar
  • Thompson G. M. Accounting for the multi-period impact of service when determining employee requirements for labor scheduling. J. Oper. Management (1993) 11:269–287CrossrefGoogle Scholar
  • Whitt W. The pointwise stationary approximation for Mt/Mt/s queues is asymptotically correct as the rates increase. Management Sci. (1991) 37:307–314LinkGoogle Scholar
  • Wragg A. The solution of an infinite set of differential-difference equations occurring in polymerization and queueing problems. Proc. Cambridge Philos. Soc. (1963) 59:117–124CrossrefGoogle Scholar
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