Please answer problem d$.)$ Use queuelng theory.

The following systems assume that each server has capacity $1,$ and all times are exponential distributions

unless otherwise specified. State any other assumptions. For each of the following systems, answer the

questions:

i$.$ Is this a stable system? If not, why not?

ii$.$ If it is a stable system, estimate the Utilization of each server.

iii. If it is a stable system, estimate the overall Number in the System and Time in the System $($in minutes$)$

a$)$ Serial system: Arrivals $15/$hour; ServerA service rate $\frac{35}{?}$ hour; ServerB service rate $\frac{25}{?}$ hour. In addition to

reporting results in the table below, show equations and calculations in detail.

b$)$ Serial system: Arrivals $60/$hour; ServerA service time $1\mathrm{.}2$ minutes; ServerB service time $0\mathrm{.}6$ minutes. In

addition to reporting results in the table below, show equations and calculations in detail.

c$)$ Parallel system: Arrivals $60/$hour; ServerA service time $1\mathrm{.}2$ minutes; ServerB senvice time $0\mathrm{.}6$ minutes.

Assume a $50-50\%$ chance of arriving at server $A$ or $B.$ In addition to reporting results in the table below, show

equation and calculations in detail.

d$)$ Serial system: Interarrival time is Exponential $(6)$ minutes; ServerA service time Uniform $(3,4)$ minutes;

ServerB service time Uniform $(4,6)$ minutes. In addition to reporting results in the table below, show

equations and calculations in detall.