An intermittently served discrete time queue with applications to meteor scatter communications (Q1111257)

After an ``inoperative'' period of discrete length \(\xi\) slots an ``operative'' period of length \(\eta\) slots follows in the system. During the whole period \(\xi +\eta\) packets are submitted for transmission, \(\xi_ n\) in slot n. They queue, and are transmitted in FIFO order, during the operative period, by one every slot. The system is modelled by a Markov chain \(\{(X_ n,Y_ n)\), \(n\geq 0\}\), where \(X_ n\) is the number of packets queueing for transmission at the beginning of the n th slot and \(Y_ n\) is the number of slots remaining in the current operative period, or 0 if the current period is inoperative. Assuming proper simple stability conditions, the steady-state distribution \(\{p_{ij}=\lim_{n\to \infty}P(X_ n=i,\quad Y_ n=j),\quad i,j\geq 0\}\) for the Markov chain is analyzed and, in some cases, solved. The situation modelled occurs when packet radio communication is performed by means of the phenomenon called ``meteor scatter''. The reflecting ionized layers in the atmosphere caused by meteors, randomly, for about 0.5 seconds in every 10 seconds, represent a server that breaks down from time to time.