A Controlled Discrete-Time Queueing System as a Model for the Orders of Two Competing Companies

Mario Lefebvre ()
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Mario Lefebvre: Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-ville, Montréal, QC H3C 3A7, Canada

Games, 2024, vol. 15, issue 3, 1-8

Abstract: We consider two companies that are competing for orders. Let X 1 ( n ) denote the number of orders processed by the first company at time n , and let τ ( k ) be the first time that X 1 ( n ) < j or X 1 ( n ) = r , given that X 1 ( 0 ) = k . We assume that { X 1 ( n ) , n = 0 , 1 , … } is a controlled discrete-time queueing system. Each company is using some control to increase its share of orders. The aim of the first company is to maximize the expected value of τ ( k ) , while its competitor tries to minimize this expected value. The optimal solution is obtained by making use of dynamic programming. Particular problems are solved explicitly.

Keywords: dynamic programming; difference equations; linear equations; first-passage time; homing problem (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2024
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