The Generalized Drift Skorokhod Problem in One Dimension: Its solution and application to the GI/GI/1 +GI and M/M/N/N transient distributions
نویسندگان
چکیده
We show how to write the solution to the generalized drift Skorokhod problem in onedimension in terms of the supremum of the solution of an unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein-Uhlenbeck (O-U) process to the first hitting time distribution of an O-U process (that is not reflected). Then, we use this relationship to approximate the transient distribution of the GI/GI/1 + GI queue in conventional heavy traffic and the M/M/N/N queue in a many-server heavy traffic regime.
منابع مشابه
On the Generalized Drift Skorokhod Problem in One Dimension
We show how to write the solution to the generalized drift Skorokhod problem in one-dimension in terms of the supremum of the solution of a tractable unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein-Uhlenbeck (O-U) process to the first hitting time distribution of an O...
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