Advances in Applied Probability

Staffing many-server systems with admission control and retrials

A. J. E. M. Janssen and J. S. H. van Leeuwaarden

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In many-server systems it is crucial to staff the right number of servers so that targeted service levels are met. These staffing problems typically lead to constraint satisfaction problems that are difficult to solve. During the last decade, a powerful many-server asymptotic theory has been developed to solve such problems and optimal staffing rules are known to obey the square-root staffing principle. In this paper we develop many-server asymptotics in the so-called quality and efficiency driven regime, and present refinements to many-server asymptotics and square-root staffing for a Markovian queueing model with admission control and retrials.

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Adv. in Appl. Probab., Volume 47, Number 2 (2015), 450-475.

First available in Project Euclid: 25 June 2015

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Primary: 60K25: Queueing theory [See also 68M20, 90B22] 68M10: Network design and communication [See also 68R10, 90B18] 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]

Many-server systems QED regime Halfin-Whitt regime heavy traffic diffusion limits admission control square-root staffing optimality gap asymptotic dimensioning


Janssen, A. J. E. M.; van Leeuwaarden, J. S. H. Staffing many-server systems with admission control and retrials. Adv. in Appl. Probab. 47 (2015), no. 2, 450--475. doi:10.1239/aap/1435236983.

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  • Abramowitz, M. and Stegun, I. A. (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. U.S. Government Printing Office, Washington, D.C.
  • Asmussen, S., Lipsky, L. and Thompson, S. (2014). Failure Recovery in Computing and Data Transmission. In Analytic and Stochastic Modelling Techniques and Applications. (Lecture Notes Comput. Sci. 8499). Springer, Berlin, pp. 253–272.
  • Asmussen, S. et al. (2008). Asymptotic behavior of total times for jobs that must start over if a failure occurs. Math. Operat. Res. 33, 932–944.
  • Bertsekas, D. P. and Gallager, R. (1992). Data Networks, 2nd edn. Prentice Hall, London.
  • Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular Variation. Cambridge University Press.
  • Fiorini, P. M., Sheahan, R. and Lipsky, L. (2005). On unreliable computing systems when heavy-tails appear as a result of the recovery procedure. ACM SIGMETRICS Performance Evaluation Rev. 33, 15–17.
  • Jelenković, P. R. and Olvera-Cravioto, M. (2012). Implicit renewal theorem for trees with general weights. Stoch. Process. Appl. 122, 3209–3238.
  • Jelenković, P. R. and Skiani, E. D. (2012). Uniform approximation of the distribution for the number of retransmissions of bounded documents. In Proc. 12th ACM SIGMETRICS/PERFORMANCE Joint International Conference on Measurement and Modeling of Computer Systems, ACM, New York, pp. 101–112. June 2012.
  • Jelenković, P. R. and Skiani, E. D. (2012). Distribution of the number of retransmissions of bounded documents. Extended version. Available at
  • Jelenković, P. R. and Tan, J. (2007). Are end-to-end acknowlegements causing power law delays in large multi-hop networks? In 14th Informs Applied Probability Conference, APS, pp. 9–11.
  • Jelenković, P. R. and Tan, J. (2007). Can retransmissions of superexponential documents cause subexponential delays? In Proc. 26th IEEE INFOCOM'07, IEEE, pp. 892–900.
  • Jelenković, P. R. and Tan, J. (2007). Is ALOHA causing power law delays? In Managing Traffic Performance in Converged Networks (Lecture Notes Comput. Sci. 4516). Springer, Berlin, pp. 1149–1160.
  • Jelenković, P. R. and Tan, J. (2008). Dynamic packet fragmentation for wireless channels with failures. In Proc. 9th ACM International Symposium on Mobile Ad Hoc Networking and Computing, ACM, New York, pp. 73–82.
  • Jelenković, P. R. and Tan, J. (2009). Stability of finite population ALOHA with variable packets. Preprint. Available at
  • Jelenković, P. R. and Tan, J. (2010). Modulated branching processes, origins of power laws, and queueing duality. Math. Operat. Res. 35, 807–829.
  • Jelenković, P. R. and Tan, J. (2013). Characterizing heavy-tailed distributions induced by retransmissions. Adv. Appl. Prob. 45, 106–138. Extended version available at
  • Nair, J. et al. (2010). File fragmentation over an unreliable channel. In Proc. IEEE INFOCOM'10, IEEE, pp. 965–973.
  • Ross, S. M. (2002). A First Course in Probability, 6th edn. Prentice Hall, Upper Saddle River, NJ.
  • Sheahan, R., Lipsky, L., Fiorini, P. M. and Asmussen, S. (2006). On the completion time distribution for tasks that must restart from the beginning if a failure occurs. ACM SIGMETRICS Performance Evaluation Rev. 34, 24–26.
  • Tan, J. and Shroff, N. B. (2010). Transition from heavy to light tails in retransmission durations. In Proc. IEEE INFOCOM'10, IEEE, pp. 1334–1342.