Dynamic Scheduling of a Multiclass Fluid Model with Transient Overload

Abstract

Abstract. We study the optimal dynamic scheduling of different requests of service in a multiclass stochastic fluid model that is motivated by recent and emerging computing paradigms for Internet services and applications. In particular, our focus is on environments with specific performance guarantees for each class under a profit model in which revenues are gained when performance guarantees are satisfied and penalties are incurred otherwise. Within the context of the corresponding fluid model, we investigate the dynamic scheduling of different classes of service under conditions where the workload of certain classes may be overloaded for a transient period of time. Specifically, we consider the case with two fluid classes and a single server whose capacity can be shared arbitrarily among the two classes. We assume that the class 1 arrival rate varies with time and the class 1 fluid can more efficiently reduce the holding cost. Under these assumptions, we characterize the optimal server allocation policy that minimizes the holding cost in the fluid model when the arrival rate function for class 1 is known. Using the insights gained from this deterministic case, we study the stochastic fluid system when the arrival rate function for class 1 is random and develop various policies that are optimal or near optimal under various conditions. In particular, we consider two different types of heavy traffic regimes and prove that our proposed policies are strongly asymptotically optimal. Numerical examples are also provided to demonstrate further that these policies yield good results in terms of minimizing the expected holding cost.

Asymptotically Optimal Controls for Time-Inhomogeneous Networks

“…In the domain of time-inhomogeneous networks, while heuristics for designing controls were proposed by Newell [41], there is relatively little rigorous work. A noteworthy example of an optimal control problem with a fluid model in the time-inhomogeneous setting is given in [8], where the authors study a particular optimal resource allocation problem for a (stochastic) fluid model with multiple classes, and a controller who dynamically schedules different classes in a system that experiences overload. To the best of the authors' knowledge, there are no general results in the time-inhomogeneous setting that rigorously show convergence of value functions of the prelimit control problems to the value function of a limiting control problem.…”

A Method for Staffing Large Call Centers Based on Stochastic Fluid Models

“…In the context of temporally varying demand, heuristics such as pointwise stationary approximations (see [10]) are often used. Fluid limits, which take a macroscopic view of the system dynamics, provide a more rigorous analysis framework for non-stationary queueing systems; see [18] for a treatment of Markovian service networks which are inspired by call center models, and [5] which studies a web-service system with transient overload and uncertain demand using stochastic fluid models. Effects of uncertainty and non-stationarity are discussed in [6], and [1] uses simulation and cutting plane methods to optimize costs subject to service level constraints.…”