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Double Skorokhod Map and Reneging Real-Time Queues

Łukasz Kruk, John Lehoczky, Kavita Ramanan, and Steven Shreve

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An explicit formula for the Skorokhod map Γ0,a on [0,a] for a>0 is provided and related to similar formulas in the literature. Specically, it is shown that on the space $\mathcal{D}$[0,) of right-continuous functions with left limits taking values in ℝ,


is the unique function taking values in [0,a] that is obtained from by minimal “pushing” at the endpoints 0 and a. An application of this result to real-time queues with reneging is outlined.

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Stewart N. Ethier, Jin Feng and Richard H. Stockbridge, eds., Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 169-193

First available in Project Euclid: 28 January 2009

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Copyright © 2008, Institute of Mathematical Statistics


Kruk, Łukasz; Lehoczky, John; Ramanan, Kavita; Shreve, Steven. Double Skorokhod Map and Reneging Real-Time Queues. Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz, 169--193, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/074921708000000372.

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