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Functional strong law of large numbers for loads in a planar network model

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  • Torrisi, Giovanni Luca

Abstract

In this note we consider a planar network with three bins located at the vertices of an equilateral triangle and customers which are uniformly distributed on the triangle and have Poisson arrival times and general sojourn times. We show that the allocation which minimizes the bin loads and that one which affiliates each customer to its less costly bin satisfy the same functional strong law of large numbers.

Suggested Citation

  • Torrisi, Giovanni Luca, 2013. "Functional strong law of large numbers for loads in a planar network model," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 718-723.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:718-723
    DOI: 10.1016/j.spl.2012.11.013
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    References listed on IDEAS

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    1. Iglehart, Donald L., 1973. "Weak convergence of compound stochastic process, I," Stochastic Processes and their Applications, Elsevier, vol. 1(1), pages 11-31, January.
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