Questions:

Using a practical examples, describe $5$ application areas of simulation

$[10]$

$2.$ Differentiate the queueing theory from simulation.

$[2]$

$3.$ 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 an open system.

$(2)$

$[4]$

$4.$ Think of an ATM:

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

$(1)$

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

$(5)$

$[6]$

$5.$ Using a practical example, explain the four types of systems illustrated in figure $1$ below:

$[12]$

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

Figure $1$: Types of systems

$6.$ 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. $(2)$

$[10]$

$7.$ Suppose customers arrive at a bank according to a Poisson process 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?

$[8]$

$8.$ An ATM has three machines. Customers queue in a single queue and are free to use a machine that is free. No one lines on a machine. By removing the input buffer on each machine and using a transfer node. Arrival rate is random and Poisson with a mean of $5$ minites, Processing time is random exponential with a mean of $3$ minutes.

$8\mathrm{.}1$ Use Simio to draw determine to me up with a running model. Export results to excel

$8\mathrm{.}2$Number of customers in the system,

$(3)$

$8\mathrm{.}3$ waiting time

$(3)$

$8\mathrm{.}4$ capacity utilisation of each ATM.

$(3)$

Hint watch the video Simio $-$ Single Queue Multiple Servers