Tolga Tezcan

Dynamic Control of N-Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic

We consider a class of parallel server systems that are known as N-systems. In an N-system, there are two customer classes that are catered by servers in two pools. Servers in one of the pools are cross-trained and can serve customers from both classes, whereas all of the servers in the other pool can serve only one of the customer classes. A customer reneges from his queue if his waiting time in the queue exceeds his patience. Our objective is to minimize the total cost that includes a linear holding cost and a reneging cost. We prove that, when the service speed is pool dependent, but not class dependent, a cμ-type greedy policy is asymptotically optimal in many-server heavy traffic.

Many-server diffusion limits for G/Ph/n+GI queues

This paper studies many-server limits for multi-server queues that have a phasetype service time distribution and allow for customer abandonment. The rst set of limit theorems is for critically loaded G=Ph=n + GI queues, where the patience times are independent, identically distributed following a general distribution. The next limit theorem is for overloaded G=Ph=n + M queues, where the patience time distribution is restricted to be exponential. We prove that a pair of diusion-scaled total-customer-count and server-allocation processes, properly centered, converges in distribution to a continuous Markov process as the number of servers n goes to innity. In the overloaded case, the limit is a multi-dimensional diusion process, and in the critically loaded case, the limit is a simple transformation of a diusion process. When

State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems

We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin-Whitt many-server asymptotic regime. Our main contribution is a general framework for establishing state space collapse results in this regime for parallel server systems. In our work, state space collapse refers to a decrease in the dimension of the processes tracking the number of customers in each class waiting for service and the number of customers in each class being served by various server pools. We define and introduce a “state space collapse” function, which governs the exact details of the state space collapse. We show that a state space collapse result holds in many-server heavy traffic if a corresponding deterministic hydrodynamic model satisfies a similar state space collapse condition. Unlike the single-server heavy traffic setting for multiclass queueing network, our hydrodynamic model is different from the standard fluid model for many-server queues. Our methodology is similar in spirit to that in Bramson [Bramson, M. 1998. State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems30 89--148.], which focuses on the single-server heavy traffic regime. We illustrate the applications of our results by establishing state space collapse results in many-server diffusion limits for V-model systems under static-buffer-priority policy and the threshold policy proposed in the literature.

Staffing Call Centers with Uncertain Demand Forecasts: A Chance-Constrained Optimization Approach

We consider the problem of staffing call centers with multiple customer classes and agent types operating under quality-of-service (QoS) constraints and demand rate uncertainty. We introduce a formulation of the staffing problem that requires that the QoS constraints are met with high probability with respect to the uncertainty in the demand rate. We contrast this chance-constrained formulation with the average-performance constraints that have been used so far in the literature. We then propose a two-step solution for the staffing problem under chance constraints. In the first step, we introduce a random static planning problem (RSPP) and discuss how it can be solved using two different methods. The RSPP provides us with a first-order (or fluid) approximation for the true optimal staffing levels and a staffing frontier. In the second step, we solve a finite number of staffing problems with known arrival rates---the arrival rates on the optimal staffing frontier. Hence, our formulation and solution approach has the important property that it translates the problem with uncertain demand rates to one with known arrival rates. The output of our procedure is a solution that is feasible with respect to the chance constraint and nearly optimal for large call centers.

Optimal control of parallel server systems with many servers in heavy traffic

We consider a parallel server system that consists of several customer classes and server pools in parallel. We propose a simple robust control policy to minimize the total linear holding and reneging costs. We show that this policy is asymptotically optimal under the many-server heavy traffic regime for parallel server systems when the service times are only server pool dependent and exponentially distributed.

Control of systems with flexible multi-server pools: a shadow routing approach

A general model with multiple input flows (classes) and several flexible multi-server pools is considered. We propose a robust, generic scheme for routing new arrivals, which optimally balances server pools’ loads, without the knowledge of the flow input rates and without solving any optimization problem. The scheme is based on Shadow routing in a virtual queueing system. We study the behavior of our scheme in the Halfin–Whitt (or, QED) asymptotic regime, when server pool sizes and the input rates are scaled up simultaneously by a factor r growing to infinity, while keeping the system load within

Optimal Control of Distributed Parallel Server Systems Under the Halfin and Whitt Regime

O(\sqrt{r}\,)

Hazard Rate Scaling of the Abandonment Distribution for the GI/M/n + GI Queue in Heavy Traffic

of its capacity.The main results are as follows. (i) We show that, in general, a system in a stationary regime has at least

Shadow-Routing Based Control of Flexible Multiserver Pools in Overload

O(\sqrt{r}\,)

Low-Cost Side Channel Remote Traffic Analysis Attack in Packet Networks

average queue lengths, even if the so called null-controllability (Atar et al., Ann. Appl. Probab. 16, 1764–1804, 2006) on a finite time interval is possible; strategies achieving this