Queues with waiting time dependent service

Motivated by service levels in terms of the waiting-time distribution seen in e.g. 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 steadystate waiting-time distributions for both models. The results are illustrated with numerical examples.

• Type: Journal
• Year: 2011
• Where: QUESTA
• Authors: René Bekker, G. M. Koole, B. F. Nielsen, T. B. Nielsen
• Keywords: Applied Computing, Level Crossings, QUESTA 2011, Service Discipline, Time Distributions