Fluid Limits for Overloaded Multiclass FIFO Single-Server Queues with General Abandonment

Published Online:https://doi.org/10.1287/12-SSY085

References

  • Ancker, C. and Gafarian, A. (1962). Queueing with impatience customers that leave at random. Journal of Industrial Engineering 13, 84–90.Google Scholar
  • Bacelli, F., Boyer, P., and Hebuterne, G. (1984). Single-server queue with impatient customers. Advances in Applied Probability 16, 887–905. MR0766784Google Scholar
  • Bacelli, F. and Hebuterne, G. (1981). On queues with impatient customers. Performance 43, 159–179. MR0727303Google Scholar
  • Billingsley, P. (1995). Probability and Measure, 3rd Edition. John Wiley & Sons Inc., New York. MR1324786Google Scholar
  • Ethier, S. and Kurtz, T. (1986). Markov Processes: Characterization and Convergence. John Wiley & Sons, Inc., New York. MR0838085Google Scholar
  • Folland, G. (1984). Real Analysis: Modern Techniques and Their Applications. John Wiley & Sons Inc., New York. MR0767633Google Scholar
  • Glynn, P. and Ward, A. (2005). A diffusion approximation for a GI/GI/1 queue with balking or reneging. Queueing Systems: Theory and Applications 50, 371–400. MR2172907Google Scholar
  • Gromoll, H., Puha, A., and Williams, R. (2003). The fluid limit of a heavily loaded processor sharing queue. Annals of Applied Probability 12, 797–859. MR1925442Google Scholar
  • Gromoll, H., Robert, P., and Zwart, B. (2008). Fluid limits for processor-sharing queues with impatience. Mathematics of Operations Research 33, 375–402. MR2415999LinkGoogle Scholar
  • Gromoll, H. and Williams, R. J. (2009). Fluid limits for networks with bandwidth sharing and general document size distributions. The Annals of Applied Probability 19, 243–280. MR2498678Google Scholar
  • Jennings, O. and Reed, J. (2012). An overloaded multiclass FIFO queue with abandonments. Operations Research 60, 1282–1295. MR2998896LinkGoogle Scholar
  • Kallenberg, O. (1986). Random Measures. Academic Press, Orlando, Florida. MR0854102Google Scholar
  • Kang, W. and Pang, G. (2013). Fluid limit of a many-server queueing network with abandonment. Preprint.Google Scholar
  • Kang, W. and Ramanan, K. (2010). Fluid limits of many-server queues with reneging. Annals of Applied Probability 20, 2204–2260. MR2759733Google Scholar
  • Kang, W. and Ramanan, K. (2012). Asymptotic approximations for stationary distributions of many-server queues with abandonment. Annals of Applied Probability 22, 477–521. MR2953561Google Scholar
  • Kaspi, H. and Ramanan, K. (2011). Law of large numbers limits for many-server queues. Annals of Applied Probability 21, 33–114. MR2759196Google Scholar
  • Pang, G. and Whitt, W. (2010). Two-parameter heavy-traffic limits for infinite-server queues. Queueing Systems 65, 325–364. MR2671058Google Scholar
  • Prohorov, Y. (1956). Convergence of random processes and limit theorems in probability theory. Theory of Probability and its Applications 1, 157–214. MR0084896Google Scholar
  • Reed, J. and Ward, A. (2008). Approximating the GI/GI/1+GI queue with a nonlinear drift diffusion: Hazard rate scaling in heavy traffic. Mathematics of Operations Research 33, 606–644. MR2442644LinkGoogle Scholar
  • Whitt, W. (2006). Fluid models for multiserver queues with abandonments. Operations Research 54, 37–54. MR2201245Google 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.