Koole, G. M.3; Nielsen, Bo Friis4; Nielsen, Thomas Bang1
1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Vrije Universiteit Amsterdam4 Department of Applied Mathematics and Computer Science, Technical University of Denmark
We introduce a new approach to modelling queueing systems where the priority or the routing of customers depends on the time the first customer has waited in the queue. This past waiting time of the first customer in line, WFIL, is used as the primary variable for our approach. A Markov chain is used for modelling the system where the states represent both the number of free servers and a discrete approximation to WFIL. This approach allows us to obtain waiting time distributions for complex systems, such as the N-design routing scheme widely used, e.g., in call centers and systems with dynamic priorities.
Operations Research, 2012, Vol 60, Issue 5, p. 1258-1266