Stochastic scheduling with event-based dynamic programming

Abstract. In this paper we apply a new framework for the study of monotonicity in queueing systems to stochastic scheduling models. This allows us a unified treatment of many different models, among which are multiple and single server models (with and without feedback), discrete and continuous time models, models with controlled and uncontrolled arrivals, etc.

[1]  Manfred SchÄl,et al.  Conditions for optimality in dynamic programming and for the limit of n-stage optimal policies to be optimal , 1975 .

[2]  Jürgen Weishaupt,et al.  Optimal myopic policies and index policies for stochastic scheduling problems , 1994, Math. Methods Oper. Res..

[3]  Jean Walrand,et al.  The c# rule revisited , 1985 .

[4]  Ger Koole.  Convexity in tandem queues , 1999 .

[5]  Steven A. Lippman,et al.  Applying a New Device in the Optimization of Exponential Queuing Systems , 1975, Oper. Res..

[6]  Armand M. Makowski,et al.  K competing queues with geometric service requirements and linear costs: The μc-rule is always optimal☆ , 1985 .

[7]  Cheng-Shang Chang,et al.  On the optimality of LEPT and cµ rules for machines in parallel , 1992, Journal of Applied Probability.

[8]  J. George Shanthikumar,et al.  Scheduling Multiclass Single Server Queueing Systems to Stochastically Maximize the Number of Successful Departures , 1989, Probability in the Engineering and Informational Sciences.

[9]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[10]  J. Walrand,et al.  The cμ rule revisited , 1985, Advances in Applied Probability.

[11]  Ger Koole,et al.  Scheduling a repairman in a finite source system , 1996, Math. Methods Oper. Res..

[12]  E. Altman,et al.  On submodular value functions and complex dynamic programming , 1998 .

[13]  Zhen Liu,et al.  Stochastic Bounds for Queueing Systems with Multiple On–Off Sources , 1998 .

[14]  Ger Koole.  Optimal server assignment in the case of service times with monotone failure rates , 1993 .

[15]  Rolando Cavazos-Cadena,et al.  Comparing recent assumptions for the existence of average optimal stationary policies , 1992, Oper. Res. Lett..

[16]  P. Nain,et al.  Interchange arguments for classical scheduling problems in queues , 1989 .

[17]  Ger Koole,et al.  Structural results for the control of queueing systems using event-based dynamic programming , 1998, Queueing Syst. Theory Appl..

[18]  A. Hordijk,et al.  Stochastic inequalities for an overflow model , 1987, Journal of Applied Probability.

[19]  Ger Koole.  Stochastic scheduling and dynamic programming , 1995 .

[20]  S. Asmussen,et al.  Marked point processes as limits of Markovian arrival streams , 1993 .

[21]  Ger Koole,et al.  On the optimality of LEPT and μc rules for parallel processors and dependent arrival processes , 1993, Advances in Applied Probability.