Consider an auto repair shop that has two mechanics: the owner and one helper. To make the

problem easier to model we will assume that the facility only has room for three vehicles. Any

arriving when the facility is full are turned away. That is$,$ they can only have one vehicle waiting

to be repaired $($and not being worked on$)$ at any time. The interval arrival time is a random

variable, assumed to be exponentially distributed, with mean rate $.$ Repaired vehicles are

removed immediately by their owner $($unrealistic$).$ The repairmen work at the same rate and

repair times are exponentially distributed random variables with a mean completion rate of $$

jobs per time unit $($maybe we use days or even hours $$ these numbers merely change$).$ When

there are two or more vehicles in the shop, both workers are repairing individual vehicles.

When there is only one vehicle being repaired and the hired worker is performing the service,

the owner uses that time to do paperwork and other necessary things. If the owner$$s vehicle

repair takes longer and he is working on the only vehicle left in the shop, then the hired worker

helps the owner and they both work on the repairs. Due to space and timing issues, the repair

time with both working on one vehicle is$,$ of course, faster than one doing it$,$ but slower than

the combined $2$ completion rate. We will assume that this rate is $1\mathrm{.}5$ per unit time. We

have one more decision to make: when the system is empty and a customer $($vehicle$)$ arrives,

which mechanic works on the job. Various things can be done here, such as a $50-50$ split for the

choice of server. But we will assume that the owner has other