The registration process at a university can be considered a closed system in

certain contexts, but it also exhibits characteristics of an open system. Discuss

$($i$)$ Discuss $2$ characteristics that make it an open system. $(2)$

$($ii$)$ Discuss $2$ characteristics that make it a closed system. $(2)$

Think of an ATM:

$($i$)$ what type of queuing system is used there? $(1)$

$($ii$)$ what are the unique features of such a queue? $(5)$

Using a practical example, explain the four types of systems illustrated in figure $1$

below :

e$.$g$.1$ queue, $1$ server, $1$ phase: withdrawing money at a garage which has $1$

ATM.

Figure $1$: Types of systems

Consider a coffee shop that uses a single$-$server queue. The inter$-$arrival time is

exponentially distributed with a mean of $10$ minutes and the service time is also

exponentially distributed with a mean of $8$ minutes. Calculate the:

$($i$)$ mean wait in the queue $(2)$

$($ii$)$ mean number in the queue $(2)$

$($iii$)$ the mean wait in the system $(2)$

$($iv$)$ mean number in the system $(2)$

$($v$)$ proportion of time the server is idle. $(2)$

The arrival of customers at a bank follows a Poisson distribution with a mean arrival

rate of $10$ customers per hour. The service time at the bank follows an exponential

distribution with a mean service rate of $6$ minutes per customer. Calculate the

average number of customers in the system $($including those being served and

waiting$)$ and the average time a customer spends in the system. How is the system

performing?