N identical users share a time-slotted communication channel. The slot time is equal to one message transmission time. E

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N identical users share a time-slotted communication
channel. The slot time is equal to one message transmission time.
Each user is equipped with a single buffer, which means that a user
that has a full buffer cannot generate another message. Each user
generates a message independently in a slot with probability
p. A user that generates a message transmits in the
following slot with probability 1. If a single transmission takes
place in a slot, the transmission is successful. However, if two or
more transmissions occur in a slot, a collision is said to have
taken place, and the users involved in it go to the blocked
state. A user in the blocked state transmits in a slot
independently with probability q, or defers for one more
slot with probability 1 − q, and then repeats the
process.
We wish to model this system as a Markovian chain. Let the state
of the system be the number of blocked users at the end of a
slot.
probability 1 − q, and then
repeats the process.
We wish to model
this system as a Markovian chain. Let the state of the system be
the number of blocked users at the end of a slot.