Effects of system parameters on the optimal policy structure in a class of queueing control problems

This paper studies a class of queueing control problems involving commonly used control mechanisms such as admission control and pricing. It is well established that in a number of these problems, there is an optimal policy that can be described by a few parameters. From a design point of view, it is useful to understand how such an optimal policy varies with changes in system parameters. We present a general framework to investigate the policy implications of the changes in system parameters by using event-based dynamic programming. In this framework, the control model is represented by a number of common operators, and the effect of system parameters on the structured optimal policy is analyzed for each individual operator. Whenever a queueing control problem can be modeled by these operators, the effects of system parameters on the optimal policy follow from this analysis.

[1]  Apostolos Burnetas,et al.  Admission policies for a two class loss system , 2001 .

[2]  Noah Gans,et al.  Pricing and Capacity Rationing for Rentals with Uncertain Durations , 2007, Manag. Sci..

[3]  Hayriye Ayhan,et al.  Sensitivity of Optimal Prices to System Parameters in a Service Facility , 2005 .

[4]  Eitan Altman,et al.  On optimal call admission control in resource-sharing system , 2001, IEEE Trans. Commun..

[5]  Jr. Shaler Stidham.  Optimal control of admission to a queueing system , 1985 .

[6]  Fikri Karaesmen,et al.  Structural results on a batch acceptance problem for capacitated queues , 2007, Math. Methods Oper. Res..

[7]  Boray Huang,et al.  Technical Note - A Make-to-Stock System with Multiple Customer Classes and Batch Ordering , 2008, Oper. Res..

[8]  James E. Smith,et al.  Structural Properties of Stochastic Dynamic Programs , 2002, Oper. Res..

[9]  Albert Y. Ha.  Stock-rationing policy for a make-to-stock production system with two priority classes and backordering , 1997 .

[10]  Lawrence M. Wein,et al.  Scheduling a Make-To-Stock Queue: Index Policies and Hedging Points , 1996, Oper. Res..

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

[12]  Mark E. Lewis,et al.  Optimal Pricing and Admission Control in a Queueing System with Periodically Varying Parameters , 2004, Queueing Syst. Theory Appl..

[13]  KooleGer.  Monotonicity in Markov Reward and Decision Chains , 2007 .

[14]  Cheng-Yuan Ku,et al.  Access control to two multiserver loss queues in series , 1997 .

[15]  Sheldon M. Ross,et al.  The Streetwalker’s Dilemma: A Job Shop Model , 1971 .

[16]  Fikri Karaesmen,et al.  On the structural properties of a discrete-time single product revenue management problem , 2009, Oper. Res. Lett..

[17]  Hayriye Ayhan,et al.  Bias optimal admission control policies for a multiclass nonstationary queueing system , 2002, Journal of Applied Probability.

[18]  E. Lerzan Örmeci,et al.  Admission Policies for a Two Class Loss System with General Interarrival Times , 1999 .

[19]  Yves Dallery,et al.  Optimal Stock Allocation for a Capacitated Supply System , 2002, Manag. Sci..

[20]  Shaler Stidham,et al.  The Underlying Markov Decision Process in the Single-Leg Airline Yield-Management Problem , 1999, Transp. Sci..

[21]  Lawrence M. Wein,et al.  Monotone control of queueing networks , 1992, Queueing Syst. Theory Appl..

[22]  Lode Li,et al.  A Stochastic Theory of the Firm , 2015, Math. Oper. Res..

[23]  D. M. Topkis.  OPTIMAL ORDERING AND RATIONING POLICIES IN A NONSTATIONARY DYNAMIC INVENTORY MODEL WITH n DEMAND CLASSES , 1968 .

[24]  Apostolos Burnetas,et al.  Admission control with batch arrivals , 2004, Oper. Res. Lett..

[25]  Albert Y. Ha.  Inventory rationing in a make-to-stock production system with several demand classes and lost sales , 1997 .

[26]  D. Towsley,et al.  Optimal control of admission to a multi-server queue with two arrival streams , 1992 .

[27]  Morris A. Cohen,et al.  Capacity Management in Rental Businesses with Two Customer Bases , 2005, Oper. Res..

[28]  N E Manos,et al.  Stochastic Models , 1960, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[29]  F. Karaesmen,et al.  OPTIMAL PRICING AND PRODUCTION POLICIES OF A MAKE-TO-STOCK SYSTEM WITH FLUCTUATING DEMAND , 2009, Probability in the Engineering and Informational Sciences.

[30]  Fikri Karaesmen,et al.  SENSITIVITY ANALYSIS ON A DYNAMIC PRICING PROBLEM OF AN M/M/c QUEUING SYSTEM , 2006 .

[31]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

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

[33]  Ger Koole,et al.  Monotonicity in Markov Reward and Decision Chains: Theory and Applications , 2007, Found. Trends Stoch. Syst..

[34]  Alfred Müller,et al.  How Does the Value Function of a Markov Decision Process Depend on the Transition Probabilities? , 1997, Math. Oper. Res..

[35]  Hayriye Ayhan,et al.  Sensitivity of optimal prices to system parameters in a steady-state service facility , 2009, Eur. J. Oper. Res..