On a Random Sum Formula for the Busy Period of the M/G/Infinity Queue With Applications | Zendy

Armand M. Makowski | Zendy

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On a Random Sum Formula for the Busy Period of the M/G/Infinity Queue With Applications

Author(s) -

Armand M. Makowski

Publication year - 2001

Publication title -

digital repository at the university of maryland (university of maryland college park)

Language(s) - English

Resource type - Reports

DOI - 10.21236/ada439467

Subject(s) - infinity , period (music) , queue , mathematics , combinatorics , discrete mathematics , computer science , mathematical analysis , physics , computer network , acoustics

: A random sum formula is derived for the forward recurrence time associated with the busy period length of the M/G/perp endicular queue. This result is then used to (i) provide a necessary and suffcient condition for the subexponentiality of this forward recurrence time, and (ii) establish a stochastic comparison in the convex increasing (variability) ordering between the busy periods in two M/G/perp endicular queues with service times comparable in the convex increasing ordering.

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