W e propose and analyze a two-dimensional Markov chain model of an Emergency Medical Services system that repositions ambulances using a compliance table policy, which is commonly used in practice. The model is solved via a fixed-point iteration. We validate the model against a detailed simulation model for several scenarios. We demonstrate that the model provides accurate approximations to various system performance measures, such as the response time distribution and the distribution of the number of busy ambulances, and that it can be used to identify near-optimal compliance tables. Our numerical results show that performance depends strongly on the compliance table that is used, indicating the importance of choosing a well-designed compliance table.

It is well known that flexibility can be created in manufacturing and service operations by using multipurpose production sources such as cross-trained labor, flexible machines, or flexible factories. We focus on flexible service centers, such as inbound call centers with cross-trained agents, and model them as parallel queueing systems with flexible servers. We propose a new approach to analyzing flexibility arising from the multifunctionality of sources of production. We create a work sharing (WS) network model for which its average shortest path length (APL) metric can predict the more effective of two alternative cross-training structures in terms of customer waiting times. We show that the APL metric of small world network (SWN) theory is one simple deterministic solution approach to the complex stochastic problem of designing effective workforce cross-training structures in call centers.

No abstract

Servers in many real queueing systems do not work at a constant speed. They adapt to the system state by speeding up when the system is highly loaded or slowing down when load has been high for an extended time period. Their speed can also be constrained by other factors, such as geography or a downstream blockage. We develop a state-dependent queueing model in which the service rate depends on the system "load" and "overwork." Overwork refers to a situation where the system has been under a heavy load for an extended time period. We quantify load as the number of users in the system and we operationalize overwork with a state variable that is incremented with each service completion in a high-load period and decremented at a rate that is proportional to the number of idle servers during low-load periods. Our model is a quasi-birth-and-death process with a special structure that we exploit to develop efficient and easy-toimplement algorithms to compute system performance measures. We use the analytical model and simulation to demonstrate how using models that ignore adaptive server behavior can result in inconsistencies between planned and realized performance and can lead to suboptimal, unstable, or oscillatory staffing decisions.

No abstract