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Ross’s second conjecture and supermodular stochastic ordering

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References

  1. Bäuerle, N., Rolski, T.: A monotonicity result for the workload in Markov-modulated queues. J. Appl. Probab. 35(3), 741–747 (1998)

    Article  Google Scholar 

  2. Błaszczyszyn, B., Yogeshwaran, D.: Directionally convex ordering of random measures, shot noise fields, and some applications to wireless communications. Adv. Appl. Probab. 41(3), 623–646 (2009)

    Article  Google Scholar 

  3. Chang, C.-S., Chao, X., Pinedo, M.: Monotonicity results for queues with doubly stochastic Poisson arrivals: Ross’s conjecture. Adv. Appl. Probab. 23(1), 210–228 (1991)

    Article  Google Scholar 

  4. Hu, T., Pan, X.: Comparisons of dependence for stationary Markov processes. Probab. Eng. Inf. Sci. 14(3), 299–315 (2000)

    Article  Google Scholar 

  5. Leskelä, L.: Stochastic relations of random variables and processes. J. Theor. Probab. 23(2), 523–546 (2010)

    Article  Google Scholar 

  6. Leskelä, L., Vihola, M.: Stochastic order characterization of uniform integrability and tightness. Statist. Probab. Lett. 83(1), 382–389 (2013)

    Article  Google Scholar 

  7. Massey, W.A.: Stochastic orderings for Markov processes on partially ordered spaces. Math. Oper. Res. 12(2), 350–367 (1987)

    Article  Google Scholar 

  8. Meester, L.E., Shanthikumar, J.G.: Regularity of stochastic processes: A theory based on directional convexity. Probab. Eng. Inf. Sci. 7(3), 343–360 (1993)

    Article  Google Scholar 

  9. Miyoshi, N., Rolski, T.: Ross-type conjectures on monotonicity of queues. Aust. N. Z. J. Stat. 46(1), 121–131 (2004)

    Article  Google Scholar 

  10. Müller, A., Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, Hoboken (2002)

    Google Scholar 

  11. Rolski, T.: Queues with nonstationary input stream: Ross’s conjecture. Adv. Appl. Probab. 13(3), 603–618 (1981)

    Article  Google Scholar 

  12. Rolski, T.: Upper bounds for single server queues with doubly stochastic Poisson arrivals. Math. Oper. Res. 11, 442–450 (1986)

    Article  Google Scholar 

  13. Ross, S.M.: Average delay in queues with non-stationary Poisson arrivals. J. Appl. Probab. 15(3), 602–609 (1978)

    Article  Google Scholar 

  14. Shaked, M., Shanthikumar, J.G.: Stochastic Orders. Springer, Berlin (2007)

    Book  Google Scholar 

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  1. Department of Mathematics and Systems Analysis, Aalto University, Espoo, Finland

    Lasse Leskelä

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  1. Lasse Leskelä
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Leskelä, L. Ross’s second conjecture and supermodular stochastic ordering. Queueing Syst 100, 213–215 (2022). https://doi.org/10.1007/s11134-022-09824-0

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