Prashant Narayanan

Prashant Narayanan, Vinod Sharma

We consider a scenario where N users try to access a common base station. Associated with each user is its channel state and a finite queue which varies with time. Each user chooses his power and the admission control variable in a dynamic manner so as to maximize his expected throughput. The throughput of each user is a function of the actions and states of all users. The scenario considers the situation where each user knows his channel and buffer state but is unaware of the states and actions taken by the other users. We consider the scenario when each user is saturated (i.e., always has a packet to transmit) as well as the case when each user is unsaturated. We formulate the problem as a Markov game and show connections with strategic form games. We then consider various throughput functions associated with the multiple user channel and provide algorithms for finding these equilibria.

Prashant Narayanan, Lakshmi Narasimhan Theagarajan

We consider a scenario where $N$ users send packets to a common access point. The receiver decodes the message of each user by treating the other user's signals as noise. Associated with each user is its channel state and a finite queue which varies with time. Each user allocates his power and the admission control variable dynamically to maximize his expected throughput. Each user is unaware of the states, and actions taken, by the other users. This problem is formulated as a Markov game for which we show the existence of equilibrium and an algorithm to compute the equilibrium policies. We then show that when the number of users exceeds a particular threshold, the throughput of all users at all the equilibria are the same. Furthermore the equilibrium policies of the users are invariant as long as the number of users remain above the latter threshold. We also show that each user can compute these policies using a sequence of linear programs which does not depend upon the parameters of the other users. Hence, these policies can be computed by each user without any information or feedback from the other users. We then provide numerical results which verify our theoretical results.