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The c/ rule for many-server queues with abandonment Rami Atar Chanit Giat Nahum Shimkin

Summary: The cµ/ rule for many-server queues with abandonment
Rami Atar Chanit Giat Nahum Shimkin
Department of Electrical Engineering
Technion­Israel Institute of Technology
Haifa 32000, Israel
April 26, 2009
We consider a multi-class queueing system with multiple homogeneous servers and
customer abandonment. For each customer class i, the holding cost per unit time, the
service rate and the abandonment rate are denoted by ci, µi and i, respectively. We
prove that under a many-server fluid scaling and overload conditions, a routing policy that
assigns priority to classes according to their index ciµi/i, is asymptotically optimal for
minimizing the overall long run average holding cost. An additional penalty on customer
abandonment is easily incorporated into this model and leads to a similar index rule.
1 Introduction
The usefulness of the well known cµ rule for service scheduling stems from its simplicity and
its robustness. This scheduling policy and its generalizations have been proved to be optimal
(in a precise [12], [6] or an asymptotic sense [19], [25], [26]) for delay and queue-length costs, in
a variety of settings. Although these settings are quite general, they do not include ones where
customers may abandon (or renege) while waiting to be served. Abandonment phenomena


Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology


Collections: Engineering