A Call-Routing Problem with Service-Level Constraints

Abstract

We consider a queueing system, commonly found in inbound telephone call centers, that processes two types of work. Type-H jobs arrive at rate H , are processed at rate H , and are served first come, first served within class. A service-level constraint of the form E delay or P delay limits the delay in queue that these jobs may face. An infinite backlog of type-L jobs awaits processing at rate L , and there is no service-level constraint on this type of work. A pool of c identical servers processes all jobs, and a system controller must maximize the rate at which type-L jobs are processed, subject to the service-level constraint placed on the type-H work.We formulate the problem as a constrained, average-cost Markov decision process and determine the structure of effective routing policies. When the expected service times of the two classes are the same, these policies are globally optimal, and the computation time required to find the optimal policy is about that required to calculate the normalizing constant for a simple M/M/c system. When the expected service times of the two classes differ, the policies are optimal within the class of priority policies, and the determination of optimal policy parameters can be determined through the solution of a linear program with O(c 3 ) variables and O(c 2 ) constraints.

Service-Level Differentiation in Call Centers with Fully Flexible Servers

“…A customer of a certain priority can enter service only if there are no higher-priority customers waiting, and the number of idle servers exceeds a class-dependent threshold. A similar threshold policy has also been proposed in a call blending environment (i.e., call centers that handle both inbound and outbound calls) (Bhulai andKoole 2003, Gans andZhou 2003). The role of the thresholds is to ensure that enough servers are available to serve future arrivals of higher priorities.…”

When Promotions Meet Operations: Cross-Selling and Its Effect on Call Center Performance

“…For each condition we also specify how the staffing and the threshold level will be determined if the condition is satisfied. (11), (12) and (7) respectively, the following conditions are sufficient for asymptotic optimality of TP and the proposed staffing levels: …”

Pooling strategies for call center agent cross-training

“…Koole and Talim (2000) modeled a multi-skill call center as a network of queues and approximated each queue as an M/M/r loss system to minimize the number of unanswered calls. Gans and Zhou (2003) studied a call routing problem with two call types where one call always has priority over the other one and used a Markov decision process model to achieve service level constraints.…”