Stochastic Order Results and Equilibrium Joining Rules for the Bernoulli Feedback Queue

A C Brooms and E J Collins
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A C Brooms: Department of Economics, Mathematics & Statistics, Birkbeck
E J Collins: University of Bristol

No 1305, Birkbeck Working Papers in Economics and Finance from Birkbeck, Department of Economics, Mathematics & Statistics

Abstract: We consider customer joining behaviour for a system that consists of a FCFS queue with Bernoulli feedback. A consequence of the feedback characteristic is that the sojourn time of a customer already in the system depends on the joining decisions taken by future arrivals to the system. By establishing stochastic order results for coupled versions of the system, we establish the existence of homogeneous Nash equilibrium joining policies for both single and multiple customer types which are distinguished through distinct quality of service preference parameters. Further, it is shown that for a single customer type, the homogeneous policy is unique.

Date: 2013-09
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https://eprints.bbk.ac.uk/id/eprint/8363 First version, 2013 (application/pdf)

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