Probably Not, 2nd Edition

9Scheduling and Waiting

Introduction

Many of our daily activities involve waiting. We wait for a bus, we wait to see our doctor in her office, we wait to meet a friend for lunch, etc. Wouldn't it be nice to have your bus pull up just a minute after you reach the bus stop, or have your doctor take you in for your examination just a minute after you reached her office? On the bus company's side, there is a tradeoff between minimizing the number of buses (operating cost), yet not overloading buses and not having people wait too long in possibly inclement weather. On the doctor's side there are clear advantages to getting to see as many patients as possible in a day while being able to go home for dinner at a regular time (yet not having patients waiting long times for treatment). When you meet a friend for lunch, the exact time of the meeting usually isn't critical, but if one of you arrives 15 minutes earlier and the other 15 minutes later than the agreed‐upon time, one of you will have to wait and ponder the value of timeliness.

Let's start with the doctor's office and see what we can learn, next we'll look at meeting friends for lunch, and then at bus schedules.

Scheduling Appointments in the Doctor's Office

Assume that the working day is from 9 to 5, 8 hours long. Even though real people like to break for lunch, assume that our doctor works straight through. We're doing this because taking account of lunch breaks complicates the calculations and conclusions without adding ...