Due-date scheduling: asymptotic optimality of generalized longest queue and generalized largest delay rules

Due-date scheduling: asymptotic optimality of generalized longest queue and generalized largest delay rules (2003)

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by Jan A. Van Mieghem

Venue:	Operations Research
Citations:	2 - 0 self

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TITLE	Due-date scheduling: asymptotic optimality of generalized longest queue and generalized largest delay rules	INFERENCE
AUTHOR NAME	Jan A. Van Mieghem	SVM HeaderParse 0.2
AUTHOR AFFIL	Kellogg School of Management, Northwestern University, Evanston	SVM HeaderParse 0.2
AUTHOR ADDR	Illinois 60208-2009, vanmieghem@kellogg.northwestern.edu	SVM HeaderParse 0.2
ABSTRACT	Consider the following due-date scheduling problem in a multiclass, acyclic, single-station service system: Any class k job arriving at time t must be served by its due date t +Dk. Equivalently, its delay �k must not exceed a given delay or lead-time Dk. In a stochastic system, the constraint �k � Dk must be interpreted in a probabilistic sense. Regardless of the precise probabilistic formulation, however, the associated optimal control problem is intractable with exact analysis. This article proposes a new formulation which incorporates the constraint through a sequence of convex-increasing delay cost functions. This formulation reduces the intractable optimal scheduling problem into one for which the Generalized c � (Gc�) scheduling rule is known to be asymptotically optimal. The Gc � rule simplifies here to a generalized longest queue (GLQ) or generalized largest delay (GLD) rule, which are defined as follows. Let Nk be the number of class k jobs in system, �k their arrival rate, and ak the age of their oldest job in the system. GLQ and GLD are dynamic priority rules, parameterized by �: GLQ(�) serves FIFO within class and prioritizes the class with highest index �kNk, whereas GLD(�) uses index �k�kak. The argument is presented first intuitively, but is followed by a limit analysis that expresses the cost objective in terms of the maximal due-date violation probability. This proves that GLQ(�∗) and GLD(�∗), where �∗�k = 1/�kDk, asymptotically minimize the probability �k�ns � of maximal due-date violation in heavy traffic. Specifically, they minimize lim inf n→ � Pr�maxk sups∈�0�t � n1/2 � x � for all positive t and Dk x, where �k�s � is the delay of the most recent class k job that arrived before time s. GLQ with appropriate parameter � � also reduces “total variability ” because it asymptotically minimizes a weighted sum of �th delay moments. Properties of GLQ and GLD, including an expression for their asymptotic delay distributions, are presented.	SVM HeaderParse 0.2
YEAR	2003	INFERENCE
VENUE	Operations Research	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	113--122	INFERENCE
VOLUME	51	INFERENCE
CITATIONS	15 found	ParsCit 1.0