Allocation of jobs and identical resources with two pooling centers

Authors:
Hui-Chih Hung;Marc E. Posner
Affiliations:
The Ohio State University, Industrial Engineering, Columbus, USA 43210;The Ohio State University, Industrial Engineering, Columbus, USA 43210
Venue:
Queueing Systems: Theory and Applications
Year:
2007

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Abstract

We examine the resource allocation problem of partitioning identical servers into two parallel pooling centers, and simultaneously assigning job types to pooling centers. Each job type has a distinct Poisson arrival rate and a distinct holding cost per unit time. Each pooling center becomes a queueing system with an exponential service time distribution. The goal is to minimize the total holding cost. The problem is shown to be polynomial if a job type can be divided between the pooling centers, and NP-hard if dividing job types is not possible. When there are two servers and jobs cannot be divided, we demonstrate that the two pooling center configuration is rarely optimal. A heuristic which checks the single pooling center has an upper bound on the relative error of 4/3. The heuristic is extended for the multiple server problem, where relative error is bounded above by the number of servers.