On the M(n)/M(n)/s queue with impatient calls
Performance Evaluation
Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System
Queueing Systems: Theory and Applications
Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Dimensioning Large Call Centers
Operations Research
Engineering Solution of a Basic Call-Center Model
Management Science
A Method for Staffing Large Call Centers Based on Stochastic Fluid Models
Manufacturing & Service Operations Management
Queueing Systems: Theory and Applications
Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue
Queueing Systems: Theory and Applications
Fluid Models for Multiserver Queues with Abandonments
Operations Research
Monotonicity in Markov Reward and Decision Chains: Theory and Applications
Foundations and Trends® in Stochastic Systems
Staffing of Time-Varying Queues to Achieve Time-Stable Performance
Management Science
Usage Restriction and Subscription Services: Operational Benefits with Rational Users
Manufacturing & Service Operations Management
Dimensioning Large-Scale Membership Services
Operations Research
Manufacturing & Service Operations Management
Multiserver Loss Systems with Subscribers
Mathematics of Operations Research
Two fluid approximations for multi-server queues with abandonments
Operations Research Letters
Cross-Selling in a Call Center with a Heterogeneous Customer Population
Operations Research
When Promotions Meet Operations: Cross-Selling and Its Effect on Call Center Performance
Manufacturing & Service Operations Management
Heavy-traffic limits for nearly deterministic queues: stationary distributions
Queueing Systems: Theory and Applications
Call Centers with Delay Information: Models and Insights
Manufacturing & Service Operations Management
Nurse Staffing in Medical Units: A Queueing Perspective
Operations Research
Refining Square-Root Safety Staffing by Expanding Erlang C
Operations Research
Queues with Many Servers and Impatient Customers
Mathematics of Operations Research
Overflow Networks: Approximations and Implications to Call Center Outsourcing
Operations Research
Queues in tandem with customer deadlines and retrials
Queueing Systems: Theory and Applications
Critically Loaded Time-Varying Multiserver Queues: Computational Challenges and Approximations
INFORMS Journal on Computing
Computers and Industrial Engineering
Computers and Operations Research
Data-stories about (im)patient customers in tele-queues
Queueing Systems: Theory and Applications
Hi-index | 0.00 |
Motivated by call center practice, we study asymptotically optimal staffing of many-server queues with abandonment. A call center is modelled as an M/M/n + G queue, which is characterized by Poisson arrivals, exponential service times, n servers, and generally distributed patience times of customers. Our asymptotic analysis is performed as the arrival rate, and hence the number of servers n, increases indefinitely. We consider a constraint satisfaction problem, where one chooses the minimal staffing level n that adheres to a given cost constraint. The cost can incorporate the fraction abandoning, average wait, and tail probabilities of wait. Depending on the cost, several operational regimes arise as asymptotically optimal: Efficiency-Driven (ED), Quality and Efficiency-Driven (QED), and also a new ED + QED operational regime that enables QED tuning of the ED regime. Numerical experiments demonstrate that, over a wide range of system parameters, our approximations provide useful insight as well as excellent fit to exact optimal solutions. It turns out that the QED regime is preferable either for small-to-moderate call centers or for large call centers with relatively tight performance constraints. The other two regimes are more appropriate for large call centers with loose constraints. We consider two versions of the constraint satisfaction problem. The first one is constraint satisfaction on a single time interval, say one hour, which is common in practice. Of special interest is a constraint on the tail probability, in which case our new ED + QED staffing turns out asymptotically optimal. We also address a global constraint problem, say over a full day. Here several time intervals, say 24 hours, are considered, with interval-dependent staffing levels allowed; one seeks to minimize staffing levels, or more generally costs, given the overall performance constraint. In this case, there is the added flexibility of trading service levels among time intervals, but we demonstrate that only little gain is associated with this flexibility if one is concerned with the fraction abandoning.