ADAPTIVE LEXICOGRAPHIC OPTIMIZATION IN MULTICLASS M GI/1 QUEUES/

We consider a multi-class M/GI/1 system, in which an average response time objective is associated with each class. The performance of each class is measured by the ratio of the average response time over the c orresponding value of the objective. To achieve fairness in service al location it is required to find a policy that lexicographically minimi zes the vector of performance ratios arranged in nonincreasing order. We provide such a policy that is adaptive, uses only knowledge of arri val and departure instants, and is thus easy to implement. We also con sider a variant of this policy which adapts faster to changes in the s tatistical parameters of the model. Both policies are analyzed via ass ociated stochastic recursions using techniques of stochastic approxima tion.