Queues with service times and interarrival times depending linearly and randomly upon waiting times
Queueing Systems: Theory and Applications
A simple proof of the optimality of a threshold policy in a two-server queueing system
Systems & Control Letters
A Call-Routing Problem with Service-Level Constraints
Operations Research
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Queues with Workload-Dependent Arrival and Service Rates
Queueing Systems: Theory and Applications
On/off Storage Systems with State-Dependent Input, Output, and Switching Rates
Probability in the Engineering and Informational Sciences
Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers
Queueing Systems: Theory and Applications
Approximating multi-skill blocking systems by hyperexponential decomposition
Performance Evaluation
Call-Routing Schemes for Call-Center Outsourcing
Manufacturing & Service Operations Management
On queues with service and interarrival times depending on waiting times
Queueing Systems: Theory and Applications
Pricing and Lead Time Decisions in Decentralized Supply Chains
Management Science
Service-Level Differentiation in Call Centers with Fully Flexible Servers
Management Science
Continuous feedback fluid queues
Operations Research Letters
First in Line Waiting Times as a Tool for Analysing Queueing Systems
Operations Research
Workload and busy period for $$M/GI/1$$M/GI/1 with a general impatience mechanism
Queueing Systems: Theory and Applications
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Motivated by service levels in terms of the waiting-time distribution seen, for instance, in call centers, we consider two models for systems with a service discipline that depends on the waiting time. The first model deals with a single server that continuously adapts its service rate based on the waiting time of the first customer in line. In the second model, one queue is served by a primary server which is supplemented by a secondary server when the waiting of the first customer in line exceeds a threshold. Using level crossings for the waiting-time process of the first customer in line, we derive steady-state waiting-time distributions for both models. The results are illustrated with numerical examples.