A network operator is planning to provide Packet Switched $($PS$)$ data services to its subscribers

by deploying a Long$-$Term Evolution $($LTE$)$ network. The number of data subscribers is

forecasted to be $325,000.$

Forecasted information for the network during the busy hour are as follows;

Active users who use data services would be $275,000.$

The average traffic profile of an active user is as provided in Table $1.$

Maximum simultaneous users are forecasted to be $42,000$ with a data rate of $1\mathrm{.}5Mbps$

per user.

Table $2$ contains the hardware capacities of couple of the network components provided by

Vendor ABC. Target of the operator is to maintain a maximum utilization of $85\%$ for all the

network nodes during the busy hour.

Table $2$: PS core network hardware capacities

Propose the number of S$-$GWs required for this network, clearly showing the steps used to

derive the answer.