| This thesis addresses issues of design and performance analysis in wireless communication networks. We investigate topics relevant to both uplink and downlink. For uplink, we study the stability region of the slotted Aloha protocol under the collision channel model, for the case of a finite number of independent users. The stability region (i.e., the set of arrival rate vectors such that the whole queueing system can be made stable) is in general unknown when the number of users is more than two. We seek to characterize the set of stabilizable rate vectors, whereas most existing works only provide bounds on the region of stabilized rate vectors under a given control (i.e., a vector of contention probabilities). We choose a natural and important inner bound on the exact Aloha stability region. The results we obtain include equivalent forms of and alternative membership testing for this set, as well as other properties such as various geometrically intuitive and explicit inner and outer bounds, and generalized convexity properties of the associated " excess rate " functions.;For downlink, we seek to characterize the delay when broadcasting (random linear combinations of) information packets over independent erasure channels to a finite number of users. Of interest is the random delay until all the receivers recover the fixed chunk of packets initially queued at the base station (i.e., the sender). This falls into the study of certain order statistic of random variables. We obtain lower and upper bounds, exact expressions and a finite-step computational procedure (recurrence) for the moments of the random delay. We also investigate the dependence of the delay on the code blocklength (under random linear combinations of packets as the scheme employed in random linear network coding), and on the number of receivers, respectively. Results here include asymptotics, monotonicity properties and asymptotically tight lower and upper bounds. |
