To model the system using an M

$/$

M

$/$

$1$

$/$

b queue, we first need to calculate the arrival rate

$($

$\backslash$

lambda

$)$

$$and service rate

$($

$\backslash$

mu

$)$

$$for each machine. The arrival rate for the first machine is given by the number of jobs in the buffer, which is

$1$

$0$

$$jobs$,$ since the buffer can hold only

$1$

$0$

$$jobs$.$ The arrival rate is therefore

$1$

$0$

$$jobs

$/$

$2$

$0$

$$minutes

$=$

$0$

$.$

$5$

$$jobs

$/$

minute

$.$

$$The arrival rate for the second machine is given by the number of jobs in the buffer, which is

$0$

$$jobs$,$ since the buffer can hold only

$1$

$0$

$$jobs$.$ The arrival rate is therefore

$0$

$$jobs

$/$

$2$

$0$

$$minutes

$=$

$0$

$$jobs

$/$

minute

$.$

$$The service rate for the first machine is given by the processing time per job, which is

$2$

$0$

$$minutes$,$ since each job takes

$2$

$0$

$$minutes to process. The service rate for the second machine is given by the processing time per job, which is

$2$

$0$

$$minutes$,$ since each job takes

$2$

$0$

$$minutes to process.