A Marginal Allocation Approach to Resource Management for a System of Multiclass Multiserver Queues Using Abandonment and CVaR QoS Measures
A class of resource allocation problems is considered where some quality of service measure is set against the agent related costs. Three multiobjective minimization problems are posed, one for a system of Erlang-C queues and two for systems of Erlang-A queues.
In the case of the Erlang-C systems we introduce a quality of service measure based on the Conditional Value-at-Risk with waiting time as the loss function. This is a risk coherent measure and is well established in the field of finance. An algebraic proof ensures that this quality of service measure is integer convex in the number of servers.
In the case of the Erlang-A systems we introduce two different quality of service measures. The first is a weighted sum of fractions of abandoning customers and the second is Conditional Value-at-Risk, with the waiting time in queue for a customer conditioned on eventually receiving service. Finally, numerical experiments on the two system types with the given quality of service measures, are presented and the optimal solutions are compared.
KeywordsQueueing Queueing networks Marginal allocation Conditional Value-at-Risk Abandonments
The authors would like to thank Teleopti AB, Stockholm Sweden, for their support of our work.
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