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A Nearly-Optimal Index Rule for Scheduling of Users with Abandonment

Summary: A Nearly-Optimal Index Rule for
Scheduling of Users with Abandonment
Urtzi Ayesta, Peter Jacko and Vladimir Novak
BCAM -- Basque Center for Applied Mathematics, 48170 Bilbao, Spain
Email: {ayesta, jacko} @ bcamath.org
IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
Comenius University, 84248 Bratislava, Slovakia
Email: novakvlado @ gmail.com
Abstract--We analyze a comprehensive model for multi-class
job scheduling accounting for user abandonment, with the
objective of minimizing the total discounted or time-average sum
of linear holding costs and abandonment penalties. We assume
geometric service times and Bernoulli abandonment probabilities.
We solve analytically the case in which there are 1 or 2 users in
the system to obtain an optimal index rule. For the case with more
users we use recent advances from the restless bandits literature
to obtain a new simple index rule, denoted by AJN, which we
propose to use also in the system with arrivals. In the problem
without abandonment, the proposed rule recovers the cµ-rule
which is well-known to be optimal both without and with arrivals.


Source: Ayesta, Urtzi - Laboratoire d'Analyse et d'Architecture des Systèmes du CNRS


Collections: Engineering