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An urn model arising from all-optical networks

Published online by Cambridge University Press:  14 July 2016

John A. Morrison*
Affiliation:
Bell Laboratories
*
Postal address: Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974, USA. Email address: [email protected]
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Abstract

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An occupancy model that has arisen in the investigation of randomized distributed schedules in all-optical networks is considered. The model consists of B initially empty urns, and at stage j of the process djB balls are placed in distinct urns with uniform probability. Let Mi(j) denote the number of urns containing i balls at the end of stage j. An explicit expression for the joint factorial moments of M0(j) and M1(j) is obtained. A multivariate generating function for the joint factorial moments of Mi(j), 0 ≤ iI, is derived (where I is a positive integer). Finally, the case in which the dj, j ≥ 1, are independent, identically distributed random variables is investigated.

Type
Research Papers
Copyright
© Applied Probability Trust 2006 

References

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Morrison, J. A., Saniee, I. and Widjaja, I. (2006). Design and performance of randomized network schedules for time-domain wavelength interleaved networks. Preprint.Google Scholar