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Limiting Behavior of the Target-Dependent Stochastic Sequential Assignment Problem

Part of: Markov processes Special processes

Published online by Cambridge University Press:  30 January 2018

Golshid Baharian  and
Sheldon H. Jacobson
Golshid Baharian*
Affiliation:
University of Illinois at Urbana-Champaign
Sheldon H. Jacobson*
Affiliation:
University of Illinois at Urbana-Champaign
*
∗ Postal address: Research Center of CHU Sainte-Justine, 3175 Cote Sainte-Catherine, local A-714, Montreal, Québec H3T 1C5, Canada. Email address: gbahari2@illinois.edu
∗∗ Postal address: Department of Computer Science, 201 N. Goodwin Ave., Urbana, IL 61801, USA. Email address: shj@illinois.edu
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Abstract

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The stochastic sequential assignment problem assigns distinct workers to sequentially arriving tasks with stochastic parameters. In this paper the assignments are performed so as to minimize the threshold probability, which is the probability of the long-run reward per task failing to achieve a target value (threshold). As the number of tasks approaches infinity, the problem is studied for independent and identically distributed (i.i.d.) tasks with a known distribution function and also for tasks that are derived from r distinct unobservable distributions (governed by a Markov chain). Stationary optimal policies are presented, which simultaneously minimize the threshold probability and achieve the optimal long-run expected reward per task.

Keywords

Sequential assignmentthreshold probabilitystationary policyhidden Markov chain

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 943 - 953
Copyright
© Applied Probability Trust 

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