Staffing Service Systems with Load Dependent Service Rate

The operations management literature tends to assume that service times are not affected by the load on the system. Practical evidence suggests otherwise. It is well known that workers adjust their working speed as they respond to different factors, such as experience, fatigue and pressure. In addition, recent research suggests that customers may also contribute to the variability in service times. For example, in health care, the medical state of patients may worsen if they do not receive care in a timely manner. Such deterioration, in physical state, may increase a patient’s recovery time.
Regardless of the source, service times depend on the state of the system. To make this more concrete, we present the service time experienced by customers at a call center as a function of the number of customers waiting in queue to be served. We show that service rate decreases with load. We then use a queueing model to analyze the implication of this fact. We show that even with what considered to be an appropriate staffing, waits may be very long and abandonment probability very high. We present some staffing procedures that eliminate that problem, for very low costs.