Delay Distributions in Appointment Systems with Generally and Non-Identically Distributed Service Times and No-Shows

34 Pages Posted: 23 Apr 2012 Last revised: 21 Aug 2012

See all articles by William P. Millhiser

William P. Millhiser

Baruch College

Bendetto Valenti

City University of New York (CUNY) - Narendra Paul Loomba Department of Management

Date Written: April 23, 2012

Abstract

We derive the probability distribution of each patient's wait time and doctor's idle time and overtime in single-server systems where healthcare providers respond to appointment-driven arrivals with generally and non-identically distributed service times. Patient no-show probabilities and appointment intervals are also non-identical. The formulation is due to a convolution-based busy period analysis that can be implemented via numerical integration methods. A special case yields the distribution of customer wait times and server idle times in transient-phase D/M/1 queues for appointments at fixed-intervals, where analytical distribution functions facilitate a mathematical proof that delays are unfair to patients. We demonstrate more generally that appointment system assessment of delay tail probabilities (rather than expectations) considers the non-linear disutility for delays, and indeed reverses conclusions made in prior analysis.

Suggested Citation

Millhiser, William P. and Valenti, Benedetto, Delay Distributions in Appointment Systems with Generally and Non-Identically Distributed Service Times and No-Shows (April 23, 2012). Available at SSRN: https://ssrn.com/abstract=2045074 or http://dx.doi.org/10.2139/ssrn.2045074

William P. Millhiser (Contact Author)

Baruch College ( email )

NY
United States
646-312-3654 (Phone)

HOME PAGE: http://blsciblogs.baruch.cuny.edu/millhiser/

Benedetto Valenti

City University of New York (CUNY) - Narendra Paul Loomba Department of Management ( email )

NY
United States

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