|M.Sc Student||Reich Michael|
|Subject||The Offered-Load Process: Modeling, Inference and|
|Department||Department of Industrial Engineering and Management||Supervisor||Professor Avishai Mandelbaum|
A standard assumption in queueing models is that the service time of customers and their patience are independent. Practice shows that this assumption is often violated, as one expects longer service times for customers who waited longer or, alternatively, higher patience for customers expecting longer services.
We introduce a model for the relationship between the service time and the patience of a customer, including a statistical test for the existence of such dependency. We show that in the presence of a relationship, various performance measures are influenced, and that the classical estimation procedures of service parameters yield biased estimators.
The above mentioned dependence affects the standard way of calculating workload. Specifically, the workload of a system must account for the work that would have been required by customers who abandon prior to service. We thus carefully define the workload process and the offered-load function, and then derive a method for estimating the workload and the offered-load, in service systems where service-times and patience are dependent. Finally, we discuss the effect of this dependence on the square-root staffing rule.