Double Skorokhod Map and Reneging Real-Time Queues
نویسندگان
چکیده
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. Specifically, it is shown that on the space D[0,∞) of right-continuous functions with left limits taking values in R, Γ0,a(ψ)(t) = ψ(t) − [( ψ(0) − a )+ ∧ inf u∈[0,t] ψ(u) ] ∨ sup s∈[0,t] [ (ψ(s) − a) ∧ inf u∈[s,t] ψ(u) ] . is the unique function taking values in [0, a] that is obtained from ψ 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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