With Christmas just around the corner, Jibbitz is planning to open a kiosk in the centre

of York Lanes where customers can create their own customized Jibbitz. On average, it

is estimated that the customers will arrive at the store every $20$ mins. Arrivals follow a

Poisson distribution. Assume customers always form one common line when arriving at

the store.

There are $3$ plans available $-$ the manager needs to decide which plan to use for this

new store.

Plan $1$ is to use a self$-$serve design machine, which can $3$D print a custom Jibbit in

exactly $10$ mins.

Plan $2$ is to hire $4$ students from the Faculty of Art to custom make Jibbitz on demand.

On average, each can serve $2$ customers per hour with the service time following an

exponential distribution.

Plan $3$ is to hire one Jibbitologist, who is specially trained in custom Jibbit making. The

time to serve a customer has a mean of $15$ minutes and a variance of $16$ minutes$2.$

Q$1.$ What is the Kendall notation for Plan $1,$ Plan $2,$ and Plan $3?$

Q$2.$ For Plan $1,$ what is the average number of customers waiting for the service?

Q$3.$ For Plan $2,$ how long does a customer need to wait before being served? $($in

minutes$)$

Q$4.$ For Plan $3,$ what is the total number of customers in the system?

Q$5.$ Which plan has the lowest utilization?

Q$6.$ If the manager wants to choose the plan with the lowest probability that zero

customers are waiting, which plan should be chosen?

Q$7.$ If the manager wants to choose the plan with the shortest time to spend in total for

a given customer, which plan should be chosen?