Consider a wireless network consists of one access point and N clients devices.

Slotted ALOHA is adopted in this network. It is assumed that in each slot, a client

device sends a packet to the access point with probability 1/N . Also, the access point

sends a packet to one of the clients with probability in each slot. Single packet

transmission time is equal to the slot length. Package transmission of a device is

considered to be successful if only one transmission takes place in the slot.

.

(a) Calculate the probability that exactly one transmission takes place in a slot?

.

(b) Let Ns and Nr denote the average number of packets successfully sent and

received by the access point per slot, respectively. As N approaches infinity,

find the value of such that Ns = Nr.