Skip to main content

Please enter a keyword and click the arrow to search the site

Hazard rate scaling for the GI/M/n+GI queue in heavy traffic


Operations Research


Management Science and Operations

Authors / Editors

Reed J;Tezcan T

Publication Year



We obtain a heavy traffic limit for the GI/M/n + GI queue, which includes the entire patience time distribution. Our main approach is to scale the hazard rate function of the patience time distribution in such a way that our resulting diffusion approximation contains the entire hazard rate function. We then show through numerical studies that for various performance measures, our approximations tend to outperform those commonly used in practice. The robustness of our results is also demonstrated by applying them to solving constraint satisfaction problems arising in the context of telephone call centers.


Heavy traffic; Many servers; Abandonment; Hazard rate

Available on ECCH


Select up to 4 programmes to compare

Select one more to compare
subscribe_image_desktop 5949B9BFE33243D782D1C7A17E3345D0

Sign up to receive our latest news and business thinking direct to your inbox


Sign up to receive our latest course information and business thinking

Leave your details above if you would like to receive emails containing the latest thought leadership, invitations to events and news about courses that could enhance your career. If you would prefer not to receive our emails, you can still access the case study by clicking the button below. You can opt-out of receiving our emails at any time by visiting: or by unsubscribing through the link provided in our emails. View our Privacy Policy for more information on your rights.