Geodesic
On increasing hazard rate of waiting time in the $M|G|1|\infty$ model
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2009), pp. 24-28.

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In the present paper for the sum of random number of independent identically distributed random variables the hazard rate increase is proven under the summanders hazard rate increase condition. With the help of obtained result the stationary waiting time hazard rate increase in the $M|G|1|\infty$ model is established under the service time hazard rate increase contition.
Keywords: $M|G|1|\infty$ model, waiting time, increasing hazard rate. 
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H. S. Harutyunyan; H. H. Igityan. On increasing hazard rate of waiting time in the $M|G|1|\infty$ model. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2009), pp. 24-28. http://geodesic.mathdoc.fr/item/UZERU_2009_1_a4/

[1] R.E.Barlow , F. Proschan, Mathematical Theory of Reliability, John Willey and Sons Inc., NY-London-Sydney, 1964 | MR

[2] B.V.Gnedenko, E.A. Danielyan at al., Preemptive Service Systems, MGU, M., 1973 (in Russian)

[3] E.A.Danielyan, A.R. Simonyan, Introduction to Queues Theory, v. 1, RAU, Yer., 2005 (in Russian)