Control of arrivals to a stochastic input–output system

Søren Glud Johansen · Shaler Stidham

75 citations0/0 files storedAdvances in Applied Probability

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Advanced Queuing Theory Analysis Optimization and Search Problems Age of Information Optimization

Abstract

The problem of controlling input to a stochastic input-output system by accepting or rejecting arriving customers is analyzed as a semi-Markov decision process. Included as special cases are a GI/G/1 model and models with compound input and/or output processes, as well as several previously studied queueing-control models. We establish monotonicity of socially and individually optimal acceptance policies and the more restrictive nature of the former, with random rewards for acceptance and both customer-oriented and system-oriented non-linear waiting costs. Distinctive features of our analysis are (i) that it allows dependent interarrival times and (ii) that the monotonicity proofs do not rely on the standard concavity-preservation arguments.

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References

1969The Regulation of Queue Size by Levying Tolls 1975Applying a New Device in the Optimization of Exponential Queuing Systems 1965Optimal Policy in a Dynamic, Single Product, Nonstationary Inventory Model with Several Demand Classes 1969A Queueing Reward System with Several Customer Classes 1971On Optimal Balking Rules and Toll Charges in the GI/M/1 Queuing Process 1972Individual and Social Optimization in a Multiserver Queue with a General Cost-Benefit Structure 1977Individual versus Social Optimization in Exponential Congestion Systems 1972Customers' Optimal Joining Rules for the GI/M/s Queue

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1985Control of arrivals to two queues in series 2002Applications of Markov Decision Processes in Communication Networks 2009Equilibrium threshold strategies in observable queueing systems with setup/closedown times 2012Equilibrium threshold strategies in observable queueing systems under single vacation policy 1988Scheduling, Routing, and Flow Control in Stochastic Networks

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