Developing effective service policies for multiclass queues with abandonment:asymptotic optimality and approximate policy improvement

We study a single server queuing model with multiple classes and impatient customers. The goal is to determine a service policy to maximize the long-run reward rate earned from serving customers net of holding costs and penalties respectively due to customers waiting for and leaving before receiving service. We first show that it is without loss of generality to study a pure-reward model. Since standard methods can usually only compute the optimal policy for problems with up to three customer classes, our focus is to develop a suite of heuristic approaches, with a preference for operationally simple policies with good reward characteristics. One such heuristic is the Rμθ rule—a priority policy that ranks all customer classes based on the product of reward R, service rate μ, and abandonment rate θ. We show that the Rμθ rule is asymptotically optimal as customer abandonment rates approach zero and often performs well in cases where the simpler Rμ rule performs poorly. The paper also develops an approximate policy improvement method that uses simulation and interpolation to estimate the bias function for use in a dynamic programming recursion. For systems with two or three customer classes, our numerical study indicates that the best of our simple priority policies is near optimal in most cases; when it is not, the approximate policy improvement method invariably tightens up the gap substantially. For systems with five customer classes, our heuristics typically achieve within 4% of an upper bound for the optimal value, which is computed via a linear program that relies on a relaxation of the original system. The computational requirement of the approximate policy improvement method grows rapidly when the number of customer classes or the traffic intensity increases

Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy traffic

We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the number actually being served, the abandonment rate, the delay experienced by customers, the number of idling servers, as well as certain combinations thereof. We study the system in an asymptotic heavy-traffic regime where the number of servers n and the offered load r are simultaneously scaled up and carefully balanced: n\approx r+\beta \sqrtr for some scalar \beta. This yields an operation that enjoys the benefits of both heavy traffic (high server utilization) and light traffic (high service levels.

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Estimation and monitoring of traffic intensities with application to control of stochastic systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106982/1/asmb1961.pd

On completion times in a two-class priority queue with impatience loane Muni Toke

Abstract: In this note, we consider a two-class priority queueing system with Poisson arrivals, general service time distribution and one server, in which customers that are not currently being served may leave the queue according to exponentially distributed patience times, i.e., a M 1 , M 2 /G/1 + M system using a generalised Kendall's notation. We expand the classic methodology to derive analytical formulas for the completion times in such a system, using preemptive repeat different and preemptive repeat identical disciplines. Known average completion times for priority queues without impatience are retrieved as limit cases. Keywords: priority queues; queues with impatience; reneging; completion times; preemptive disciplines. Reference to this paper should be made as follows: Toke, I.M. (2014) 'On completion times in a two-class priority queue with impatience', Int

Modeling And Optimization Of Non-Profit Hospital Call Centers With Service Blending

This dissertation focuses on the operations problems in non-profit hospital call centers with inbound and outbound calls service blending. First, the routing policy for inbound and outbound calls is considered. The objective is to improve the system utilization under constraints of service quality and operators\u27 quantity. A collection of practical staffing assignment methods, separating and mixing staffing policy are evaluated. Erlang C queuing model is used to decide the minimum number of operators required by inbound calls. Theoretical analysis and numerical experiments illustrate that through dynamically assigning the inbound and outbound calls to operators under optimal threshold policy, mixing staffing policy is efficient to balance the system utilization and service quality. Numerical experiments based on real-life data demonstrate how this method can be applied in practice. Second, we study the staffing shift planning problem based on the inbound and outbound calls routing policies. A mathematical programming model is developed, based on a hospital call center with one kind of inbound calls and multiple kinds of outbound calls. The objective is to minimize the staffing numbers, by deciding the shift setting and workload allocation. The inbound calls service level and staffing utilization are taken into consideration in the constraints. Numerical experiments based on actual operational data are included. Results show that the model is effective to optimize the shift planning and hence reduce the call centers\u27 cost. Third, we model the staffing shift planning problem for a hospital call center with two kinds of service lines. Each kind of service is delivered through both inbound calls and outbound calls. The inbound calls can be transferred between these two service lines. A mathematical programming model is developed. The objective is to minimize the staffing cost, by deciding the shift setting and workload allocation. The inbound calls service level and staffing utilization are taken into consideration in the constraints. Numerical experiments are carried out based on actual operational data. Results show that the model is effective to reduce the call centers\u27 labor cost