Study the following system and identify all the associated queueing situations. For each situation, define the customers, the server$($s$),$ the service discipline, the service time, the maximum queue length, and the calling source. Draw flow charts which show who$/$what arrive at which queue and then go to the first server$($s$).$ Then $...$ go to the $2$ nd server$($s$).$ Then $...$ go to the nth server$($s$).($refer to the flow chart on lecture note Topic One page $1).$

a$)$ queuing system $1$ :

Orders for jobs are received at a workshop for processing. Upon receipt, the supervisor decides whether it is a rush job or a regular job. Some of these orders require use of one type of machine, of which several are available. The remaining orders are processed in a two$-$stage production line, of which only two are available. In each of the two groups, one facility is especially assigned to handle rush jobs. Jobs arriving at any facility are processed in order of arrival. Completed orders are shipped upon arrival from a terminal shipping zone having a limited capacity.

$($b$)$ queuing system $2$:

Sharpened tools for the different machines are supplied from a central tool crib, where operators exchange old tools for new ones. When a machine breaks down, a repairman is called from the service pool to attend it$.$ Machines working on rush orders always receive priorities both in acquiring new tools from the crib and in receiving repair service.