An Example

The Acme Machine Shop has a tool crib to store tools required by the shop mechanics. Two

clerks run the tool crib. The clerks hand out the tools as the mechanics arrive and request

them. The tools then are returned to the clerks when they are no longer needed. There have

been complaints from supervisors that their mechanics have had to waste too much time

waiting to be served at the tool crib, so it appears as if there should be more clerks. On the

other hand, management is exerting pressure to reduce overhead in the plant, and this

reduction would lead to fewer clerks. To resolve these conflicting pressures, an OR study is

being conducted to determine just how many clerks the tool crib should have.

The tool crib constitutes a queueing system, with the clerks as its servers and the me$-$

chanics as its customers. After gathering some data on interarrival times and service times,

the OR team has concluded that the queueing model that fits this queueing system best is