Consider a grain elevator at a small county town in Victoria where grapes are the principal crop. During the harvest season, trucks loaded with grapes from fields arrive at the elevator. At the elevator, trucks deposit their loads after a check-in-process and return to the fields for another load. Suppose the average inter-arrival time of trucks is 20/3 minutes and the average service time at the elevator is 6 minutes. This business operation may be modelled as M/M/1/queuing system. Famers find that the average time they spend currently is excessive.

Proposal 1: At a farmers' meeting, they proposed to add sideboards to allow the trucks to carry larger loads. At the same time, an extra worker is planned to help in the check-in-process at the elevator. These changes cost additional $10,000 per 8-hour operation, reduces service time at the elevator to 4 minutes and lengthens the average inter-arrival time to 10 minutes.

Proposal 2: Some farmers do not like Proposal 1. They believe that more significant changes are needed. The new proposal is to add another identical elevator. This would double the service capacity. Arriving trucks would join a single line and move to the first available of the two elevators.

Proposal 3: A few farmers are of the opinion that a second elevator should be installed on another site. This proposal would split the arrivals equally.

(a)Do you agree with the belief that, other things being equal, it is preferable to design a service system so that one-line feeds two identical servers instead of two lines feed two identical individual servers? Discuss with numerical evidence from the above proposals.

(b) Based on your judgement, under what condition would you choose Proposal 1 over the current system?