Preemptive Service

Abstract

A small city has a small municipal garage that does maintenance and repair on city owned vehicles. There are two types of vehicles: (1) TYPE 1 is the city owned cars, trucks, etc.; and (2) TYPE 2 is all the police cars. TYPE 1 vehicles get scheduled, from time to time, for maintenance and repair. All TYPE 1 vehicles scheduled for maintenance/repair on a certain day arrive before the garage opens at 8 am on that day and queue up ready for service. The number of TYPE 1 vehicles scheduled for maintenance/repair on any day is uniformly distributed between one and ten. That is, there is a random variable X with values $1,2,...,10 each with probability 0.1 and the value of X is the number of vehicles ready for service on any day. The city garage is small with one service bay and only one mechanic at work. Service can be performed on only one vehicle at a time. The garage is open from 8 am to 4pm seven days per week. The 8 hours per day seven day per week requires hiring more than one mechanic, but only one mechanic is working at any time. The service time for TYPE 1 vehicles is normally distributed with mean μ₁ approximately 2 hours. Any TYPE 1 vehicle not serviced on its scheduled day waits for service on the following day. The time units in this chapter will be minutes so μ₁ ≈ 120.