MONOTONE OPTIMAL-CONTROL OF PERMUTABLE GSMPS

被引:41
作者
GLASSERMAN, P [1 ]
YAO, DD [1 ]
机构
[1] COLUMBIA UNIV,DEPT IE OR,NEW YORK,NY 10027
关键词
D O I
10.1287/moor.19.2.449
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
We consider Markovian GSMPs (generalized semi-Markov processes) in which the rates of events are subject to control. A control is monotone if the rate of one event is increasing or decreasing in the number of occurrences of other events. We give general conditions for the existence of monotone optimal controls. The conditions are functional properties for the one-step cost functions and, more importantly, structural properties for the GSMP. The main conditions on costs are submodularity or supermodularity with respect to pairs of events. The key structural condition is strong permutability, requiring that the state at any time be determined by the number of events of each type that have occurred, regardless of their order. This permits a reformulation of the original control problem into one based only on event counting processes. This reformulation leads to a unified treatment of a broad class of class of models and to meaningful generality beyond existing results.
引用
收藏
页码:449 / 476
页数:28
相关论文
共 25 条
[1]  
BARTROLI M, 1987, UNIFIED THEORY STRUC
[2]  
BJORNER A, 1985, COLL MATH SOC J BOLY, V40, P25
[3]  
CHEN H, 1991, CONTROL SCHEDLING 2
[4]  
DIETRICH BL, 1989, DISCRETE MATH, V78, P233
[5]   SHARING MEMORY OPTIMALLY [J].
FOSCHINI, GJ ;
GOPINATH, B .
IEEE TRANSACTIONS ON COMMUNICATIONS, 1983, 31 (03) :352-360
[6]   CONTROL OF ARRIVALS TO 2 QUEUES IN SERIES [J].
GHONEIM, HA ;
STIDHAM, S .
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 1985, 21 (03) :399-409
[7]   STRUCTURAL CONDITIONS FOR PERTURBATION ANALYSIS DERIVATIVE ESTIMATION - FINITE-TIME PERFORMANCE INDEXES [J].
GLASSERMAN, P .
OPERATIONS RESEARCH, 1991, 39 (05) :724-738
[8]   MONOTONICITY IN GENERALIZED SEMI-MARKOV PROCESSES [J].
GLASSERMAN, P ;
YAO, DD .
MATHEMATICS OF OPERATIONS RESEARCH, 1992, 17 (01) :1-21
[9]   GENERALIZED SEMI-MARKOV PROCESSES - ANTIMATROID STRUCTURE AND 2ND-ORDER PROPERTIES [J].
GLASSERMAN, P ;
YAO, DD .
MATHEMATICS OF OPERATIONS RESEARCH, 1992, 17 (02) :444-469
[10]   OPTIMAL-CONTROL OF 2 INTERACTING SERVICE STATIONS [J].
HAJEK, B .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1984, 29 (06) :491-499