Artikel,
Waiting patiently.
The New England journal of medicine, 323 (9): 604--8 (August 1990)
DOI: 10.1056/NEJM199008303230911
Zusammenfassung
This article has no abstract; the first 100 words appear below. I have attended a hospital clinic as a patient several times during the past few years. Most of my visits were scheduled, although a few were made on very short notice. Rarely have I waited for less than an hour past the time of my appointment, and sometimes for two or more hours. Being on the staff of an affiliated institution, I probably receive preferential treatment. From conversations with other patients in the clinic it is clear that many are kept waiting even longer than I. First, I want to say that I have received excellent medical care and am . . . Michael Goitein, Ph.D. Massachusetts General Hospital Boston, MA 02114 APPENDIX The Monte Carlo simulation included the following features. Length of Consultation The nominal duration of a consultation was taken to be unity — i.e., it was considered to be the fundamental unit of time to which all other times were scaled. (In the examples in the text, the nominal duration was taken to be 20 minutes, and all durations predicted by the model were scaled by this factor.) Consultations were initially chosen by random throw from a normal (gaussian) distribution centered on the nominal duration. For the reference case, the normal distribution was considered to have a standard deviation of 0.25 (five minutes). Consultation times were subject to the restriction that they were not allowed to be less than 0.5 (10 minutes); random throws that gave values of less than 0.5 were adjusted to be equal to 0.5. Consequently, the adjusted consultation times were drawn from a somewhat skewed distribution. Patients' Arrival Time Patients were assumed to arrive on average 0.25 (five minutes) before their scheduled appointment. Arrival times were chosen by random throw from a normal distribution centered about the average time of arrival. For the reference case, the normal distribution was considered to have a standard deviation of 0.4 (eight minutes). Scheduling of Appointments Appointments were scheduled at intervals calculated by multiplying the booking factor by the nominal consultation time. The physician was assumed to be on time — i.e., available for consultation at the start of the session. The physician's strategy was to see the next available patient with the earliest scheduled appointment. As a result, patients who arrive late, after another patient has taken their "slot," will still be seen. Emergencies There can be a specified probability (Pe) that a patient with an emergency will arrive unscheduled. At the start of each consultation, a random throw is made, with the specified probability Pe of an emergency, and if the throw is successful, the patient with an emergency will then fill the consultation slot, displacing any regularly scheduled patients who are waiting. The emergency consultation is assumed to last for 1.0 (20 minutes). There are no emergencies (Pe = 0) in the reference case. Outcomes The two main results of the simulation reported here are (1) the patients' average waiting time, defined as the time that a patient has to wait beyond the scheduled start of an appointment (not relative to the time of arrival) and determined by taking an average over the 10 appointments in the clinic, and (2) the physician's idle time per patient, defined as the period during which the physician is available for consultation but no patient is waiting to be seen and determined by taking an average over the 10 appointments in the clinic. Histories The accuracy of a Monte Carlo simulation depends in part on the number of times that the process is traced. In the results reported here, the process in a clinic of 10 appointments was traced 100 times, with random choices of the various quantities with each repetition. Statistical Uncertainties The statistical uncertainties in the analyses were estimated by repeating one case (the reference situation, with a booking factor of 1.2) 50 times and computing the standard deviations of the outcomes of interest, some of which are shown in Figure 2. The standard deviation of the patients' waiting times was 0.11 minute and of the physician's idle time 0.10 minute (values too small to be plotted in Fig. 1). The standard deviation of dismay was 0.17, 0.25, 0.43, and 0.81 minute for values of $\delta$ of 1, 2, 4, and 8, respectively.
