Q$.6($a$)$ Construct an accumulation diagram $($deterministic queuing diagram$)$ for the following numerical example:

I. Vehicles approach at a uniform flow rate of $600$ vehicles$/$h

II$.$ Vehicles are served during the green time $($when queue is present$)$ at a uniform flow rate of $1800$ vehicles$/$h

III. The queue discipline is FIFO system.

IV$.$ The effective green time is $40s,$ while the cycle length is $60s.$

Vary the mean arrival rate over a wider range that causes the approach to be loaded to capacity. Develop a conceptual relationship between a measure of performance and mean arrival rate. The measures of performance should include maximum queue length, maximum delay in queue, total delay, average delay, etc.