Optimal Scheduling in a Queue with Differentiated Impatient Users

We consider a M/M/1 queue in which the average reward for servicing a job is an exponentially decaying function of the job’s sojourn time. The maximum reward and mean service times of a job are i.i.d. and chosen from arbitrary distributions. The scheduler is assumed to know the maximum reward, service rate, and age of each job. We prove that the scheduling policy that maximizes average reward serves the customer with the highest product of potential reward and service rate

An Empirical Study on Multicriteria Scheduling

This paper presents an empirical study of non-preemptive Multicriteria-Based, called MCB for short, scheduling policy. MCB scheduling policy uses multiple criteria of each request: arrival time, deadline, and processing time, to balance the requirements on both client and server sites. Weighted aggregation method is applied in this study to conduct the different measurements to a single figure of merit. For the empirical study, an M/G/1 queuing simulation system is implemented with MATLAB to represent a general server's incoming request scheduling system. Comparative simulation results of MCB with best effort scheduling policy on an overload situation show that MCB is an optimal scheduling policy

Asymptotically optimal priority policies for indexable and non-indexable restless bandits

We study the asymptotic optimal control of multi-class restless bandits. A restless bandit is a controllable stochastic process whose state evolution depends on whether or not the bandit is made active. Since finding the optimal control is typically intractable, we propose a class of priority policies that are proved to be asymptotically optimal under a global attractor property and a technical condition. We consider both a fixed population of bandits as well as a dynamic population where bandits can depart and arrive. As an example of a dynamic population of bandits, we analyze a multi-class M/M/S+M queue for which we show asymptotic optimality of an index policy.We combine fluid-scaling techniques with linear programming results to prove that when bandits are indexable, Whittle's index policy is included in our class of priority policies. We thereby generalize a result of Weber and Weiss (1990) about asymptotic optimality of Whittle's index policy to settings with (i) several classes of bandits, (ii) arrivals of new bandits, and (iii) multiple actions. Indexability of the bandits is not required for our results to hold. For non-indexable bandits we describe how to select priority policies from the class of asymptotically optimal policies and present numerical evidence that, outside the asymptotic regime, the performance of our proposed priority policies is nearly optimal