A unified approach to linear programming bounds for queueing networks: systems with polyhedral invariance of transition probabilities

2002 ◽  
Author(s):  
J.R. Morrison ◽  
P.R. Kumar
Keyword(s):  
Linear Programming ◽  
Queueing Networks ◽  
Transition Probabilities ◽  
Unified Approach

Linear Programming Performance Bounds for Markov Chains With Polyhedrally Translation Invariant Probabilities and Applications to Unreliable Manufacturing Systems and Enhanced Wafer Fab Models

2002 ◽  
Author(s):  
James R. Morrison ◽  
P. R. Kumar
Keyword(s):  
Markov Chains ◽  
Queueing Networks ◽  
Manufacturing Systems ◽  
Transition Probabilities ◽  
Invariance Property ◽  
Translation Invariance ◽  
Performance Bounds ◽  
Translation Invariant ◽  
Wafer Fab ◽  
Index Policies

Our focus is on a class of Markov chains which have a polyhedral translation invariance property for the transition probabilities. This class can be used to model several applications of interest which feature complexities not found in usual models of queueing networks, for example failure prone manufacturing systems which are operating under hedging point policies, or enhanced wafer fab models featuring batch tools and setups or affine index policies. We present a new family of performance bounds which is more powerful both in expressive capability as well as the quality of the bounds than some earlier approaches.

Queueing networks with instantaneous movements: a unified approach by quasi-reversibility

2000 ◽  
Vol 32 (01) ◽  
pp. 284-313 ◽  
Author(s):  
Xiuli Chao ◽  
Masakiyo Miyazawa
Keyword(s):  
Queueing Networks ◽  
Product Form ◽  
Unified Approach ◽  
Stationary Distributions ◽  
Batch Arrivals ◽  
Unified View ◽  
Batch Services ◽  
Product Form Queueing Networks

In this paper we extend the notion of quasi-reversibility and apply it to the study of queueing networks with instantaneous movements and signals. The signals treated here are considerably more general than those in the existing literature. The approach not only provides a unified view for queueing networks with tractable stationary distributions, it also enables us to find several new classes of product form queueing networks, including networks with positive and negative signals that instantly add or remove customers from a sequence of nodes, networks with batch arrivals, batch services and assembly-transfer features, and models with concurrent batch additions and batch deletions along a fixed or a random route of the network.

Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games

2015 ◽  
Vol 32 (06) ◽  
pp. 1550043 ◽  
Author(s):  
Prasenjit Mondal
Keyword(s):  
Linear Programming ◽  
Transition Probabilities ◽  
Optimal Solution ◽  
Programming Algorithm ◽  
Stationary Strategy ◽  
Markov Games ◽  
Markov Decision ◽  
Transition Times ◽  
Optimal Stationary Strategies ◽  
Zero Sum

In this paper, zero-sum two-person finite undiscounted (limiting average) semi-Markov games (SMGs) are considered. We prove that the solutions of the game when both players are restricted to semi-Markov strategies are solutions for the original game. In addition, we show that if one player fixes a stationary strategy, then the other player can restrict himself in solving an undiscounted semi-Markov decision process associated with that stationary strategy. The undiscounted SMGs are also studied when the transition probabilities and the transition times are controlled by a fixed player in all states. If such games are unichain, we prove that the value and optimal stationary strategies of the players can be obtained from an optimal solution of a linear programming algorithm. We propose a realistic and generalized traveling inspection model that suitably fits into the class of one player control undiscounted unichain semi-Markov games.

Queueing networks with instantaneous movements: a unified approach by quasi-reversibility

2000 ◽  
Vol 32 (1) ◽  
pp. 284-313 ◽  
Author(s):  
Xiuli Chao ◽  
Masakiyo Miyazawa
Keyword(s):  
Queueing Networks ◽  
Product Form ◽  
Unified Approach ◽  
Stationary Distributions ◽  
Batch Arrivals ◽  
Unified View ◽  
Batch Services ◽  
Product Form Queueing Networks

In this paper we extend the notion of quasi-reversibility and apply it to the study of queueing networks with instantaneous movements and signals. The signals treated here are considerably more general than those in the existing literature. The approach not only provides a unified view for queueing networks with tractable stationary distributions, it also enables us to find several new classes of product form queueing networks, including networks with positive and negative signals that instantly add or remove customers from a sequence of nodes, networks with batch arrivals, batch services and assembly-transfer features, and models with concurrent batch additions and batch deletions along a fixed or a random route of the network.

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