$($operation research problem$)$Assume that in a queueing system with one server, first come first served queue discipline, unlimited queue length, unlimited input source, the inter$-$arrival time $($X$)$ distribution is uniformly distributed between $1$ and $3$ and the service time $($Y$)$ distribution is also uniformly distributed between $2$ and $5$

$($a$)$ What are a scheme to generate inter$-$arrival time and service time?

$($b$)$ Using above schemes and the three digits random numbers from sequence $9281526008$

$0843672907$ for inter arrival times and $21495081701280010827$ for the service times,

simulate the system for $10$ units of time $($assume initially there is one customer in the system$).$

Prepare the table with the following headings $($with usual notations$)$ T$,$ CE CNA, CND$,$ NS$,$ NQ$,$ CWTS$,$ CWTQ$,$ STS$,$ CIDT, UA$,$ IAT, NAT, US$,$ ST$,$ NDT$,$ NET, NE

$($c$)$ Hence, estimate L and the fraction of the time the server is busy.