Given the provided conditions answer the questions below.

a$)$ Does a sustainable queueing event occur in the context described above? Clearly explain your response by defining sustainable queuing and then presenting evidence.

b$)$ Draw the cumulative arrival and cumulative departure graph for the above queuing scenario. The drawing must present arrivals and departures from $7$:$30$am to $9$:$00$am where the blockage occurs from $8$:$00$am to $8$:$15$am$.$ Clearly present the arrival curve and the departure curve $($in different colours$)$ and label both axes $($include units$).$

c$)$ What is the maximum queue of vehicles? Approximate the queue length $($in metres$).$Does this queueing event confirm residents' complaints of excessive queuing?

d$)$ What is the total delay of the queuing event? Calculate the number of vehicles that will be affected by the queuing event and the average individual delay of the vehicles affected.

e$)$ Propose two possible traffic management solutions to alleviate the queueing concerns raised by the community.